StudyText (12447.0K) - McGraw-Hill Higher Education

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Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Except as permittedunder the United States Copyright Act, no part of this publication may be reproduced ordistributed in any form or by any means, or stored in a database or retrieval system, withoutthe prior permission of the publisher.Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240-4027ISBN: 978-0-07-890683-1MHID: 0-07-890683-0 South Carolina StudyText, Course 3Printed in the United States of America.1 2 3 4 5 6 7 8 9 10 045 16 15 14 13 12 11 10 09 08

Using Your South Carolina StudyTextSouth Carolina Math Connects StudyText, Course 3 is a practice workbookdesigned to help you master the South Carolina Academic Standards for Grade 8Mathematics. It is divided into three sections.Prerequisite Skills CheckThis is an assessment of the South Carolina Mathematics Standards fromGrade 7. This will help you determine which topics you may need to review beforebeginning your studies this year.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Chapter Resources• Each chapter begins with two activities. The Anticipation Guide is aninformal assessment of what you may think you know about the topics in thechapter. This can help you determine how well you are prepared for the contentof the chapter. The Family Activity is a problem-solving opportunity topractice at home. Each question has a full solution to help you check your work.• The chapter contains four pages for each Key Lesson in your Student Edition ofSouth Carolina Math Connects, Course 3. Your teacher may ask you to completeone or more of these worksheets as an assignment.• Each chapter ends with a two-page Chapter Test that assesses the SouthCarolina Academic Standards in that chapter with questions designed similarlyto those you might see on the PASS (Palmetto Assessment of State Standards).Mastering the PASSThis section of StudyText is composed of many sections that can help you studyfor the Grade 8 PASS (Palmetto Assessment of State Standards).• Tips for Taking the PASS tells you about the types of questions you mightfind on the PASS and how to correctly complete those types of questions.• The Diagnostic Test can help you determine which Academic Standards youmight need to review before taking the PASS. Each question lists whichstandard it is assessing.• The Practice by Standard gives you more practice problems to help youbecome a better test-taker. The problems are organized by the five standards inyour math curriculum: Number and Operations, Algebra, Geometry,Measurement, and Data Analysis and Probability.• The Practice Test can be used to simulate what a PASS test might be like sothat you will be better prepared to take the PASS in the spring.SC StudyText, Course 3iii

Contents in BriefChapter-by-Chapter Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viSouth Carolina Academic Standards, Grade 8 Mathematics . . . . . . . . . . xixPrerequisite Skills Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Chapter Resources1 Algebra: Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Algebra: Rational Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 Real Numbers and the Pythagorean Theorem . . . . . . . . . . . . . . . . . . . . . . . . 794 Proportions and Similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115 Percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1516 Geometry and Spatial Reasoning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1677 Measurement: Area and Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1758 Algebra: More Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . 2159 Algebra: Linear Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24310 Algebra: Nonlinear Functions and Polynomials . . . . . . . . . . . . . . . . . . . . . . 27111 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28312 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311Mastering the PASSTips for Taking the PASS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A1Diagnostic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A9Practice by StandardNumber and Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A19Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A21Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A23Measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A25Data Analysis and Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A27Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A29SC StudyText, Course 3v

Chapter-by-Chapter Contents1 Algebra: IntegersUse with Glencoe SouthPageLessonAcademic MathStandard(s) FocusCarolina Math Connects,Course 3 (pages)11 Chapter 1 Anticipation Guide12 Chapter 1 Family Activity1-2 Variables, Expressions, and Properties 29–3413 Explore Through Reading 8-3.3, 8-1.614 Study Guide 8-3.3, 8-1.615 Homework Practice 8-3.3, 8-1.616 Problem-Solving Practice 8-3.3, 8-1.61-3 Integers and Absolute Value 35–3917 Explore Through Reading 8-2.4, 8-2.518 Study Guide 8-2.4, 8-2.519 Homework Practice 8-2.4, 8-2.520 Problem-Solving Practice 8-2.4, 8-2.51-4 Adding Integers 41–4521 Explore Through Reading 8-2.122 Study Guide 8-2.123 Homework Practice 8-2.124 Problem-Solving Practice 8-2.11-5 Subtracting Integers 46–4925 Explore Through Reading 8-2.126 Study Guide 8-2.127 Homework Practice 8-2.128 Problem-Solving Practice 8-2.11-6 Multiplying and Dividing Integers 51–5629 Explore Through Reading 8-2.130 Study Guide 8-2.131 Homework Practice 8-2.132 Problem-Solving Practice 8-2.11-7 Writing Equations 57–6133 Explore Through Reading 8-3.234 Study Guide 8-3.235 Homework Practice 8-3.236 Problem-Solving Practice 8-3.21-8 Problem-Solving Investigation: Work Backward 62–6337 Study Guide 8-1.138 Skills Practice 8-1.139 Homework Practice 8-1.140 Problem-Solving Practice 8-1.1(continued on the next page)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.vi SC StudyText, Course 3

1 Algebra: Integers (continued)Use with Glencoe SouthPageLessonAcademic MathStandard(s) FocusCarolina Math Connects,Course 3 (pages)1-9 Solving Addition and Subtraction Equations 65–6941 Explore Through Reading 8-3.242 Study Guide 8-3.243 Homework Practice 8-3.244 Problem-Solving Practice 8-3.21-10 Solving Multiplication and Division Equations 70–7345 Explore Through Reading 8-3.246 Study Guide 8-3.247 Homework Practice 8-3.248 Problem-Solving Practice 8-3.249 Chapter 1 TestAdditional ResourceMath Triumphs, Grade 8 [Book 1]: Chapter 1 (Integers) and Chapter 3 (Expressions and Equations)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.SC StudyText, Course 3vii

2 Algebra: Rational NumbersPageLessonAcademic MathStandard(s) FocusUse with Glencoe SouthCarolina Math Connects,Course 3 (pages)51 Chapter 2 Anticipation Guide52 Chapter 2 Family Activity2-2 Comparing and Ordering Rational Numbers 91–9553 Explore Through Reading 8-2.454 Study Guide 8-2.455 Homework Practice 8-2.456 Mini-Project 8-2.42-3 Multiplying Positive and Negative Fractions 96–10157 Explore Through Reading 8-2.258 Study Guide 8-2.259 Homework Practice 8-2.260 Problem-Solving Practice 8-2.22-4 Dividing Positive and Negative Fractions 102–10761 Explore Through Reading 8-2.262 Study Guide 8-2.263 Homework Practice 8-2.264 Problem-Solving Practice 8-2.22-7 Solving Equations with Rational Numbers 119–12365 Explore Through Reading 8-3.266 Study Guide 8-3.267 Homework Practice 8-3.268 Problem-Solving Practice 8-3.22-8 Problem-Solving Investigation: Look for a Pattern 124–12569 Study Guide 8-1.170 Skills Practice 8-1.171 Homework Practice 8-1.172 Problem-Solving Practice 8-1.12-9 Powers and Exponents 126–12973 Explore Through Reading 8-1.674 Study Guide 8-1.675 Homework Practice 8-1.676 Problem-Solving Practice 8-1.677 Chapter 2 TestAdditional ResourceMath Triumphs, Grade 8 [Book 2]: Chapter 5 (Ratios, Rates, and Similarity)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.viii SC StudyText, Course 3

3 Real Numbers and the Pythagorean TheoremCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Use with Glencoe SouthPageLessonAcademic MathStandard(s) FocusCarolina Math Connects,Course 3 (pages)79 Chapter 3 Anticipation Guide80 Chapter 3 Family Activity3-2 Estimating Square Roots 148–15181 Explore Through Reading 8-2.6, 8-2.382 Study Guide 8-2.6, 8-2.383 Homework Practice 8-2.6, 8-2.384 Problem-Solving Practice 8-2.6, 8-2.33A Approximating Cube RootsLA12–LA1485 Study Guide 8-2.686 Skills Practice 8-2.687 Homework Practice 8-2.688 Problem-Solving Practice 8-2.63-3 Problem-Solving Investigation: Use a Venn Diagram 152–15389 Study Guide 8-1.890 Skills Practice 8-1.891 Homework Practice 8-1.892 Problem-Solving Practice 8-1.83-4 The Real Number System 155–15993 Explore Through Reading 8-2.3, 8-2.494 Study Guide 8-2.3, 8-2.495 Homework Practice 8-2.3, 8-2.496 Problem-Solving Practice 8-2.3, 8-2.43-5 The Pythagorean Theorem 162–16697 Explore Through Reading 8-4.198 Study Guide 8-4.199 Homework Practice 8-4.1100 Problem-Solving Practice 8-4.13-6 Using the Pythagorean Theorem 167–171101 Explore Through Reading 8-4.1102 Study Guide 8-4.1103 Homework Practice 8-4.1104 Problem-Solving Practice 8-4.13-7 Geometry: Distance on the Coordinate Plane 173–178105 Explore Through Reading 8-4.2, 8-4.1106 Study Guide 8-4.2, 8-4.1107 Homework Practice 8-4.2, 8-4.1108 Mini-Project 8-4.2, 8-4.1109 Chapter 3 TestAdditional ResourceMath Triumphs, Grade 8 [Book 2]: Chapter 6 (Squares, Square Roots, and the Pythagorean Theorem)SC StudyText, Course 3ix

4 Proportions and SimilarityPageLessonAcademic MathStandard(s) FocusUse with Glencoe SouthCarolina Math Connects,Course 3 (pages)111 Chapter 4 Anticipation Guide112 Chapter 4 Family Activity4-1 Ratios and Rates 190–193113 Explore Through Reading 8-2.7114 Study Guide 8-2.7115 Homework Practice 8-2.7116 Problem-Solving Practice 8-2.74-2 Proportional and Nonproportional Relationships 194–197117 Explore Through Reading 8-2.7118 Study Guide 8-2.7119 Homework Practice 8-2.7120 Problem-Solving Practice 8-2.74-3 Rate of Change 198–203121 Explore Through Reading 8-2.7122 Study Guide 8-2.7123 Homework Practice 8-2.7124 Problem-Solving Practice 8-2.74-5 Solving Proportions 210–214125 Explore Through Reading 8-2.7126 Study Guide 8-2.7127 Homework Practice 8-2.7128 Problem-Solving Practice 8-2.74-6 Problem-Solving Investigation: Draw a Diagram 216–217129 Study Guide 8-1.8130 Skills Practice 8-1.8131 Homework Practice 8-1.8132 Problem-Solving Practice 8-1.84-7 Similar Polygons 218–223133 Explore Through Reading 8-5.1134 Study Guide 8-5.1135 Homework Practice 8-5.1136 Problem-Solving Practice 8-5.14-8 Dilations 225–230137 Explore Through Reading 8-4.3, 8-4.4138 Study Guide 8-4.3, 8-4.4139 Homework Practice 8-4.3, 8-4.4140 Problem-Solving Practice 8-4.3, 8-4.44-9 Indirect Measurement 232–235141 Explore Through Reading 8-5.1142 Study Guide 8-5.1143 Homework Practice 8-5.1144 Problem-Solving Practice 8-5.1(continued on the next page)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.x SC StudyText, Course 3

4 Proportions and Similarity (continued)Page5 PercentLessonAcademic MathStandard(s) FocusUse with Glencoe SouthCarolina Math Connects,Course 3 (pages)4-10 Scale Drawings and Models 236–241145 Explore Through Reading 8-2.7146 Study Guide 8-2.7147 Homework Practice 8-2.7148 Mini-Project 8-2.7149 Chapter 4 TestAdditional ResourceMath Triumphs, Grade 8 [Book 2]: Chapter 5 (Ratios, Rates, and Similarity)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Use with Glencoe SouthPageLessonAcademic MathStandard(s) FocusCarolina Math Connects,Course 3 (pages)151 Chapter 5 Anticipation Guide152 Chapter 5 Family Activity5-3 Algebra: The Percent Proportion 263–267153 Explore Through Reading 8-2.7154 Study Guide 8-2.7155 Homework Practice 8-2.7156 Problem-Solving Practice 8-2.75-5 Problem-Solving Investigation: Reasonable Answers 272–273157 Study Guide 8-1.1158 Skills Practice 8-1.1159 Homework Practice 8-1.1160 Problem-Solving Practice 8-1.15-6 Percent and Estimation 275–278161 Explore Through Reading 8-2.7162 Study Guide 8-2.7163 Homework Practice 8-2.7164 Problem-Solving Practice 8-2.7165 Chapter 5 TestAdditional ResourcesMath Triumphs, Grade 8 [Book 2]: Chapter 5 (Ratios, Rates, and Similarity)Math Triumphs, Grade 8 [Book 3]: Chapter 8 (Percents and Circle Graphs)SC StudyText, Course 3xi

6 Geometry and Spatial ReasoningPageLesson7 Measurement: Area and VolumeAcademic MathStandard(s) FocusUse with Glencoe SouthCarolina Math Connects,Course 3 (pages)167 Chapter 6 Anticipation Guide168 Chapter 6 Family Activity6-2 Problem-Solving Investigation: Use Logical Reasoning 314–315169 Study Guide 8-1.3, 8-1.5170 Skills Practice 8-1.3, 8-1.5171 Homework Practice 8-1.3, 8-1.5172 Problem-Solving Practice 8-1.3, 8-1.5173 Chapter 6 TestAdditional ResourceMath Triumphs, Grade 8 [Book 2]: Chapter 4 (Angle Measures)PageLessonAcademic MathStandard(s) FocusUse with Glencoe SouthCarolina Math Connects,Course 3 (pages)175 Chapter 7 Anticipation Guide176 Chapter 7 Family Activity7-1 Circumference and Area of Circles 352–357177 Explore Through Reading 8-5.4178 Study Guide 8-5.4179 Homework Practice 8-5.4180 Problem-Solving Practice 8-5.47-2 Problem-Solving Investigation: Solve a Simpler Problem 360–361181 Study Guide 8-1.8182 Skills Practice 8-1.8183 Homework Practice 8-1.8184 Problem-Solving Practice 8-1.87-3 Area of Composite Figures 363–367185 Explore Through Reading 8-5.4, 8-5.5186 Study Guide 8-5.4, 8-5.5187 Homework Practice 8-5.4, 8-5.5188 Problem-Solving Practice 8-5.4, 8-5.57A Perimeter of Quadrilaterals 739–740189 Study Guide 8-5.5190 Skills Practice 8-5.5191 Homework Practice 8-5.5192 Problem-Solving Practice 8-5.57-6 Volume of Pyramids and Cones 380–384193 Explore Through Reading 8-5.3194 Study Guide 8-5.3195 Homework Practice 8-5.3196 Mini-Project 8-5.3(continued on the next page)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.xii SC StudyText, Course 3

7 Measurement: Area and Volume (continued)PageLessonAcademic MathStandard(s) FocusUse with Glencoe SouthCarolina Math Connects,Course 3 (pages)7B Volume of Pyramids, Cones, and Spheres 741197 Study Guide 8-5.3198 Skills Practice 8-5.3199 Homework Practice 8-5.3200 Problem-Solving Practice 8-5.37-9 Similar Solids 399–404201 Explore Through Reading 8-5.1, 8-5.2202 Study Guide 8-5.1, 8-5.2203 Homework Practice 8-5.1, 8-5.2204 Problem-Solving Practice 8-5.1, 8-5.27C Precision and Accuracy 736205 Study Guide 8-5.6206 Skills Practice 8-5.6207 Homework Practice 8-5.6208 Problem-Solving Practice 8-5.67D Converting Between Metric and Customary Units 742–745209 Study Guide 8-5.7210 Skills Practice 8-5.7211 Homework Practice 8-5.7212 Problem-Solving Practice 8-5.7213 Chapter 7 TestCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Additional ResourceMath Triumphs, Grade 8 [Book 2]: Chapter 4 (Angle Measures)SC StudyText, Course 3xiii

8 More Equations and InequalitiesPageLessonAcademic MathStandard(s) FocusUse with Glencoe SouthCarolina Math Connects,Course 3 (pages)215 Chapter 8 Anticipation Guide216 Chapter 8 Family Activity8-1 Simplifying Algebraic Expressions 416–421217 Explore Through Reading 8-3.3218 Study Guide 8-3.3219 Homework Practice 8-3.3220 Problem-Solving Practice 8-3.38-2 Solving Two-Step Equations 422–426221 Explore Through Reading 8-3.4222 Study Guide 8-3.4223 Homework Practice 8-3.4224 Problem-Solving Practice 8-3.48-3 Writing Two-Step Equations 427–431225 Explore Through Reading 8-3.2226 Study Guide 8-3.2227 Homework Practice 8-3.2228 Problem-Solving Practice 8-3.28-4 Solving Equations with Variables on Each Side 434–437229 Explore Through Reading 8-3.4, 8-3.2230 Study Guide 8-3.4, 8-3.2231 Homework Practice 8-3.4, 8-3.2232 Problem-Solving Practice 8-3.4, 8-3.28-5 Problem-Solving Investigation: Guess and Check 438–439233 Study Guide 8-1.1234 Skills Practice 8-1.1235 Homework Practice 8-1.1236 Problem-Solving Practice 8-1.18-6 Inequalities 441–444237 Explore Through Reading 8-3.2238 Study Guide 8-3.2239 Homework Practice 8-3.2240 Problem-Solving Practice 8-3.2241 Chapter 8 TestAdditional ResourceMath Triumphs, Grade 8 [Book 1]: Chapter 2 (Patterns and Graphs) and Chapter 3 (Expressionsand Equations)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.xiv SC StudyText, Course 3

9 Algebra: Linear FunctionsCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.PageLessonAcademic MathStandard(s) FocusUse with Glencoe SouthCarolina Math Connects,Course 3 (pages)243 Chapter 9 Anticipation Guide244 Chapter 9 Family Activity9-2 Functions 469–473245 Explore Through Reading 8-3.1246 Study Guide 8-3.1247 Homework Practice 8-3.1248 Problem-Solving Practice 8-3.19-3 Representing Linear Functions 475–480249 Explore Through Reading 8-3.1, 8-4.2250 Study Guide 8-3.1, 8-4.2251 Homework Practice 8-3.1, 8-4.2252 Problem-Solving Practice 8-3.1, 8-4.29-4 Slope 481–486253 Explore Through Reading 8-3.7254 Study Guide 8-3.7255 Homework Practice 8-3.7256 Problem-Solving Practice 8-3.79-6 Slope Intercept Form 495–499257 Explore Through Reading 8-3.7, 8-3.1258 Study Guide 8-3.7, 8-3.1259 Homework Practice 8-3.7, 8-3.1260 Problem-Solving Practice 8-3.7, 8-3.19-8 Problem-Solving Investigation: Use a Graph 508–509261 Study Guide 8-1.8262 Skills Practice 8-1.8263 Homework Practice 8-1.8264 Problem-Solving Practice 8-1.89-9 Scatter Plots 510–515265 Explore Through Reading 8-6.1, 8-6.2266 Study Guide 8-6.1, 8-6.2267 Homework Practice 8-6.1, 8-6.2268 Problem-Solving Practice 8-6.1, 8-6.2269 Chapter 9 TestAdditional ResourcesMath Triumphs, Grade 8 [Book 1]: Chapter 2 (Patterns and Graphs) and Chapter 3 (Expressions andEquations)Math Triumphs, Grade 8 [Book 3]: Chapter 7 (One-Variable Data) and Chapter 9 (Two-Variable Data)SC StudyText, Course 3xv

10 Algebra: Nonlinear Functions and PolynomialsPageLessonAcademic MathStandard(s) FocusUse with Glencoe SouthCarolina Math Connects,Course 3 (pages)271 Chapter 10 Anticipation Guide272 Chapter 10 Family Activity10-1 Linear and Nonlinear Functions 528–533273 Explore Through Reading 8-3.5274 Study Guide 8-3.5275 Homework Practice 8-3.5276 Problem-Solving Practice 8-3.510-3 Problem-Solving Investigation: Make a Model 538–539277 Study Guide 8-1.8278 Skills Practice 8-1.8279 Homework Practice 8-1.8280 Problem-Solving Practice 8-1.8281 Chapter 10 TestAdditional ResourcesMath Triumphs, Grade 8 [Book 1]: Chapter 2 (Patterns and Graphs) and Chapter 3 (Expressions andEquations)Math Triumphs, Grade 8 [Book 3]: Chapter 9 (Two-Variable Data)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.xvi SC StudyText, Course 3

11 StatisticsCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.PageLessonAcademic MathStandard(s) FocusUse with Glencoe SouthCarolina Math Connects,Course 3 (pages)283 Chapter 11 Anticipation Guide284 Chapter 11 Family Activity11-1 Problem-Solving Investigation: Make a Table 574–575285 Study Guide 8-1.8286 Skills Practice 8-1.8287 Homework Practice 8-1.8288 Problem-Solving Practice 8-1.811-2 Histograms 576–580289 Explore Through Reading 8-1.8290 Study Guide 8-1.8291 Homework Practice 8-1.8292 Problem-Solving Practice 8-1.811-4 Measures of Central Tendency and Range 591–596293 Explore Through Reading 8-6.8294 Study Guide 8-6.8295 Homework Practice 8-6.8296 Problem-Solving Practice 8-6.811-7 Stem-and-Leaf Plots 612–616297 Explore Through Reading 8-1.8298 Study Guide 8-1.8299 Homework Practice 8-1.8300 Problem-Solving Practice 8-1.811-8 Select an Appropriate Display 617–621301 Explore Through Reading 8-1.7302 Study Guide 8-1.7303 Homework Practice 8-1.7304 Problem-Solving Practice 8-1.711A Organize Data in MatricesLA15–LA18305 Study Guide 8-6.2306 Skills Practice 8-6.2307 Homework Practice 8-6.2308 Problem-Solving Practice 8-6.2309 Chapter 11 TestAdditional ResourcesMath Triumphs, Grade 8 [Book 2]: Chapter 5 (Ratios, Rates, and Similarity)Math Triumphs, Grade 8 [Book 3]: Chapter 7 (One-Variable Data), Chapter 8 (Percent and Circle Graphs),and Chapter 9 (Two-Variable Data)SC StudyText, Course 3xvii

12 ProbabilityPageLessonAcademic MathStandard(s) FocusUse with Glencoe SouthCarolina Math Connects,Course 3 (pages)311 Chapter 12 Anticipation Guide312 Chapter 12 Family Activity12-2 Probability of Compound Events 637–642313 Explore Through Reading 8-6.4314 Study Guide 8-6.4315 Homework Practice 8-6.4316 Problem-Solving Practice 8-6.412-3 Experimental and Theoretical Probability 643–647317 Explore Through Reading 8-6.3318 Study Guide 8-6.3319 Homework Practice 8-6.3320 Mini-Project 8-6.312-4 Problem-Solving Investigation: Act It Out 650–651321 Study Guide 8-1.8322 Skills Practice 8-1.8323 Homework Practice 8-1.8324 Problem-Solving Practice 8-1.812A Probability with Geometric Models 747–748325 Study Guide 8-6.7326 Skills Practice 8-6.7327 Homework Practice 8-6.7328 Problem-Solving Practice 8-6.7329 Chapter 12 TestAdditional ResourceMath Triumphs, Grade 8 [Book 3]: Chapter 8 (Percent and Circle Graphs)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.xviii SC StudyText, Course 3

South Carolina Academic StandardsGrade 8 MathematicsThis diagram shows what each part of the Indicator number means.←8 is the grade level. → 8-1.7 7 is the indicator number.↑8-1 is the standard number.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Mathematical ProcessesStandard 8-1: The student will understand and utilize the mathematical processes of problem solving,reasoning and proof, communication, connections, and representation.8-1.1 Generate and solve complex abstract problems that involve modeling physical, social, or mathematicalphenomena.8-1.2 Evaluate conjectures and pose follow-up questions to prove or disprove conjectures.8-1.3 Use inductive and deductive reasoning to formulate mathematical arguments.8-1.4 Understand equivalent symbolic expressions as distinct symbolic forms that represent the samerelationship.8-1.5 Generalize mathematical statements based on inductive and deductive reasoning.8-1.6 Use correct and clearly written or spoken words, variables, and notations to communicate aboutsignificant mathematical tasks.8-1.7 Generalize connections among a variety of representational forms and real-world situations.8-1.8 Use standard and nonstandard representations to convey and support mathematical relationships.Number and OperationsStandard 8-2: The student will demonstrate through the mathematical processes an understanding ofoperations with integers, the effects of multiplying and dividing with rational numbers, thecomparative magnitude of rational and irrational numbers, the approximation of cube andsquare roots, and the application of proportional reasoning.8-2.1 Apply an algorithm to add, subtract, multiply, and divide integers.8-2.2 Understand the effect of multiplying and dividing a rational number by another rational number.8-2.3 Represent the approximate location of irrational numbers on a number line.8-2.4 Compare rational and irrational numbers by using the symbols ≤, ≥, , and =.8-2.5 Apply the concept of absolute value.8-2.6 Apply strategies and procedures to approximate between two whole numbers the square roots or cuberoots of numbers less than 1,000.8-2.7 Apply ratios, rates, and proportions.SC StudyText, Course 3xix

South Carolina Academic StandardsGrade 8 Mathematics (continued)AlgebraStandard 8-3: The student will demonstrate through the mathematical processes an understanding ofequations, inequalities, and linear functions.8-3.1 Translate among verbal, graphic, tabular, and algebraic representations of linear functions.8-3.2 Represent algebraic relationships with equations and inequalities.8-3.3 Use commutative, associative, and distributive properties to examine the equivalence of a variety ofalgebraic expressions.8-3.4 Apply procedures to solve multistep equations.8-3.5 Classify relationships between two variables in graphs, tables, and/or equations as either linear ornonlinear.8-3.6 Identify the coordinates of the x- and y-intercepts of a linear equation from a graph, equation, and/ortable.8-3.7 Identify the slope of a linear equation from a graph, equation, and/or table.GeometryStandard 8-4: The student will demonstrate through the mathematical processes an understanding of thePythagorean theorem; the use of ordered pairs, equations, intercepts, and intersections to locatepoints and lines in a coordinate plane; and the effect of a dilation in a coordinate plane.8-4.1 Apply the Pythagorean theorem.8-4.2 Use ordered pairs, equations, intercepts, and intersections to locate points and lines in a coordinateplane.8-4.3 Apply a dilation to a square, rectangle, or right triangle in a coordinate plane.8-4.4 Analyze the effect of a dilation on a square, rectangle, or right triangle in a coordinate plane.MeasurementStandard 8-5: The student will demonstrate through the mathematical processes an understanding of theproportionality of similar figures; the necessary levels of accuracy and precision in measurement;the use of formulas to determine circumference, perimeter, area, and volume; and theuse of conversions within and between the U.S. Customary System and the metric system.8-5.1 Use proportional reasoning and the properties of similar shapes to determine the length of a missingside.8-5.2 Explain the effect on the area of two-dimensional shapes and on the volume of three-dimensionalshapes when one or more of the dimensions are changed.8-5.3 Apply strategies and formulas to determine the volume of the three-dimensional shapes cone andsphere.8-5.4 Apply formulas to determine the exact (pi) circumference and area of a circle.8-5.5 Apply formulas to determine the perimeters and areas of trapezoids.8-5.6 Analyze a variety of measurement situations to determine the necessary level of accuracy andprecision.8-5.7 Use multistep unit analysis to convert between and within U.S. Customary System and the metricsystem.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.xx SC StudyText, Course 3

South Carolina Academic StandardsGrade 8 Mathematics (continued)Data Analysis and ProbabilityStandard 8-6: The student will demonstrate through the mathematical processes an understanding of therelationships between two variables within one population or sample.8-6.1 Generalize the relationship between two sets of data by using scatterplots and lines of best fit.8-6.2 Organize data in matrices or scatterplots as appropriate.8-6.3 Use theoretical and experimental probability to make inferences and convincing arguments aboutan event or events.8-6.4 Apply procedures to calculate the probability of two dependent events.8-6.5 Interpret the probability for two dependent events.8-6.6 Apply procedures to compute the odds of a given event.8-6.7 Analyze probability using area models.8-6.8 Interpret graphic and tabular data representations by using range and the measures of centraltendency (mean, median, and mode).Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.SC StudyText, Course 3xxi

NameDatePrerequisite Skills Check1 △ABC is similar to △PQR. The scalefactor of △ABC to △PQR is 3:2. If −− AB is18 centimeters, what is the length of −− PQ ?A 12 cmB 18 cmC 21 cmD 27 cm4 Which point is located at √16 ?AB C D0 1 2 3 4 5 6 7 8 910A AB BC CD DCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2 Emily wants to find the value of x in theequation 2x + 4 = 16. What would be thebest first step to solve for x?A Add 4 to both sides of the equation.B Subtract 4 from both sides of theequation.C Multiply both sides of the equation by2.D Divide both sides of the equation by 2.3 Which symbol correctly compares thenumbers below?A C =D +7 √365 A surfboard shop in Myrtle Beach madethe following box chart showing the ages ofits customers:Age of Customers0 10 20 30 40 50 60 70 80What conclusion can be drawn from thedata’s interquartile range?A Half of the customers were between 20and 50 years old.B Half of the customers were between 30and 50 years old.C All of the customers were between 20and 50 years old.D Half of the customers were between 20and 30 years old.Prerequisite Skills Check SC StudyText, Course 3 1

NameDatePrerequisite Skills Check (continued)8 What is the volume of the cylinder?6 The box plot below shows the number ofA1_2 × 1_2 = 1_14 in.1_4B2 + 1_2 = 1What is the area of the shaded trapezoid?1_ C2 ÷ 1_A2 = 144 in 21_ D2 - 1_B 50 in 22 = 0 C 56 in 2points scored by a football team.(V = π r 2 h)Points Scored18240 10 20 30 40 50 60What is the median number of pointsscored by the football team?A 1,356.48 cubic unitsB 2,712.96 cubic unitsA 7C 6,104.16 cubic unitsB 21D 24,416.64 cubic unitsC 35D 569 Megan cuts a triangle off one corner of arectangle to make the trapezoid below.7 When a coin is flipped, the probability ofthe coin landing on heads is 1_3 in.. Nina wants2to know the probability of the coin landingon heads twice in a row. Which equation4 in.shows this probability?D 70 in 2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2 SC StudyText, Course 3 Prerequisite Skills Check

NameDatePrerequisite Skills Check (continued)10 Which measure is equivalent to 1 squareyard?A 3 square feetB 6 square feetC 9 square feetD 12 square feet13 Which two shapes come next in thepattern?ACopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.11 John has 3 red shirts, 5 blue shirts, and2 orange shirts. If he randomly choosesa shirt, what is the probability of Johnchoosing a red or a blue shirt?A3_10B 1_2C 3_5D 4_512 What is the measure of ∠A below?A 30°B 60°C 120°D 150°60BCD14 The graph below shows the relationshipbetween the total cost of renting a boat atMurray Lake and the number of hours theboat is used. How much does it cost perhour to rent the boat?Total Cost$20$16$12$8$40 1 2 3 4 5Number of HoursA $0.25 C $4.00B $1.00 D $20.00Prerequisite Skills Check SC StudyText, Course 3 3

NameDatePrerequisite Skills Check (continued)15 Which has the greatest value?A ⎪-7.5⎥B ⎪-10⎥C ⎪9.1⎥D ⎪-8.9⎥18 A map is drawn to a scale of 1:2,400.How long would the image be on the mapof a soccer field that is 120 yards long?A 0.5 inchB 1.8 inchesC 2.0 inchesD 3.6 inches16 Which number line shows the value of b inthe inequality below?2b - 4 > 619 The triangles below are similar.A012345678910B0123456789105CD00112233445566778891091017 Which regular shape below cannot makea tessellation?ABCD6What is the value of x?A 8B 9C 10D 1120 There are about 1.09 yards in 1 meter.About how many yards are in 5 meters?A 4.59 yardsB 4.91 yardsC 5.09 yardsD 5.45 yards12Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.4 SC StudyText, Course 3 Prerequisite Skills Check

NameDatePrerequisite Skills Check (continued)21 What is 120% of 50?23 What is the slope of the line shown below?A 40B 60C 80D 110-4-3-2x321O 1 2 3 4y4-2-3-422 At Joe’s Restaurant, customers choose1 drink, 1 main course, and 1 vegetablefrom the menu below.Drinks Main Courses VegetablesMilk Pasta CarrotsJuice Steak BroccoliChickenA 2B -2C1_2D -1_2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.How many combinations can be made fromthe menu choices?A 7B 9C 12D 1524 The square root of 72 is between whichtwo integers?A 7 and 8B 8 and 9C 9 and 10D 10 and 11Prerequisite Skills Check SC StudyText, Course 3 5

NameDatePrerequisite Skills Check (continued)25 Which shape below could be a crosssection of a sphere?28 The two triangles are similar. What is thevalue of x?A10 cmxB15 cm 9 cmCA 6 cmB 7 cmC 8 cmD 9 cmD26 Which symbol correctly compares thenumbers below?A C =D +3 2 √8127 What is 7.85 × 10 5 in standard notation?A 7,850B 78,500C 785,000D 7,850,00029 A 13-foot ladder rests against the side of abuilding. The base of the ladder is 5 feetfrom the building. What is the distancebetween the base of the building and theheight of the ladder?A 11.3 ftB 12.0 ft5 ft13 ftC 13.0 ftD 14.3 ftCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6 SC StudyText, Course 3 Prerequisite Skills Check

NameDatePrerequisite Skills Check (continued)30 Jerome bought 12 eggs for $2.40. What isthe unit cost of the eggs that Jeromebought?A $0.15/eggB $0.20/eggC $0.25/eggD $0.40/egg31 What value is equal to 6 3 ?A 18B 216C 729D 1,29633 Melissa rolled a number cube labeled1–6. She rolled the cube 20 times and itlanded on an even number 12 times.Which choice below has both thetheoretical and experimental probabilityof Melissa rolling an even number?A theoretical: 1_3experimental: 3_5B theoretical: 3_5experimental: 1_2C theoretical: 1_2experimental: 3_5D theoretical: 1_2experimental: 2_5Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.32 Which equation shows a directlyproportional relationship?A y = 2x - 1By = 4xC y = x + 3Dy = 5_ x34 Which expression 5_shows another way ofsolving4 ?ABC3_6 ÷6_5 × 3_46_5 × 4_35_6 × 3_45_ D6 × 4_3Prerequisite Skills Check SC StudyText, Course 3 7

NameDatePrerequisite Skills Check (continued)35 Carol modeled a subtraction problem onthe number line below.8765 43210 1 2 3 4 5 6 7 8Which problem did she solve?A 8 - 12B 12 - 8C 4 - 12D -4 + 838 The approximate population of a city from2004 to 2008 is shown below.Population18,00016,00014,00012,00010,0008,0006,0004,0002,0000Population in the City2004 2005 2006 2007 2008YearWhich of these statements is supported bythe data?36 What is the interquartile range of the databelow?2, 3, 11, 12, 15, 19, 20, 21, 27, 29, 32A 16B 19C 25D 3037 How many inches are in 1 yard?A 3 inchesB 12 inchesC 24 inchesD 36 inchesA The population of the city is likely todecrease over the next 5 years.B The population of the city is likely toincrease over the next 5 years.C The population of the city is likely tostay the same over the next 5 years.D The population of the city is likely todecrease over the next 2 years and thenincrease after that.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.8 SC StudyText, Course 3 Prerequisite Skills Check

NameDatePrerequisite Skills Check (continued)39 Kevin wants to solve for a in the equationbelow.6a + 4 = 16Which choice below shows the sameequation after Kevin subtracts 4 from eachside?A 2a + 4 = 12B 6a = 12C 2a = 12D 6a = 2041 The rectangles below are similar. The areaof rectangle A is 3 square units.3 6What is the area of rectangle B?AB6 square units9 square unitsC 12 square unitsD 18 square unitsCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.40 What three-dimensional figure has the top,side, and front views shown?A conetop front sideB cylinderC pyramidD triangular prism42 Marcia flips two coins. What is theprobability that both coins will land ontails?ABC1_41_23_4D 1Prerequisite Skills Check SC StudyText, Course 3 9

NameDatePrerequisite Skills Check (continued)43 Claire wrote the equation y = 1_ x. Which3choice below describes the relationship ofx and y?A directly proportionalB indirectly proportionalC exponentially proportionalD nonproportional44 What is the area of the shaded part of thefigure below? Use 3.14 for π.45 In a regular tessellation, the interior anglesof the regular polygon can add up to 360°.RegularPolygonInteriorAngleSum ofInteriorAnglesTriangle 60° 180°Square 90° 360°Pentagon 108° 540°Hexagon 120° 720°Heptagon 4_ 1287 ° 900°Octagon 135° 1,080°Which shapes in the table above can betessellated?2 cmWhy do the interior angles of thesepolygons have to be factors of 360°?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.10 SC StudyText, Course 3 Prerequisite Skills Check

1NAME DATE PERIODAnticipation GuideAlgebra: IntegersSTEP 1 Before you begin Chapter 1• Read each statement.• Decide whether you Agree (A) or Disagree (D) with the statement.• Write A or D in the first column OR if you are not sure whether you agreeor disagree, write NS (Not Sure).STEP 1A, D, or NSStatement1. A conjecture is a statement proven to be true.2. Algebraic expressions are any mathematical expressions thatcontain at least one operation symbol.3. According to the Order of Operations, all operations withingrouping symbols must be completed first.4. According to the Order of Operations, all addition andsubtraction should be done before multiplication and division.5. The Commutative Property is true only for addition andmultiplication.STEP 2A or DCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6. Negative integers can be used to express values less thanzero.7. When comparing two negative integers, the greater integer isthe one with the greater absolute value.8. The sum of a positive integer and a negative integer is alwaysnegative.9. When subtracting a negative integer, add its opposite.10. The product of two negative integers is always positive.11. The quotient of two negative integers is always negative.12. Any letter can be used to represent an unknown in anexpression or equation.STEP 2 After you complete Chapter 1• Reread each statement and complete the last column by entering an A or a D.• Did any of your opinions about the statements change from the first column?• For those statements that you mark with a D, use a piece of paper to writean example of why you disagree.Chapter 1 SC StudyText, Course 3 11

1NAME DATE PERIODFamily ActivityState Test PracticeFold the page along the dashed line. Work each problem on another pieceof paper. Then unfold the page to check your work.1. Evan stepped into an elevator in a verytall building in downtown New York City.The buttons he could choose from rangedfrom Basement Le vel D (-4) to 64.640 street level-1-2-3D -4How many stories high is this building(including its basements)?A 60 stories highB 68 stories highC 67 stories highD 61 stories highFold here.Solution1. There are 64 stories above ground and4 stories below ground, which meansthere are 64 + 4, or 68 stories.2. Jarred has six fewer model cars thanCammie. Half of the sum of theircombined model cars is equal to 10.How many model cars does Cammiehave?Which equation can be used to find thenumber of model cars Cammie has?A _ c - 6 = 102B c __ + c - 6 = 102C c - c - 6 = 10 ÷ 2D c - 6_2 = 10Solution2. Hint: A letter (or variable) is used torepresent a number that we do not know,in this case the number of cars Cammiehas. In order to solve the problem, youalso will need to write an expression forthe number of cars that Jared has basedon the number Cammie has.The number of cars that Cammie hascan be represented by the letter c. Weknow that Jared has 5 less cars thanCammie, or c - 5. If we add their carstogether (c + c - 5) and divide by 2,the number should equal 10.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.The answer is B. The answer is B.12 SC StudyText, Course 3 Chapter 1

NAME DATE PERIOD1-2Explore Through ReadingSCAS8-3.3, 8-1.6,8-1.4Variables, Expressions, and PropertiesGet Ready for the LessonComplete the Mini Lab at the top of page 29 in your textbook.Write your answers below.1. Complete the table below.Figure Number 1 2 3 4 5 6Number of Triangles 3 4 5 6 7 8Perimeter 6 8What is the relationship between the number of triangles used to make the figure andthe perimeter of the figure?2. What would be the perimeter of Figure 10?Read the Lesson3. Number the operations in the correct order for simplifying2 + 4 (9 - 6 ÷ 3) . Then simplify the expression.AdditionMultiplicationSubtractionDivisionCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.For Exercises 4–8, describe how each pair of numerical expressions isdifferent. Then determine whether the two expressions are equal toeach other. If the expressions are equal, name the property that saysthey are equal.4. 2 + 5, 5 + 25. (6 - 4) - 1, 6 - (4 - 1)6. 2 (5 - 3) , 2 · 5 - 2 · 37. 5 · (4 · 7) , (5 · 4) · 78. 10 ÷ 2, 2 ÷ 10Remember What You Learned9. The word counter has several meanings in the English language. Use adictionary to find the meaning of counter when it is used as a prefix inthe word counterexample. Then write your own definition ofcounterexample.Chapter 1 SC StudyText, Course 3 13

NAME DATE PERIOD1-2Study GuideSCAS8-3.3, 8-1.6,8-1.4Variables, Expressions, and PropertiesWhen fi nding the value of an expression with more than one operation, perform the operations in theorder specifi ed by the order of operations.Order of Operations1. Perform all operations within grouping symbols fi rst; start with the innermost grouping symbols.2. Evaluate all powers before other operations.3. Multiply and divide in order from left to right.4. Add and subtract in order from left to right.Example 1 Evaluate the expression (5 + 7) ÷ 2 × 3 - (8 + 1) .(5 + 7) ÷ (2 × 3) - 8 + 1 = 12 ÷ 2 × 3 - (8 + 1) Add inside the left parentheses.= 12 ÷ 2 × 3 - 9 Add inside the remaining parentheses.= 6 × 3 - 9 Divide.= 18 - 9 Multiply.= 9 Subtract.Example 2 Evaluate the expression 3 x 2 - 4y if x = 3 and y = 2.3 x 2 - 4y = 3 (3) 2 - 4 (2) Replace x with 3 and y with 2.= 3 (9) - 4 (2) Evaluate the power first.= 27 - 8 Do all multiplications.= 19 Subtract.ExercisesEvaluate each expression.1. 4 × 5 + 8 2. 16 - 12 ÷ 43. 14 ÷ 2 + 3 (5) 4. 5 - 6 × 2 ÷ 35. 2 · 3 2 + 10 - 14 6. 2 2 + 32 ÷ 8 - 57. (10 + 5) ÷ 3 8. 5 2 · (8 - 6)9. (17 - 5) (6 + 5) 10. 3 + 7 (14 - 8 ÷ 2)11. 5[24 - (6 + 8) ] 12.__ 143 2 - 2Evaluate each expression if a = 3, b = 5, and c = 6.13. a + 3b 14. 4b - 3c 15. 2a - b + 5c16. (ab) 2 17. a (b + c) 18. 3 (bc - 8) ÷ aCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.14 SC StudyText, Course 3 Chapter 1

1-2NAME DATE PERIODHomework PracticeVariables, Expressions, and PropertiesEvaluate each expression if r = 3, s = 5, and t = 2.1. 3r + s 2. 4s - 5t 3. 8 + 6t - r 4. r s 25. (st) 2 6.__ r 2 + 1t + 3Name the property shown by each statement.7. s (7 + t) - r 8. 2 s 2 - 8s + 39. 6 (5 + 1) = 6 (5) + 6 (1) 10. 1 (2 + 3) = 2 + 3SCAS8-3.3, 8-1.6,8-1.411. (10 + 7) + 4 = 10 + (7 + 4) 12. 5 + (1 + 9) = 5 + (9 + 1)State whether each conjecture is true or false. If false, provide acounter example.13. The sum of an even number and an odd number is always even.14. Multiplication of whole numbers is associative.Rewrite each expression using the indicated property.15. (x + 7) + 3, Associative Property 16. 5 (3) + 5 (4) , Distributive PropertyCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.17. INTERNET A bookstore offers wireless Internet access to its customers for a charge. Thecost of using this service is given by the expression $1.50 + m_ , where m is the number20of minutes online. How much would it cost to be online 40 minutes?18. TEMPERATURE When a temperature in degrees Celsius C is known, the expression__ 9C + 160can be used to find the temperature in degrees Fahrenheit. If a thermometer5shows that a temperature is 20°C, what is the temperature in degrees Fahrenheit?Chapter 1 SC StudyText, Course 3 15

NAME DATE PERIOD1-2 Problem-Solving PracticeVariables, Expressions, and PropertiesFOOTBALL For Exercises 1 and 2, use the table that shows statisticsfrom the 2006 Super Bowl.SCAS8-3.3, 8-1.6,8-1.4Team Touchdowns Extra Points Field GoalsPittsburgh 3 3 0Seattle 1 1 11. Each team’s final score for a footballgame can be found using the expression6t + e + 3f, where t is the number oftouchdowns, e is the number of extrapoints, and f is the number of fieldgoals. Find Pittsburgh’s final score inthe 2006 Super Bowl.2. Use the expression 6t + e + 3f tofind Seattle’s final score in the 2006Super Bowl.3. GEOMETRY The expression 6 s 2 can beused to find the surface area of a cube,where s is the length of an edge of thecube. Find the surface area of a cubewith an edge of length 10 centimeters.10 cm5. MOVIE RENTALS Mario intends to rent10 movies for his birthday party. Hecan rent new releases for $4 each,while older ones are $2 each. If herents n new releases, the total cost, indollars, of the 10 movies is representedby the expression 4n + 2 (10 - n) .Evaluate the expression to find thetotal cost if he rents 7 new releases.4. VERTICAL MOTION The height of anobject dropped from the top of a300-foot tall building can be describedby the expression 300 - 16 t 2 , where tis the time, in seconds, after the ball isdropped. Find the height of the object3 seconds after it is dropped.6. CIRCULAR MOTION Pelipa is able to spinher yo-yo along a circular path. Theyo-yo is kept in this path by a forcewhich can be described by theexpression_ m v 2r . Evaluate theexpression to find the force whenm = 12, v = 4, and r = 8.rCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.16 SC StudyText, Course 3 Chapter 1

NAME DATE PERIOD1-3 Explore Through ReadingSCASIntegers and Absolute ValueGet Ready for the LessonRead the introduction at the top of page 35 in your textbook.Write your answers below.1. What does a temperature of -34°F represent?8-2.4, 8-2.5,8-1.62. Which temperature is closer to zero?Read the LessonThe symbol … is called an ellipsis.3. Look on page 35 in your textbook to find the meaning of the ellipsis as itis used in the list 1, 4, 7, 10,... .4. Use a dictionary to find the meaning of the ellipsis as it is used in thesentence The marathon began... downtown.5. How can you explain the usage of the ellipsis in the list in Exercise 3 interms of the meaning for the ellipsis in the sentence in Exercise 4?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6. Look at the number line on page 35 of your textbook. How are the ellipses(plural of ellipsis) in the set of integers {..., -4, -3, -2, -1, 0, 1, 2, 3, 4,...}represented on the number line?Complete each sentence with either left or right to make a truesentence. Then write a statement comparing the two numbers witheither < or >.7. -45 lies to the of 0 on a number line.8. 72 lies to the of 0 on a number line.9. -3 lies to the of -95 on a number line.10. 6 lies to the of -7 on a number line.11. Describe the symbol for the absolute value of 3. Then write the symbol.Remember What You Learned12. Write a mathematical expression that represents the following sentence.(Hint: Let f represent the 49ers’ score and s represent the Seahawks’ score.)The Seahawks and the 49ers scored within 3 points of each other.Chapter 1 SC StudyText, Course 3 17

NAME DATE PERIOD1-3 Study GuideSCASIntegers and Absolute Value8-2.4, 8-2.5,8-1.6A number line can help you order a set of integers. When graphed on a number line, the smaller oftwo integers is always to the left of the greater integer.Example 1Order the set of integers {10, -3, -9, 4, 0} from least to greatest.Graph each integer on a number line.-10 -8-6-4-202 4 6 8 10The numbers from left to right are {-9, -3, 0, 4, 10}.The absolute value of a number is the distance of that number from 0 on a number line.Example 2 Evaluate the expression ⎪-20⎥ + ⎪10⎥ .⎪-20⎥ + ⎪10⎥ = ⎪20⎥ + ⎪10⎥ The absolute value of -20 is 20.= 20 + 10 The absolute value of 10 is 10.= 30 Simplify.ExercisesOrder each set of integers in each set from least to greatest.1. {3, 0, -5, 1, 4} 2. {-6, -8, 3, -1, -4}3. {2, 13, -11, -21, 5} 4. {31, 0, -34, -9, 7}Evaluate each expression.5. ⎪-13⎥ 6. ⎪21⎥ 7. ⎪-3⎥ + ⎪-5⎥8. ⎪9⎥ + ⎪-8⎥ 9. ⎪-13⎥ + ⎪15⎥ 10. ⎪21 - 18⎥11. ⎪-11⎥ - ⎪-5⎥ 12. ⎪4⎥ - ⎪-4⎥ 13. ⎪23 + 15⎥Evaluate each expression if a = -6, b = 4, and c = 5.14. ⎪a⎥ + 14 15. ⎪c - b⎥ 16. b + ⎪c⎥17. ⎪3b⎥ 18. 2 ⎪a⎥ + c 19. ⎪2b + c⎥Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.18 SC StudyText, Course 3 Chapter 1

NAME DATE PERIOD1-3 Homework PracticeSCASIntegers and Absolute ValueReplace each with , or = to make a true sentence.1. 0 8 2. -5 -3 3. 1 -78-2.4, 8-2.5,8-1.64. -4 -4 5. -12 10 6. 5 -67. -6 -7 8. 0 -8 9. -10 -10Order each set of integers from least to greatest.10. {-5, -7, 0, 5, 7} 11. {-1, 2, -3, 4}12. {-2, -4, -6, -8, -10, -12} 13. {0, -9, -3, -7, 1, -1}Evaluate each expression.14. ⎪-19⎥ 15. ⎪15⎥ 16. |0|17. ⎪-1⎥ + ⎪3⎥ 18. ⎪-19⎥ + ⎪-8⎥ 19. ⎪-12⎥ - ⎪4⎥Evaluate each expression if k = 4, m = -2, n = 7, and p = -5.20. ⎪m⎥ + 6 21. n - ⎪p⎥ 22. k + ⎪p⎥Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.23. 5 ⎪n⎥ + k 24. ⎪n⎥ - 4 25. 9 ⎪m⎥ - 14TEMPERATURE For Exercises 26 and 28, use the following information.During a five-day cold spell, Jose recorded the temperature each day at noon.The temperature was -3°F on Monday, -5°F on Tuesday, -4°F on Wednesday,-1°F on Thursday, and 0°F on Friday.26. On which day was it the coldest at noon?27. On which day was it the warmest at noon?28. The temperature at noon on Saturday was 25° warmer than thetemperature on Tuesday. What was the temperature on Saturday?Justify your answer using a number line.-555 5 5 50 5 10 15 20Chapter 1 SC StudyText, Course 3 19

NAME DATE PERIOD1-3 Problem-Solving PracticeIntegers and Absolute ValueGOLF For Exercises 1 and 2, use the table that lists ten players andtheir scores in Round 3 of the 2005 60th U.S. Women’s Open.SCAS8-2.4, 8-2.5,8-1.6Player Score Player ScoreGulbis, Natalie 0 Kim, Birdie -2Icher, Karine +1 Kung, Candie 0Jo, Young -1 Lang, Brittany +1Kane, Lorie +5 Pressel, Morgan -1Kerr, Cristie +1 Ochoa, Lorena +61. Order the scores in the table from leastto greatest.2. Who had the lowest score?3. LONGITUDE London, England, is locatedat 0° longitude. Write integers forthe locations of New York City whoselongitude is 74° west and Tokyo whoselongitude is 140° east. Assume thateast is the positive direction.5. SOLAR SYSTEM The averagetemperature of Saturn is -218°F, whilethe average temperature of Jupiter is-162°F. Which planet has the loweraverage temperature?4. STOCK MARKET Your stock loses 53points on Monday and 23 points onTuesday, but gains 67 points onWednesday. Write an integer for eachday's change.6. OCEAN TRENCHES The elevation of thePuerto Rican Trench in the AtlanticOcean is -8,605 meters, the elevationof the Mariana Trench in the PacificOcean is -10,924 meters, and theelevation of the Java Trench in theIndian Ocean is -7,125 meters. Whichtrench has the the lowest elevation?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.20 SC StudyText, Course 3 Chapter 1

NAME DATE PERIOD1-4 Explore Through ReadingSCAS 8-2.1Adding IntegersGet Ready for the LessonRead the introduction at the top of page 41 in your textbook.Write your answers below.1. Write an integer that describes the amount of money Jack owes hisbrother for the three days he downloads songs.2. Write an addition sentence that describes this situation.Read the Lesson3. Look at your answer for Exercise 2. Identify each number in the additionsentence as either an addend or a sum.Identify the number with the greater absolute value.4. 4, 8 5. -3, 56. 9, -12 7. -23, -16Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Determine whether you add or subtract the absolute values of thenumbers to find the sum. Give a reason for your answer.8. 4 + 8 9. -3 + 510. 9 + (-12) 11. -23 + (-16)Determine whether the sum is positive or negative. Then find the sum.12. 4 + 8 13. -3 + 514. 9 + (-12) 15. -23 + (-16)Add.16. 3 + (-4) 17. -3 + 4 18. -6 + (-4) 19. 7 + 820. 25 + (-17) 21. -34 + (-17) 22. -43 + 4 23. 11 + (-30)24. -81 + (-63) 25. -39 + 124 26. 97 + (-165) 27. -49 + (-75)Remember What You Learned28. You have seen what a negative number means in terms of weather ormoney. Describe what a negative number means on a video cassetterecorder.Chapter 1 SC StudyText, Course 3 21

NAME DATE PERIOD1-4 Study GuideSCAS 8-2.1Adding IntegersTo add integers with the same sign, add their absolute values. The sum has the same sign as theintegers.Example 1 Find -3 + (-4) .-3 + (-4) =-7 Add ⎪-3⎥ + ⎪-4⎥ . Both numbers are negative, so the sum is negative.To add integers with different signs, subtract their absolute values. The sum has the same sign as theinteger with the greater absolute value.Example 2 Find -16 + 12.-16 + 12 = -4 Subtract ⎪12⎥ from ⎪-16⎥ . The sum is negative because ⎪-16⎥ > ⎪12⎥ .ExercisesAdd.1. 9 + 16 2. -10 + (-10) 3. 18 + (-26)4. -23 + (-15) 5. -45 + 35 6. 39 + (-38)7. -55 + 81 8. -61 + (-39) 9. -74 + 3610. 5 + (-4) + 8 11. -3 + 10 + (-6) 12. -13 + (-8) + (-12)13. 3 + (-10) + (-16) + 11 14. -17 + 31 + (-14) + 26Evaluate each expression if x = 4 and y = -3.15. 11 + y 16. x + (-6) 17. y + 218. ⎪x + y⎥ 19. ⎪x⎥ + y 20. x + ⎪y⎥Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.22 SC StudyText, Course 3 Chapter 1

NAME DATE PERIOD1-4 Homework PracticeSCAS 8-2.1Adding IntegersFind each sum.1. -1 + (-8) 2. 13 + 15 3. 19 + (-7)4. -14 + (-14) 5. -12 + 10 6. -5 + (-26)7. -46 + 27 8. -33 + 55 9. -29 + (-25)10. 6 + 14 + (-12) 11. -15 + (-17) + 10 12. -13 + (-13) + (-18)13. -5 + 8 + (-1) + (-6) 14. 8 + (-7) + (-8) + (-9) 15. -15 + 10 + -16 + 12POPULATION For Exercises 16 and 17, use the table below that shows thechange in population for four cities between 2000 and 2005.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.City2000 Population(thousands)Change as of 2005(thousands)Boston, Massachusetts 589 -30Las Vegas, Nevada 478 +67Pittsburgh, Pennsylvania 335 -18Rochester, New York 220 -8Source: U.S. Census Bureau16. What is the population of each of these cities as of 2005 in thousands?17. What was the total population change for these four cities?Write an addition expression to describe each situation. Then find eachsum and explain its meaning.18. GAMES On one turn, you move 10 spaces forward around the game board.On the next turn, you move 4 spaces backward.19. CAMPING While hiking down into a canyon, Manuel passed a sign statingthat the elevation was 100 feet below sea level. He descended another56 feet before reaching his campsite.20. WEATHER Before you went to sleep last night, the temperature was -3°F.During the night the temperature dropped by 5°.21. ELEVATOR Mrs. Brown parked in the parking garage 30 feet below street level.She then got in an elevator and went up 80 feet to her office.Chapter 1 SC StudyText, Course 3 23

NAME DATE PERIOD1-4 Problem-Solving PracticeSCAS 8-2.1Adding Integers1. FOOTBALL A football team loses 5 yardson one play and then loses 8 yards onthe next play. Write an additionexpression that represents the changein position of the team for the twoplays. Then find the sum.2. ELEVATOR You park in a garage 3 floorsbelow ground level. Then you get in theelevator and go up 12 floors. Write anaddition expression to represent thissituation. Then find the sum.3. GOLF In 2005, Tiger Woods won theMasters Tournament. His scores were+2, -6, -7, and -1 for four rounds.Write an addition expression thatrepresents his final score. Then find thesum.5. OCEANOGRAPHY A research teamaboard an underwater research vesseldescends 1,500 feet beneath the surfaceof the water. They then rise 525 feetand descend again 350 feet. Write anaddition expression to represent thissituation. Then find the sum.4. INVENTORY A local bookstore has30 copies of a bestseller when it opensMonday morning. On Monday, it sells6 copies of the book. On Tuesday, itsells 3 copies. On Wednesday, it receivesa shipment containing 24 copies of thebook and also sells 8 copies. Write anaddition expression that represents thenumber of copies of the book that storehas at the end of the day onWednesday. Then find the sum.6. SPORTS Peter weighs 156 pounds, buthe would like to wrestle in a lowerweight class. He loses 4 pounds oneweek, gains back 2 pounds the nextweek, loses 5 pounds the third week,and loses 3 pounds the fourth week.Write an addition expression torepresent this situation. Then find thesum.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.24 SC StudyText, Course 3 Chapter 1

NAME DATE PERIOD1-5 Explore Through ReadingSCAS 8-2.1Get Ready for the LessonComplete the Mini Lab at the top of page 46 in your textbook.Write your answers below.1. How does this result compare with the result of 2 + (-5) ?2. Use algebra tiles to find -3 - 4.3. How does this result compare to -3 + (-4) ?4. Use algebra tiles to find each difference and sum. Compare the results ineach group.a. 3 - 6; 3 + (-6) b. -4 - 2; -4 + (-2)Read the LessonSubtracting Integers5. Find the opposite of 7.6. Find the additive inverse of 7.7. How is the opposite of a number different from the additive inverse of thenumber?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Rewrite each difference as a sum. Then find the sum.8. 2 - 9 9. -3 - 810. 10 - (-12) 11. -5 - (-16)Subtract.12. 3 - (-5) 13. -3 - 5 14. -7 - (-3) 15. 6 - 816. 23 - (-17) 17. -24 - (-12) 18. -41 - 4 19. 31 - (-26)20. -81 - (-33) 21. -139 - 134 22. 97 - (-265) 23. -59 - (-77)24. Describe the method for subtracting integers.Remember What You Learned25. Subtraction and addition are often referred to as opposite operations.Explain in your own words the relationship between addition and subtraction.Chapter 1 SC StudyText, Course 3 25

NAME DATE PERIOD1-5 Study GuideSCAS 8-2.1Subtracting IntegersTo subtract an integer, add its opposite or additive inverse.Example 1 Find 8 - 15.8 - 15 = 8 + (-15) To subtract 15, add -15.=-7 Add.Example 2 Find 13 - (-22) .13 - (-22) = 13 + 22 To subtract -22, add 22.= 35 Add.ExercisesSubtract.1. -3 - 4 2. 5 - (-2) 3. -10 - 84. -15 - (-12) 5. -23 - (-28) 6. 16 - 97. 9 - 16 8. -21 - 16 9. 28 - 3710. -34 - (-46) 11. 65 - (-6) 12. 19 - ⎪29⎥Evaluate each expression if a =-7, b =-3, and c = 5.13. a - 8 14. 20 - b 15. a - c16. c - b 17. b - a - c 18. c - b - aCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.26 SC StudyText, Course 3 Chapter 1

NAME DATE PERIOD1-5 Homework PracticeSCAS 8-2.1Subtracting IntegersSubtract.1. 15 - 7 2. 3 - 12 3. -8 - 94. 4 - (-12) 5. 18 - (-7) 6. -8 - (-9)7. -14 - (-18) 8. -19 - (-13) 9. 8 - (-22)10. -1 - 15 11. 12 - 19 12. -10 - (-5)Evaluate each expression if d = -4, f = -7, and g = 11.13. d - 10 14. g - 15 15. d - g16. d - f 17. d - f - g 18. g - d - fCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.GEOGRAPHY For Exercises 19–21, usethe table that shows the elevationsabove sea level of the lowest andhighest points on six continents.19. How far below the highest pointin Australia is the lowest pointin Australia?20. How far below the highest point inNorth America is the lowest pointin Asia?21. Find the difference between thelowest point in South America andthe lowest point in Africa.Simplify.ContinentLowestHighestPoint (m)Point (m)Africa -156 5,895Asia -400 8,850Australia -12 2,228Europe -28 5,642North America -86 6,194South America -42 6,96022. 29 - (-4) - (-15) 23. -10 - [8 + (-16) ]24. 25 - [16 + (-9) ] 25. [22 - (-18) ] - (-5 + 11)26. (-5 + 9) - (-20 - 12) 27. [-15 + (-7) ] - (-8 - 11)Chapter 1 SC StudyText, Course 3 27

NAME DATE PERIOD1-5 Problem-Solving PracticeSCAS 8-2.1Subtracting IntegersGEOGRAPHY For Exercises 1 and 2, use the table. The table shows theelevations of several places on Earth.PlaceElevation (feet)Mt. McKinley +20,320Puerto Rican Trench -28,232Mt. Everest +29,035Dead Sea -1,348Death Valley -2821. Find the difference in elevationbetween the top of Mt. McKinley andthe top of Mt. Everest.2. Find the difference in elevationbetween Death Valley and theDead Sea.3. TEMPERATURE The highest recordedtemperature on Earth was recorded inAfrica at 136°F, while the lowest was-129°F in Antarctica. What is therange of temperatures recordedon Earth?5. WATER The boiling point of water is212°F, while -460°F is its absolutelowest temperature. Find thedifference between these twotemperatures.4. WEATHER If the overnight temperatureat the Arctic Circle was -14°F, butthe temperature rose to 8°F duringthe day, what was the differencebetween these high and lowtemperatures?6. STOCK MARKET During the course ofone day, the price of a stock fluctuatedbetween a high of $3 above theprevious day’s closing price and a low of$2 below the previous day’s closingprice. What was the difference betweenthe high and low prices for that day?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.28 SC StudyText, Course 3 Chapter 1

NAME DATE PERIOD1-6 Explore Through ReadingSCAS 8-2.1Multiplying and Dividing IntegersGet Ready for the LessonRead the introduction at the top of page 51 in your textbook.Write your answers below.1. Write an addition sentence that could be used to find the change in theplane’s elevation after 3 seconds. Then find the sum.2. Write a multiplication sentence that could be used to find this same changein elevation. Explain your reasoning.3. Write a multiplication sentence that could be used to find the change inthe plane’s elevation after 12 seconds. Then find the product.Read the Lesson4. Identify each number in the multiplication sentence 3 (-120) = -360 aseither a factor or a product.Complete each sentence with either positive or negative.5. The product of two integers with different signs is .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6. The product of two integers with the same signs is .7. The quotient of two integers with different signs is .8. The quotient of two integers with the same signs is .Determine whether each product or quotient is positive or negative.Then evaluate the expression.9. 4 · 8 10. -3 · 511. 9 (-2) 12. -6 (-7)13. 12 ÷ (-4) 14. -35 ÷ (-7)15. _ 213Remember What You Learned16. _-64817. Explain how to find the mean of a set of numbers. What is another namefor the mean?Chapter 1 SC StudyText, Course 3 29

NAME DATE PERIOD1-6 Study GuideSCAS 8-2.1Multiplying and Dividing IntegersUse the following rules to determine whether the product or quotient of two integers is positive ornegative.• The product of two integers with different signs is negative.• The product of two integers with the same sign is positive.• The quotient of two integers with different signs is negative.• The quotient of two integers with the same sign is positive.Example 1 Find 7 (-4).7 (-4) =-28 The factors have different signs. The product is negative.Example 2 Find -5(-6).-5(-6) = 30 The factors have the same sign. The product is positive.Example 3 Find 15 ÷ (-3).15 ÷ -3 = -5 The dividend and divisor have different signs. The quotient is negative.Example 4 Find -54 ÷ (-6).-54 ÷ (-6) = 9 The dividend and divisor have the same sign. The quotient is positive.ExercisesMultiply or divide.1. 8 (-8) 2. -3 (-7) 3. -9 (4) 4. 12 (8)5. 33 ÷ (-3) 6. -25 ÷ 5 7. 48 ÷ 4 8. -63 ÷ (-7)9. (-4) 2 10._-7515Evaluate each expression if a =-1, b = 4, and c =-7.11. -6 (3)(-5) 12.13. 3c + b 14. a (b + c) 15. c 2 - 5b 16._-143-13a - 6 _cCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.30 SC StudyText, Course 3 Chapter 1

NAME DATE PERIOD1-6 Homework PracticeSCAS 8-2.1Multiplying and Dividing IntegersMultiply.1. 5 (-7) 2. -3 · 12 3. -8(-9)4. -4 (-12) 5. (-7) 2 6. -2 (-5) (-3)Divide.7. -14 ÷ 2 8. 35 ÷ -7 9. -48 ÷ (-6)10. _-66611. _ 56-712. _-80-5Evaluate each expression if r = -4, s = 11, and t = -7.13. s + 5t 14. 10 - rt 15._ 5st - 416. _-42r - t17. - r 2 - 16 18. (2t + 4) 2 ÷ 4Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Find the mean of each set of integers.19. -8, -5, 3, -9, 5, 2 20. 11, -15, -16, 17, -20, -18, -2221. -5, 4, 8, -12, 10 22. -22, -19, -14, -17, -18Find each product or quotient.23. (3) 2 · (-4) 2 24. -3 (-5) 2 25. -5 (-2) (4) (-3)26.__ -10 (15)627._ 122-1228.__ -4 · 12829. MONEY If you have $216 and you spend $12 each day, how long would it be untilyou had no money left?30. WEATHER During a six hour period, the temperature dropped 18°F. Find theaverage hourly change in the temperature.Chapter 1 SC StudyText, Course 3 31

NAME DATE PERIOD1-6 Problem-Solving PracticeMultiplying and Dividing IntegersSCAS 8-2.11. STOCK MARKET The price of a stockdecreased $2 per day for fourconsecutive days. What was the totalchange in value of the stock over thefour-day period?2. EVAPORATION The height of the waterin a tank decreases 3 inches each weekdue to evaporation. What is the changein the height of the water over a fiveweekperiod due to evaporation?3. FOOTBALL A football team lost 9 yardson each of three consecutive plays.What was the team’s total change inposition for the three plays?4. HIKING A group of hikers is descendinga mountain at a rate of 400 feetper hour. What is the change in theelevation of the hikers after 6 hours?G102030405040302010 G5. WEATHER On a certain day, thetemperature changed at a rateof -2°F per hour. How long didit take for the change intemperature to be -14°F?-14°F7. DEPRECIATION The value of a piece ofoffice equipment is changing at a rateof -$175 per year. How long will it takefor the change in value to be -$1,050?6. GEOLOGY The length of an island ischanging at the rate of -17 inches peryear. How long will it take for thechange in the length of the island to be-255 inches?8. POPULATION The population of a smalltown is changing at a rate of -255people per year. How long will it takefor the change in population to be-2,040 people?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.32 SC StudyText, Course 3 Chapter 1

NAME DATE PERIOD1-7 Explore Through ReadingSCAS 8-3.2, 8-1.6Writing EquationsGet Ready for the LessonRead the introduction at the top of page 57 in your textbook.Write your answers below.1. What is the relationship between the number of uniforms and the total cost?2. Write an expression representing the total cost for n uniforms.3. What does the equation 32n = 384 represent in this situation?Read the LessonLook at the steps for writing an algebraic equation on page 57. Thendetermine whether each situation requires addition, subtraction,multiplication, or division.4. Find the difference between the cost of a gallon of premium gasoline andthe cost of a gallon of regular gasoline.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5. Find the cost per person when the price of a pizza is split among severalpeople.6. Find the price of an airline ticket after the price has been decreased by $50.7. Find how much an executive spent on breakfast, lunch, and dinner.8. Find the flight time after the time has been increased by 15 minutes.9. Find the product of the price of a calculator and the number of studentsin the class.10. Find the high temperature on Wednesday if this temperature is 3º lessthan the high temperature on Tuesday.11. Find the ratio of the amount of gasoline used and the distance traveled.Remember What You Learned12. Devise your own way to determine how a verbal description should be translatedas an algebraic equation.Chapter 1 SC StudyText, Course 3 33

NAME DATE PERIOD1-7 Study GuideSCAS 8-3.2, 8-1.6Writing EquationsThe table shows several verbal phrases for each algebraic expression.Phrases Expression Phrases Expression8 more than a numberthe sum of 8 and a numberx plus 8x increased by 8x + 8the difference of r and 66 subtracted from a number6 less than a numberr minus 6r - 6Phrases Expression Phrases Expression4 multiplied by n4 times a numberthe product of 4 and n4na number divided by 3the quotient of z and 3the ratio of z and 3The table shows several verbal sentences that represent the same equation.z_3Sentences9 less than a number is equal to 45.The difference of a number and 9 is 45.A number decreased by 9 is 45.45 is equal to a number minus 9.Equationn - 9 = 45ExercisesWrite each verbal phrase as an algebraic expression.1. the sum of 8 and t 2. the quotient of g and 153. the product of 5 and b 4. p increased by 105. 14 less than f 6. the difference of 32 and xWrite each verbal sentence as an algebraic equation.7. 5 more than a number is 6.8. The product of 7 and b is equal to 63.9. The sum of r and 45 is 79.10. The quotient of x and 7 is equal to 13.11. The original price decreased by $5 is $34.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.12. 5 shirts at $d each is $105.65.34 SC StudyText, Course 3 Chapter 1

NAME DATE PERIOD1-7 Homework PracticeSCAS 8-3.2, 8-1.6Writing EquationsDefine a variable. Then write an equation to model each situation.1. After receiving $25 for her birthday, Latisha had $115.2. At 14 years old, Adam is 3 years younger than his brother Michael.3. A class of 30 students separated into equal sized teams results in 5 studentsper team.4. When the bananas were divided evenly among the 6 monkeys, eachmonkey received 4 bananas.Define a variable. Then write an equation that could be used to solveeach problem.5. GRADES Kelly’s test score was 6 points higher than Michelle’s. If Kelly’stest score was 88, what was Michelle’s test score?6. GEOMETRY A rectangle’s width is one-third its length. If the width is8 inches, what is the length of the rectangle?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.7. FOOTBALL A team had a total gain of -15 yards over several plays withan average gain of -5 yards per play. How many plays are represented?Write an equation to model the relationship between the quantities ineach table.8. Kilograms, k Grams, g1 1,0002 2,0003 3,0004 4,000kg9. Feet, f Yards, y3 16 29 312 4fy10. MONEY Carlotta earns $3 for every hourthat she baby sits. Complete the table ofHours, h Amount, avalues showing the amount she earns forbaby sitting 1, 2, 3, 4, and h hours. Givenh, a number of hours, write an equation tofind a, the amount that Carlotta earns.Chapter 1 SC StudyText, Course 3 35

NAME DATE PERIOD1-7 Problem-Solving PracticeWriting EquationsSCAS 8-3.2, 8-1.61. AGE Julia is 3 years younger thanKevin. Kevin is 13. Define a variableand write an equation to find Julia’sage.2. CIVICS In the 2004 presidential election,Texas had 23 more electoral votes thanTennessee. Define a variable and writean equation to find the number ofTennessee’s electoral votes if Texas had34 votes.3. ENERGY One year, China consumed4 times as much energy as Brazil.Define a variable and write an equationto find the amount of energy Brazilused that year if China used 12,000kilowatt-hours.4. CHEMISTRY The atomic number ofcadmium is half the atomic number ofcurium. The atomic number forcadmium is 48. Define a variable andwrite an equation to find the atomicnumber of curium.5. LIBRARIES The San Diego Public Libraryhas 44 fewer branches than the ChicagoPublic Library. Define a variable andwrite an equation for the numberof branches in the San Diego PublicLibrary if Chicago has 79 branches.7. POPULATION The population of Oakland,California, is 9,477 more than thepopulation of Omaha, Nebraska.Omaha has a population of 390,007.Define a variable and write an equationto find the population of Oakland.6. ASTRONOMY Saturn is 6 times fartherfrom the Sun than Mars. Define avariable and write an equation to findthe distance of Mars from the Sun ifSaturn is about 1,429,400,000 km fromthe sun.8. GEOGRAPHY Kings Peak in Utah is8,667 feet taller than Spruce Knobin West Virginia. Spruce Knob is4,861 feet tall. Define a variable andwrite an equation to find the height ofKings Peak.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.36 SC StudyText, Course 3 Chapter 1

NAME DATE PERIOD1-8 Study GuideProblem-Solving Investigation: Work BackwardYou may need to work backward to solve a problems.SCAS 8-1.1UnderstandPlanSolveCheck• Determine what information is given in the problem and what you need to fi nd.• Select a strategy including a possible estimate.• Solve the problem by carrying out your plan.• Examine your answer to see if it seems reasonable.Example 1Mari put money in her savings account each week. She put a certain amount of money inthe bank on the first week. On the second week she put twice as much money in the bankas the first week. On the third week, she put $40 less in the bank than on the secondweek. On the fourth week, she put $20 more in the bank than on the third week. Mari put$200 in the bank on the fourth week. How much money did Mari put in the bank on thefirst week?UnderstandPlanSolveYou know that Mari put $200 in the bank on the fourth week. You need toknow how much money she put in the bank on the first week.Start with the amount she put in the bank on the last week and workbackward.Start with the $200 Mari put in the bank on the fourth week.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Fourth Week Third Week Second Week First Week$200 -$20 $180 + $40 $220 ÷ 2 $110This is $20more than thethird week.CheckExercisesWorkbackward.Subtract$20.This is $40 lessthan the secondweek.Workbackward.Add $40.This is twice asmuch as thefirst week.Workbackward.Divideby 2.Start with $110 for the first week and work forward. On the second week shedeposited twice as much money in the bank than on the first week, whichis $220. On the third week, she deposited $40 less than the second week,which is $180. On the fourth week she deposited $20 more than on the thirdweek, or $200. This is what you know she deposited on the fourth week.Use the work backward strategy to solve each problem.1. SHOPPING Jack spent a total of $87.58 when he went shopping for camping supplies. Hespent $36.89 on food, $23.24 on a sleeping bag, and bought lunch. When he got home,he had $15.70. How much did he spend on lunch?2. AGE Sam is 4 years older than Eliot. Eliot is 9 years younger than Xing. Xing is 3 yearsolder than Damien. If Damien is 15 years old, how old are each of the other boys?Chapter 1 SC StudyText, Course 3 37

NAME DATE PERIOD1-8 Skills PracticeSCAS 8-1.1Problem-Solving Investigation: Work BackwardUse the work backward strategy to solve each problem.1. SKATEBOARDS On Monday, David’s skateboard shop received its first shipment ofskateboards. David sold 12 skateboards that day. On Thursday, he sold 9 skateboards.On Friday, he received a shipment of 30 more skateboards and sold 10 skateboards. Hethen had a total of 32 skateboards in his shop. How many skateboards were deliveredon Monday?2. SHIPPING An overseas cargo ship was being loaded. At the end of each day, a scaleshowed the total weight of the ship’s cargo. On Monday, 48 tons of cargo were loadedonto the ship. On Tuesday, three times as much cargo was loaded on to the ship ason Monday. On Wednesday, 68 tons of cargo were loaded onto the ship. On Thursday,0.75 as much cargo was loaded onto the ship as on Wednesday. On Friday, 120 tonsof cargo were loaded onto the ship. At the end of the day on Friday, the scale showedthat the ship was carrying 690 tons of cargo. How much cargo was the ship carryingwhen it first came into port on Monday?3. NUMBERS Jana is thinking of a number. If she divides her number by 12 and thenmultiplies the quotient by 8, the result is 520. What number is Jana thinking of?4. JOGGING Edmund is training for a marathon. He ran a certain number of miles onMonday. On Wednesday, he ran 2 more miles than on Monday. On Saturday, he rantwice as far as on Wednesday. On Sunday, he ran 6 miles less than on Saturday. He ran8 miles on Sunday. How many miles did Edmund run on Monday?Use the table to solve each problem.Airline ScheduleMinneapolis, MN to Dallas, TXFlight Number Departure Time Arrival Time253 8:20 A.M. 10:37 A.M.142 11:52 A.M. 1:45 P.M.295 12:00 P.M. 3:30 P.M.5. Charles needs to take Flight 295. He needs 45 minutes to eat breakfast and pack. Ittakes 25 minutes to get to the airport. To be at the airport 90 minutes early, what isthe latest time he can start eating breakfast?6. Mrs. Gonzales left her office at 7:25 A.M. She planned that it would take her 30 minutesto get to the airport, but the traffic was so heavy it took an additional 20 minutes. Ittakes 30 minutes to check her baggage and walk to the boarding gate. What is thefirst flight she can take to Dallas?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.38 SC StudyText, Course 3 Chapter 1

NAME DATE PERIOD1-8Homework PracticeProblem-Solving Investigation: Work BackwardSCAS 8-1.1Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Mixed Problem SolvingUse the work backward strategy tosolve Exercises 1 and 2.1. TRAVEL Rajiv and his family left homeon a trip and drove for 2 hours beforethey stopped to eat. After 1.5 hours,they were back on the road. Theyarrived at their destination 3 hourslater at 5:00 P.M. What time did theyleave home?2. GRADES Kumiko had an average of 92on her first three math tests. Her scoreson the second and third tests were 97and 89. What was her score on the firsttest?Use any strategy to solve Exercises 3–6.Some strategies are shown below.Problem-Solving Strategies• Work backward.• Find a pattern.3. BAKING Isabel doubled her recipe forchocolate chip cookies. After herbrothers ate 8 cookies, she set asidehalf of the remaining cookies for aschool party. Isabel then gave 2 dozencookies to her neighbor. She had 12cookies left over. How many cookiesdoes one recipe make?4. ANALYZE TABLES The table below givesthe results from a poll taken at schoolabout the times in minutes that boysand girls spend using the Internet forschool work and the total time spentusing the Internet each week.GenderTime Used forSchool WorkTotal Timeper WeekBoys 33 min 255 minGirls 72 min 213 minHow many more minutes per week doboys spend using the Internet forpurposes other than school work thangirls?5. MOVIES The two animated films withthe highest box office receipts broughtin a total of $775 million. If one filmbrought in $97 million more than theother, how much did the film with thehighest receipts bring in?6. U.S. PRESIDENTS Harry S Truman waselected president in 1944. He died in1972 at the age of 88. How old was heat the time he was elected?Chapter 1 SC StudyText, Course 3 39

NAME DATE PERIOD1-8 Problem-Solving PracticeSCAS 8-1.1Problem-Solving Investigation: Work BackwardUse the work backward strategy to solve each problem.CLARINET PRACTICE For Exercises 1 and 2, use the table at the right. It is arecord of the amount of time Elena practiced her clarinet in a week.Monday Tuesday Thursday Saturday Sunday? 20 minutesmore thanMonday10 minutesless thanTuesdayTwice aslong asThursday15 minutesless thanSaturday—45 minutes1. How many minutes did Elena practicethe clarinet on Thursday?2. How many minutes did Elena practiceon Monday?3. HOCKEY During a hockey game,Brandon played 7 less minutes thanNick. Zach played 12 minutes morethan Brandon. Hunter played twiceas long as Zach. Hunter played for 44minutes. How many minutes did Nickplay in the hockey game?5. WEATHER On Monday, Eliza read herbook. On Tuesday, she read three timesas long as she read on Monday. OnWednesday she read 20 minutes lessthan Tuesday. On Thursday she readfor 20 minutes, which was half as longas she read on Wednesday How manyminutes did Eliza read over the 4-dayperiod?4. PACKAGES In the morning, a deliverytruck delivers 24 of it packages to afactory. It then goes to a distributionlot, where the remaining packages areseparated into 4 equal groups and puton other trucks. There were 18packages in each of the groups. Howmany packages were on the deliverytruck to begin with?6. STAMPS Zoe added 23 stamps to hercollection. Three months later hercollection had tripled in number to atotal of 159 stamps. How many stampdid Zoe have to start her collection?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.40 SC StudyText, Course 3 Chapter 1

NAME DATE PERIOD1-9 Explore Through ReadingSolving Addition and Subtraction EquationsGet Ready for the LessonComplete the Mini Lab at the top of page 65 in your textbook.Write your answers below.Solve each equation using algebra tiles.1. x + 1 = 4 2. x + 3 = 7 3. x + (-4) = -5SCAS 8-3.2, 8-1.64. Explain how you would find a value of x that makes x + (-3) = -8 truewithout using models.Read the Lesson5. Match the method of solving with the appropriate equation.x + 6 = 9a. Subtract 11 from each side.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.s - 5 = 14b. Subtract 6 from each side.4 = -3 + p c. Add 3 to each side.11 + m = 33 d. Add 5 to each side.For Exercises 6–8, explain how to solve each equation.6. w - 7 + -27. c + 3 = 98. 17 = 11 + kSolve each equation.9. z + 8 = 2 10. 3 = -7 + r 11. -9 = g - 14Remember What You Learned12. Write two addition and two subtraction equations of your own. Trade yourequations with a partner and solve. Explain to each other the method youused to solve the equations.Chapter 1 SC StudyText, Course 3 41

NAME DATE PERIOD1-9 Study GuideSolving Addition and Subtraction EquationsYou can use the following properties to solve addition and subtraction equations.• Addition Property of Equality — If you add the same number to each side of an equation, the twosides remain equal.• Subtraction Property of Equality — If you subtract the same number from each side of an equation,the two sides remain equal.Example 1Solve w + 19 = 45. Check your solution.w + 19 = 45w + 19 - 19 = 45 - 19w = 26Write the equation.Subtract 19 from each side.19 - 19 = 0 and 45 - 19 = 26. w is by itself.Check w + 19 = 45 Write the original equation.Example 226 + 19 45 Replace w with 26. Is this sentence true?45 = 45 ✓ 26 + 19 = 45Solve h - 25 = -76. Check your solution.h - 25 = -76h - 25 + 25 = -76 + 25h =-51Write the equation.Add 25 to each side.-25 + 25 = 0 and -76 + 25 = -51. h is by itself.SCAS 8-3.2, 8-1.6Check h - 25 = -76 Write the original equation.-51 - 25 -76 Replace h with -51. Is this sentence true?-76 = -76 ✓ -51 - 25 = -51 + (-25) or -76ExercisesSolve each equation. Check your solution.1. s - 4 = 12 2. d + 2 = 21 3. h + 6 = 154. x + 5 = -8 5. b - 10 = -34 6. f - 22 = -67. 17 + c = 41 8. v - 36 = 25 9. y - 29 = -5110. 19 = z - 32 11. 13 + t =-29 12. 55 = 39 + kCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.13. 62 + b = 45 14. x - 39 = -65 15. -56 = -47 + n42 SC StudyText, Course 3 Chapter 1

NAME DATE PERIOD1-9 Homework PracticeSolving Addition and Subtraction EquationsSolve each equation. Check your solution.1. t + 7 = 12 2. h - 3 = 8 3. 8 = b - 94. k - 4 = -14 5. m + 9 = -7 6. y - 10 = -37. -14 = 2 + d 8. 15 + n = 10 9. -8 = r - 610. 11 = w - 5 11. -9 = g + 9 12. 12 + c = 16SCAS 8-3.2, 8-1.613. GEOMETRY Two angles are supplementary ifthe sum of their measures is 180°. The twoangles shown are supplementary. Write andsolve an equation to find the measure ofangle R.140°R S14. ARCHITECTURE The Sears Tower in Chicago was the tallest building in theworld when it was completed. Twenty-three years later, a taller buildingwas completed in 1996 on Taiwan. Write and solve an equation to find theyear that the Sears Tower was completed.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.15. FUNDRAISING During a five-day fundraiser, Shantell sold 8 boxes ofgreeting cards the first day, 6 boxes the second day, 10 boxes the thirdday, and 7 boxes the fourth day. If she sold a total of 45 boxes of greetingcards during the five days, write an equation that can be used to findthe number of boxes Shantell sold the fifth day. Explain two methods ofsolving this equation. Then solve the equation.16. ANALYZE TABLES The total points scored by bothteams in the 2006 Super Bowl was 14 less thanthe total points for 2005. Write and solve anequation to find the total points for 2005.Total Points Scored by BothTeams in Super BowlYearPoints2005 p2006 31Chapter 1 SC StudyText, Course 3 43

NAME DATE PERIOD1-9 Problem-Solving PracticeSolving Addition and Subtraction EquationsSCAS 8-3.2, 8-1.61. AGE Walter lived 2 years longer thanhis brother Martin. Walter was 79 atthe time of his death. Write and solvean addition equation to find Martin’sage at the time of his death.2. CIVICS New York has 24 fewer membersin the House of Representatives thanCalifornia. New York has 29representatives. Write and solve asubtraction equation to find thenumber of California representatives.3. GEOMETRY Two angles aresupplementary if the sum of theirmeasures is 180°. Angles A and B aresupplementary. If the measure ofangle A is 78°, write and solve anaddition equation to find the measureof angle B.4. BANKING After you withdraw $40 fromyour checking account, the balance is$287. Write and solve a subtractionequation to find your balance beforethis withdrawal.180° 5. WEATHER After the temperaturehad risen 12°F, the temperaturewas 7°F. Write and solve anaddition equation to find thestarting temperature.m∠ 78°7° F7. ELEVATION The lowest point inLouisiana is 543 feet lower than thehighest point in Louisiana. Theelevation of the lowest point is -8 feet.Write and solve a subtraction equationto find the elevation of the highestpoint in Louisiana.6. CHEMISTRY The atomic number ofmercury is the sum of the atomicnumber of aluminum and 67. Theatomic number of mercury is 80. Writeand solve an addition equation to findthe atomic number of aluminum.8. POPULATION In 2005, the population ofHonduras is the population of Haitidecreased by 832,598. The population ofHonduras is 6,823,568. Write and solvea subtraction equation to find thepopulation of Haiti.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.44 SC StudyText, Course 3 Chapter 1

NAME DATE PERIOD1-10 Explore Through ReadingSCAS 8-3.2, 8-1.6Algebra: EquationsGet Ready for the LessonRead the introduction at the top of page 70 in your textbook.Write your answers below.1. If h represents the number of hours the train has traveled, write amultiplication equation you could use to find how long it would take thetrain to travel 675 miles.Read the LessonComplete each sentence.2. To solve 3x = 51, each side by 3.3. To solve b_-2= 4, each side by -2.4. To solve -65 = -5t, each side by -5.5. To solve -7 = d_ , each side by 6.6Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Explain how to solve each equation.6. u_6 = 137. -2c = -148. 64 = 16kSolve each equation.9. 8r = 32 10. 3 = x_7Remember What You Learned11. -9 = -9g12. Write two multiplication and two division equations of your own. Tradeyour equations with a partner and solve. Explain to each other themethod you used to solve the equations.Chapter 1 SC StudyText, Course 3 45

NAME DATE PERIOD1-10 Study GuideAlgebra: EquationsSCAS 8-3.2, 8-1.6You can use the following properties to solve multiplication and division equations.• Multiplication Property of Equality — If you multiply each side of an equation by the same number,the two sides remain equal.• Division Property of Equality — If you divide each side of an equation by the same nonzero number,the two sides remain equal.Example 1Solve 19w = 114. Check your solution.19w = 114 Write the equation._ 19w19 = 11419Divide each side of the equation by 19.1w = 6 19 ÷ 19 = 1 and 114 ÷ 19 = 6.w = 6Identity Property; 1w = wCheck 19w = 114 Write the original equation.19 (6) 114 Replace w with 6.114 = 114 This sentence is true.Example 2CheckExercisesd_ Solve =-9. Check your solution.15d_15 =-9d_15 ( 15) =-9 (15) Multiply each side of the equation by 15.d_15_-13515d =-135=-9 Write the original equation.-9 Replace d with -135.-9 -9 -135 ÷ 15 = -9Solve each equation. Check your solution.1.r_5= 6 2. 2d = 12 3. 7h =-21f_4. -8x = 40 5.8 =-6 6. x_-10 =-77. 17c =-68 8.h_= 12-119. 29t =-14510. 125 = 5z 11. 13t =-182 12. 117 = -39kCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.46 SC StudyText, Course 3 Chapter 1

NAME DATE PERIOD1-10 Homework PracticeAlgebra: EquationsSolve each equation. Check your solution.1. 5s = 45 2. 8h = 64 3. 36 = 9bSCAS 8-3.2, 8-1.64. -3p = 24 5. -12m = -72 6. -56 = 7d7. x_5= 11 8.v_4 = 20 9. c_-2 = 4310. 16 = y _-311. -9 = n_812. a_25 = -313. CARS Mrs. Alvarez bought a new car. Her monthly payments are $525. If she will paya total of $25,200 in payments, write and solve a multiplication equation to find thenumber of payments.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.14. POPULATION The population of South Africa is four times the population of Greece. Ifthe population of South Africa is 44 million, write and solve a multiplication equation tofind the population of Greece.MEASUREMENT For Exercises 15 and 16, refer to the table. Write andsolve an equation to find each quantity.15. the number of quarts in 24 pints16. the number of gallons in 104 pintsSolve each equation.17. 3 = _-84g18. _-4xCustomary SystemConversions (capacity)1 pint = 2 cups1 quart = 2 pints1 quart = 4 cups1 gallon = 4 quarts1 gallon = 8 pints-144= -8 19. _r = -16Chapter 1 SC StudyText, Course 3 47

NAME DATE PERIOD1-10 Problem-Solving PracticeAlgebra: EquationsSCAS 8-3.2, 8-1.61. WAGES Felipe earns $9 per hour forhelping his grandmother with her yardwork. Write and solve a multiplicationequation to find how many hours hemust help his grandmother in order toearn $54.2. SHOPPING Granola bars are on salefor $0.50 each. If Brad paid $5 forgranola bars, write and solve amultiplication equation to find howmany bars he bought.3. EXERCISE Jasmine jogs 3 miles each day.Write and solve a multiplicationequation to find how many days it willtake her to jog 57 miles.4. TRAVEL On a trip, the Rollins familydrove at an average rate of 62 miles perhour. Write and solve a multiplicationequation to find how long it took themto drive 558 miles.5. ROBOTS The smallest robot can travel20 inches per minute through a pipe.Write and solve a multiplicationequation to find how long it will takethis robot to travel through 10 feet ofpipe.7. AGE The product of Bart’s age and 26 is338. Write and solve a multiplicationequation to find Bart’s age.6. BANKING Nate withdraws $40 from hischecking account each day. Write andsolve a multiplication equation to findhow long it will take him to withdraw$680.8. POPULATION The population of a smalltown is increasing at a rate of 325people per year. Write and solve amultiplication equation to find howlong it will take the population toincrease by 6,825.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.48 SC StudyText, Course 3 Chapter 1

NameChapter 1 TestMastering the SC StandardsDate1 Which number has the greatest value?ABCD⎪-12.5⎥⎪-2.7⎥⎪14.1⎥⎪-18⎥2 Cara wants to solve 52 × -6. Whichchoice below shows an equivalentexpression?8-2.54 Which step(s) could be used to solve theequation 2_3 x = 18?A Subtract 2_ from both sides of the3equation.B Divide both sides of the equation bythe reciprocal of 2_3 .C Divide both sides of the equation by 2,then multiply both sides by 3.D Multiply both sides of the equation bythe reciprocal of 2_3 . 8-3.4Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A (-6 × 2) + (-6 × 50)B (6 + 2) × (6 + 50)C (-6 × 2) + (-6 × 5)D (-6 × 2) × (-6 × 50)3 Which property is used in the equationbelow?21 + 3x = 3 (7 + x)A distributive propertyB commutative property of additionC commutative property of additionD associative property of addition8-2.18-3.35 Last year, Carla and her mom spent sometime on the South Carolina coast. Theydecided to collect lettered olive shells,which are the state shell of South Carolina.This year, they went back to the samebeach and collected 9 fewer shells than lastyear. They counted a total of 27 shells thisyear. To find out how many shells theyfound last year, or s, Carla wrote theequation s - 9 = 27. What should beCarla’s first step to solve the equation?A Divide both sides of the equationby 9.B Add 9 to both sides of the equation.C Multiply both sides of the equationby 9.D Subtract 9 from both sides of theequation.8-3.2Chapter 1 SC StudyText, Course 3 49

NameDateChapter 1 Test (continued)Mastering the SC Standards6 Which property is used in the equationbelow?3y × (6 × 2) = (3y × 6) × 2A Distributive PropertyB Commutative Property of additionC Commutative Property of additionD Associative Property of Multiplication9 The table below shows the cost, c, of ttheater tickets.Cost of Theater Ticketst 1 2 3 4c $8.50 $17.00 $25.50 $34.00Which equation matches the information inthe table?7 What is the value of t in the equation12t = 108?8-3.3A t = c - 7.5B c = 8.5tC c = 7.5t + 1D c = 30 + tA y = 7B y = 8C y = 9D y = 1210 Which expression is equivalent to12 + 8?8-3.28 Masako owes his mother $15 dollars.Yesterday, he gave his mother the $7 heearned from shoveling a neighbor’sdriveway. Which equation can Masakouse to model how much money he stillowes his mother?A 15 - (-7) = 8B 15 + 7 = 22C 15 ÷ 7 = 2.14D -15 + 7 = -88-3.28-2.1A 12 - 8B -12 - 8C -12 - (-8)D 12 - (- 8)8-2.111 What number has the smallest value?A ⎪2⎥B ⎪-16.2⎥C ⎪8.1⎥D ⎪-3.2⎥8-2.5Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.50 SC StudyText, Course 3 Chapter 1

2NAME DATE PERIODAnticipation GuideAlgebra: Rational NumbersSTEP 1 Before you begin Chapter 2• Read each statement.• Decide whether you Agree (A) or Disagree (D) with the statement.• Write A or D in the first column OR if you are not sure whether you agreeor disagree, write NS (Not Sure).Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.STEP 1A, D, or NSStatement1. 3, 1_ , 0.4, and 23_are all examples of rational numbers.2 52. To write a fraction as a decimal, divide the numerator into thedenominator.3. 4_7is greater than4_5because 7 is greater than 5.4. When multiplying two fractions, first find a commondenominator, and then multiply numerators anddenominators.5. Before multiplying two mixed numbers, rewrite both asimproper fractions.6. 12 and 1_ are multiplicative inverses of each other.127. To divide by a fraction, multiply by its opposite.8. To subtract two fractions with a common denominator,subtract the numerators and then the denominators.9. A common denominator must be found before adding orsubtracting fractions with different denominators.10. The equation 0.7 = x - 2.4 would be solved by addition.11. Any non zero number to the zero power equals 1.12. Any number written as a product of a number and a power of10 is written in scientific notation.STEP 2 After you complete Chapter 2• Reread each statement and complete the last column by entering an A or a D.• Did any of your opinions about the statements change from the first column?• For those statements that you mark with a D, use a piece of paper to write anexample of why you disagree.STEP 2A or DChapter 2 SC StudyText, Course 3 51

2NAME DATE PERIODFamily ActivityState Test PracticeFold the page along the dashed line. Work each problem on anotherpiece of paper. Then unfold the page to check your work.1. Use the model below to find the answerto the following multiplication problem.1_3 of 32. The sun is about 92,000,000 miles fromthe Earth.MarsVenusMercuryEarthPlutoSaturnJupiterUranusNeptuneWhat is the product for 1_3A 1_9B 1C 1_3D 2_3of 3?How can this distance be expressed inscientific notation?A 9.2 × 10 6B 9.2 × 10 7C 9.2 × 10 8D 9.2 × 10 9Fold here.Solution1.3 1 3 1 3 11_3 + 1_3 + 1_3 = 3_Solution2. Hint: Scientific notation is used to3 or 1represent very large or very small numbersand is written as the product of a numberand a factor of 10. The decimal point isplaced after the first non-zero digit and theexponent is the number of spaces that thedecimal place is moved to the right (forsmall numbers) or left (for large numbers).In this case, the decimal is moved to theleft seven spaces, or9 2 0 0 0 0 0 0so the resulting scientific notationis 9.2 × 10 7 .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.The answer is B. The answer is B.52 SC StudyText, Course 3 Chapter 2

NAME DATE PERIOD2-2 Explore Through ReadingSCAS 8-2.4Comparing and Ordering Rational NumbersGet Ready for the LessonRead the introduction at the top of page 91 in your textbook. Writeyour answers below.1. Do more or less than half of the students prefer buttered popcorn? Explain howyou know.2. Which category is preferred by more students: caramel or plain? Explain.3. Which category of popcorn is preferred by about one fourth of the class?Explain.4. Using estimation, order the fractions from least to greatest.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Read the Lesson5. Read Example 4 on page 93. Explain how to use a number line to determinewhich of two rational numbers is the lesser number.For Exercises 6 and 7, graph each pair of rational numbers on a numberline. Then identify the lesser number.6. 1_5 , 1_3Remember What You Learned8. Order the numbers 3_7 , 3_5 , 3_8 , 3_47. -4_5 , - 9_10, and3_from least to greatest. Then write11a rule that helps you compare two positive fractions with the samenumerator.Chapter 2 SC StudyText, Course 3 53

NAME DATE PERIOD2-2 Study GuideSCAS 8-2.4Comparing and Ordering Rational NumbersWhen comparing two or more rational numbers, either write the numbers as fractions with the samedenominator or write the numbers as decimals.4_Example 1 Replace with , or = to make7_a true sentence.5 10Write as fractions with the same denominator. The least common denominator is 10.4_5 = _ 4 · 2 or8_5 · 2 107_10 = _ 7 · 1 or7_10 · 1 10Since 8_10 > 7_10 , 4_5 > 7_10 .1_Example 2 Order the set of rational numbers -3.25, -3 , -32_3 5 , and -3.2 − 5 fromleast to greatest.Write -3 1_ and -32_as decimals.3 51_3 = 0. − 3 , so -3 1_3 = -3. − 3 .2_= 0.4, so -32_5 5 = -3.4.Since -3.4 < -3. − 3 < -3.2 − 5 < -3.25, the numbers from least to greatest are-3 2_ , -31_5 3 , -3.2 − 5 , and -3.25.ExercisesReplace each1. 5_ 2_6 34. -2_37_-107. 2.6 2 5_8with or = to make a true sentence.2. 4_ 13_5 155. 3 7_108. 4 1_63 4_53. 1_96. -2 3_71_8-2 4_94.1 − 6 9. -4.5 − 8 4. −− 58Order each set of rational numbers from least to greatest.10. 0.5, 0.1, 1_4 , 2_312. 1_ , -0.7, 0.25, -3_5 514. -2 1_ , -2.28, -2.7, -24_4 511. 2.4, 2 4_ , 2.13, 19_7 1013. 1 2_15. 4 2_9 , 1 2_33 , 4 5_6, 1.45, 1.67, 4.6, 5.3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.54 SC StudyText, Course 3 Chapter 2

NAME DATE PERIOD2-2 Homework PracticeSCAS 8-2.4Replace each1. 3_ 5_5 7Comparing and Ordering Rational Numberswith , or = to make a true sentence.2. 4_ 5_3. 3 2_ 3 1_9 1111 94. 5 7_155 8_175. 0.22_116. 0.255_217. 8 10_278.3 8. 4 8_304.38_9. -135_-1310. -3_8- 7_811. -2_5-6_712. -2_99_-1113. -4.5 -4.55 14. -6.14 -6.15 15. -3.57 -3.5 16. -1.9 -1.9917. Which is least: 3_ , 0.4,4_8 11 , 0.03 5 − , or 5_13 ?18. Which is greatest: 7_−−, 0.778, 0. 78 , 11_ or 0.787?9 13Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Order each set of rational numbers from least to greatest.19. -5.81, -5 3_ , -53_4 5, -5.69 20. -1.01, -1.1, -11_9, -11_1121. Which point on the number line isP Q SRthe graph of 0.875?011342422. STATISTICS If you order a set of numbers from least to greatest, themiddle number is the median. Find the median of 43.7, 41.3, 44.5,42 4_ , and 433_5 4 .1Chapter 2 SC StudyText, Course 3 55

NAME DATE PERIODMini-Project(Use with Lesson 2-2)Comparing and Ordering Rational NumbersSCAS 8-2.4Rational numbers can be compared by using many different methods. Forinstance, you can express them as fractions with like denominators. You can alsoexpress them as decimals and compare the decimals. You can even draw lines torepresent each fraction and compare their lengths.Use a ruler to draw a segment having the length of each fraction.Rewrite the length as a fraction with a denominator of 16. Then writethe fraction as a decimal.Length Segment Fraction Decimal1. 1_2 inch2. 5_16 inch3. 3_4 inch4. 5_8 inch5. 1_4 inch6. Order the fractions from least to 7. How did you order the fractionsgreatest.and why did you choose this method?leastCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.greatest56 SC StudyText, Course 3 Chapter 2

NAME DATE PERIOD2-3 Explore Through ReadingGet Ready for the LessonComplete the Mini Lab at the top of page 96 in your textbook. Writeyour answers below.1. What is the product of 1_and2_5 ?32. Use an area model to find each product.a. 3_4 · 1_2Multiplying Positive and Negative Fractionsb. 2_5 · 2_3c. 1_4 · 3_5d. 2_3 · 4_53. What is the relationship between the numerators of the factors and thenumerator of the product?4. What is the relationship between the denominators of the factors and thedenominator of the product?SCAS 8-2.2Read the Lesson5. What is the greatest common factor of two numbers?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6. How is the greatest common factor used when multiplying fractions?7. How is dimensional analysis defined on page 98 in your textbook?8. How is dimensional analysis used in Example 5 on page 98 in yourtextbook?Remember What You Learned9. If you were to visit Europe, you may need to exchange some of yourmoney for Euros. The exchange rate tells you how many dollars equalshow many Euros. How would you use dimensional analysis to computethe number of Euros you would get from $50?Chapter 2 SC StudyText, Course 3 57

2-3NAME DATE PERIODStudy GuideMultiplying Positive and Negative FractionsSCAS 8-2.2To multiply fractions, multiply the numerators and multiply the denominators.3_ 4_Example 1 Find8 · . Write in simplest form.113_8 · 4_11 = 3_8 · 4_111_2= 3 · 12 · 11= 3_22Divide 8 and 4 by their GCF, 4.Multiply the numerators and denominators.Simplify.To multiply mixed numbers, first rewrite them as improper fractions.Example 2 Find -23 · 3 . Write in simplest form.5-2 1_3 · 3 3_5 = - 7_3 · _ 18-2 1_53 = - 7_3 , 3 3_ 5 = 185= - 7_63 · _ 185Divide 18 and 3 by their GCF, 3.= -7 1· 61 · 5Multiply the numerators and denominators.= -42_5Simplify.= -8 2_5Write the result as a mixed number.ExercisesMultiply. Write in simplest form.1. 2_3 · 3_54. 9_10 · 2_37. 2 2_5 · 1_62. 4_7 · 3_43. - 1_2 · 7_95. 5_8 · 4_(-9) 6. -4_7 · 2_(-3)8. -3 1_3 · 1 1_210. -1 7_8 · (-2 2_5) 11. -1 3_4 · 2 1_59. 3 3_7 · 2 5_812. 2 2_3 · 2 3_7Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.58 SC StudyText, Course 3 Chapter 2

NAME DATE PERIOD2-3 Homework PracticeMultiplying Positive and Negative FractionsFind each product. Write in simplest form.1. 1_4 · 4_52. 6_7 · 1_23. 3_10 · 2_3SCAS 8-2.24. -15_16 · 4_57. 1 1_4 · 1_58_5. (-25) 15_168. 1 1_4 · 1 1_51_6.7_(-8)(-7)9. -2 2_3 · 1_(-4)10. 1_4 · (-4_15) · 5_711. 2 2_5 · 2 1_ · 2 12. 10 · 8.56 ·1_3 2ALGEBRA Evaluate each expression if a = -1_5 , b = 2_3 , c = 7_8, and d = -3_4 .13. bc 14. ab 15. abc 16. abdCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.17. COOKING A recipe calls for 2 1_cups of flour. How much flour would you4need to make 1_ of the recipe?318. FARMING A farmer has 6 1_3_5acres of land for growing crops. If she plants corn on2of the land, how many acres of corn will she have?ALGEBRA Evaluate each expression if e = -1 1_4 , f = 2 2_3, g = -21_, and h = 11_6 5 .19. efh 2 20. e 2 h 2 21. 1_8 f 2 g 22. -2ef (-gh)Chapter 2 SC StudyText, Course 3 59

NAME DATE PERIOD2-3 Problem-Solving PracticeMultiplying Positive and Negative Fractions1. NUTRITION Maria’s favorite granola barhas 230 Calories. The nutrition labelstates that 7_ of the Calories come from8fat. How many Calories in the granolabar come from fat?SCAS 8-2.22. ELECTIONS In the last election, 3_ of the8voters in Afton voted for the incumbentmayor. If 424 people voted in Afton inthe last election, how many voted forthe incumbent mayor?3. HOBBIES Jerry is building a 1_9 scalemodel of a race car. If the tires on theactual car are 33 inches in diameter,what is the diameter of the tires on themodel?4. COOKING Enola’s recipe for cookiescalls for 2 1_ cups of flour. If she wants2to make 3_ of a batch of cookies, how4much flour should she use?5. TRANSPORTATION Hana’s car used 3_4 ofa tank of gas to cross Arizona. The gastank on her car holds 15 1_ gallons. How2many gallons of gas did it take to crossArizona?7. COOKING A recipe for ice cream callsfor 3 1_ cups of heavy cream. If Steve3wants to make 2 1_ times the normal2amount, how much heavy creamshould he use?6. GEOMETRY The area of a rectangle isfound by multiplying its length timesits width. What is the area of arectangle with a length of 2 1_4 inchesand a width of 1 5_9 inches?8. ADVERTISING A jewelry advertisementshows a bracelet at 6 times its actualsize. If the actual length of the braceletis 5 3_ inches, what is the length of the10bracelet in the photograph?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.60 SC StudyText, Course 3 Chapter 2

NAME DATE PERIOD2-4 Explore Through ReadingDividing Positive and Negative FractionsGet Ready for the LessonRead the introduction at the top of page 102 in your textbook.Write your answers below.1. Find the value of 60 ÷ 5.2. Find the value of 60 × 1_5 .3. Compare the values of 60 ÷ 5 and 60 × 1_5 .SCAS 8-2.24. What can you conclude about the relationship between dividing by 5 andmultiplying by 1_5 ?Read the Lesson5. Describe the process for finding the multiplicative inverse of a mixednumber.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.For Exercises 6–9, write the multiplicative inverse of each mixednumber.6. 2 1_57. -1 3_810. Explain how to divide by a fraction.8. 3 4_79. 5 5_911. Look at your answers for Exercises 6 and 10 above. How do you divide anumber by 2 1_5 ?Remember What You Learned12. Look up the word invert in the dictionary. Draw a simple picture and theninvert it. Explain how this helps you remember how to divide fractions.Chapter 2 SC StudyText, Course 3 61

NAME DATE PERIOD2-4 Study GuideSCAS 8-2.2Dividing Positive and Negative FractionsTwo numbers whose product is 1 are multiplicative inverses, or reciprocals, of each other.Example 1 Write the multiplicative inverse of -2 3_4 .-2 3_4 = - 11_411Since -_4 (-Write -2 3_ as an improper fraction.44_11) = 1, the multiplicative inverse of -2 3_4 is - 4_11To divide by a fraction or mixed number, multiply by its multiplicative inverse.Example 2 Find 3_3_8 ÷ 6_7 = 3_8 · 7_6= 3_18 · 7_6= 7_2168 ÷ 6_7. Write in simplest form.Multiply by the multiplicative inverse of 6_ , which is7_7 6 .Divide 6 and 3 by their GCF, 3.Simplify.ExercisesWrite the multiplicative inverse of each number.1. 3_3. 1_5105. 2 3_52. -8_96. -1 2_3Divide. Write in simplest form.9. 1_3 ÷ 1_611. -5_6 ÷ 3_413. 3 1_7 ÷ (-3 2_15. 6_117. -5 2_510. 2_5 ÷ 4_712. 1 1_5 ÷ 2 1_43) 14. -9 ÷ 2÷ (-4) 16. 5 ÷ 21_34_4. -1_68. 7 1_4Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.62 SC StudyText, Course 3 Chapter 2

NAME DATE PERIOD2-4 Homework PracticeDividing Positive and Negative FractionsWrite the multiplicative inverse of each number.1. 4_2. 7_3. -20 4. -5 3_5128SCAS 8-2.2Find each quotient. Write in simplest form.5. 1_5 ÷ 1_46. 2_5 ÷ 5_67. 3_7 ÷ 6_118. 3_10 ÷ 4_59. 3_8÷ 6 10.6_7 ÷ 311. 4_5÷ 10 12.6_11 ÷ 8 13. - 4_5 ÷ 5_614. 5_12 ÷ 3_(-5) 15. -3_10 ÷ 2_(-5) 16. -13_18 ÷ 8_(-9)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.17. 4 1_5 ÷ 1 3_418. 8 1_3 ÷ 3 3_420. OFFICE SUPPLIES A regular paper clip is 1 1_19. -10 1_2 ÷ 2 1_3inches long, and a jumbo paper clip is4inches long. How many times longer is the jumbo paper clip than the regular8paper clip?1 7_21. STORAGE The ceiling in a storage unit is 7 2_in a single stack if each box is 3_4foot tall?ALGEBRA Evaluate each expressin for the given values.7_22. r ÷ s if r = -20and s =7_153feet high. How many boxes may be stacked23. m ÷ n if m = 4_9and n =11_12Chapter 2 SC StudyText, Course 3 63

NAME DATE PERIOD2-4 Problem-Solving PracticeDividing Positive and Negative Fractions1. CONTAINER GARDENING One bag ofpotting soil contains 8 1_ quarts of4soil. How many clay pots can be filledfrom one bag of potting soil if each potholds 3_inches longfor storing CDs. Each CD is 3_8 inchwide. How many CDs will fit on oneshelf?2. MUSIC Doug has a shelf 9 3_44 quart?SCAS 8-2.23. SERVING SIZE A box of cereal contains15 3_ ounces of cereal. If a bowl holds52 2_ ounces of cereal, how many bowls of5cereal are in one box?4. HOME IMPROVEMENT Lori is buildinga path in her backyard using squarepaving stones that are 1 3_ feet on each4side. How many paving stones placedend-to-end are needed to make a paththat is 21 feet long?5. GEOMETRY Given the length of arectangle and its area, you can findthe width by dividing the area bythe length. A rectangle has an areaof 6 2_ square inches and a length of32 1_ inches. What is the width of the2rectangle?7. HOBBIES Dena has a picture frame thatis 13 1_ inches wide. How many pictures2that are 3 3_ inches wide can be placed8beside each other within the frame?6. GEOMETRY Given the length of arectangle and its area, you can findthe width by dividing the area by thelength. A rectangle has an area of 4 5_7square feet and a length of 3 2_3 feet.What is the width of the rectangle?8. YARD WORK Leon is mowing his yard,which is 21 2_ feet wide. His lawn3mower makes a cut that is 1 2_3 feetwide on each pass. How many passeswill Leon need to finish the lawn?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.64 SC StudyText, Course 3 Chapter 2

NAME DATE PERIOD2-7 Explore Through ReadingSolving Equations with Rational NumbersGet Ready for the LessonRead the introduction at the top of page 119 in your textbook.Write your answers below.1. Multiply each side of the equation by 3. Then divide each side by 2. Writethe result.SCAS8-3.2, 8-2.2,8-1.62. Multiply each side of the original equation by the multiplicativeinverse of 2_ . Write the result.33. What was Kenseth’s average life speed in Michigan?4. Which method of solving the equation seems most efficient?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Read the Lesson5. Match the method of solving with the appropriate equation.1.25a = 3.75 a. Subtract 3_5from each side.x + 1.25 = 5.25 b. Multiply each by 5_3 .3_5 m = 7_10c. Add 1.25 to each side.r – 1.25 = 4.5 d. Divide each side by 1.25.3_5 + f = 1_2Explain in words how to solve each equation.6.y_3.2 = 1.17. 3_8 + v = 7_12Remember What You Learnede. Subtract 1.25 from each side.8. The description of a problem often has more information than you need todesign an equation and solve it. Describe the process of writing anequation to solve a problem.Chapter 2 SC StudyText, Course 3 65

NAME DATE PERIOD2-7 Study GuideSCASSolving Equations with Rational Numbers8-3.2, 8-2.2,8-1.6The Addition, Subtraction, Multiplication, and Division Properties of Equality can be used to solveequations with rational numbers.Example 1Solve x - 2.73 = 1.31. Check your solution.x - 2.73 = 1.31x - 2.73 + 2.73 = 1.31 + 2.73x = 4.04Write the equation.Add 2.73 to each side.Simplify.Check x - 2.73 = 1.31 Write the original equation.4.04 - 2.73 1.31 Replace x with 4.04.1.31 = 1.31 ✓ Simplify.Example 2 Solve 4_Check4_5 y = 2_35_4( 4_5 y ) = 5_4 · 2_3y = 5_64_5 y = 2_36) 2_34_5( 5_Exercises5 y = 2_3. Check your solution.Write the equation.Multiply each side by 5_4 .Simplify.2_3 = 2_3 ✓ Simplify.Write the original equation.Replace y with 5_6 .Solve each equation. Check your solution.1. t + 1.32 = 3.48 2. b - 4.22 = 7.08 3. -8.07 = r - 4.484. h + 4_9 = 7_95. -5_8 = x - 1_46. -2_3 + f = 3_57. 3.2c = 9.6 8. -5.04 = 1.26d 9. 3_5 x = 610. -2_3 = 3_4 t 11. w_= 4.2 12. 13_2.5 4 r = 3 5_8Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.66 SC StudyText, Course 3 Chapter 2

NAME DATE PERIOD2-7 Homework PracticeSCASSolving Equations with Rational NumbersSolve each equation. Check your solution.1. m + 0.88 = 1.64 2. t - 2.89 = 9.15 3. -3_5 = d - 5_68-3.2, 8-2.2,8-1.64. -7_16 = b + 1_45. h - (-6.3) = 8.12 6. -2.5 = n - (-5.37)7. -5_8 k = 25 8. - 3_7v = -27 9. -2.94 = -0.42a10. -8.4 = 1.4y 11.f___2.4 = -7.5 12. p-6.25 = -3.6_1313. 2.5x = -1614. -4.5w = -8 1_315. 8 2_3 = -1. − 3 gCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.16. MONEY The currency in Switzerland is called a franc. On a certain day,one U.S. dollar equaled 1 1_ Swiss francs. Write and solve a multiplication4equation to find the number of U.S. dollars that would equal 15 Swissfrancs.FOOTBALL For Exercise 18, refer to the table.17. Let s equal the number of additional seatsthat the Pittsburgh Steelers’ stadium needsto equal the number of seats in Kansas CityChiefs’ stadium. Write and solve an additionequation to determine the number of seatsthat the Steelers’ stadium needs to equalthe number of seats in the Chiefs’ stadium.NFL StadiumsSeating CapacityStadiumSeats(thousands)Dallas Cowboys 65.7Kansas City Chiefs 79.4Pittsburgh Steelers 64.5San Diego Chargers 71.3Chapter 2 SC StudyText, Course 3 67

NAME DATE PERIOD2-7 Problem-Solving PracticeSolving Equations with Rational NumbersSCAS8-3.2, 8-2.2,8-1.61. NATURE The height of a certain tree is12.85 meters. The length l of its longestbranch can be found using the equationl + 3.23 = 12.85. Solve the equation.2. SHOPPING Kristen went shopping andspent $84.63 on books and CDs. Theequation 84.63 = b + 43.22 can beused to determine the amount b thatshe spent on books. Solve the equation.3. ENERGY PRICES Suppose regularunleaded gasoline costs $2.40 pergallon. The price p of premium gasolinecan be found using the equationp_= 2.40. What is the price of the1.2premium gasoline?4. DRIVING TIME Sam went for a drivelast Sunday. His average speed was 46miles per hour and he drove 115 miles.The equation 115 = 46t can be used tofind the time t that he spent driving.Solve the equation.5. AUTOMOBILES The bed of Julian’struck is 2 1_ yards long. The length l of3the truck can be found by solving the. What is the3length of the truck?equation l - 2 4_9 = 2 1_7. SPEED Ella rode the bus to work today.The distance she traveled was 4 1_4 milesand the ride took 1_ of an hour. The3equation 1_3 s = 4 1_ can be used to find4the average speed s of the bus. Whatwas the average speed of the bus?6. SPORTS Leo and Ted both ran in a race.Leo’s time was 9 minutes, which was 3_4of Ted’s time. Using t for Ted’s time,write a multiplication equation torepresent the situation.8. GEOMETRY A rectangle has area6 2_ square inches and length 21_3 2 inches.The equation 6 2_3 = 2 1_ w can be used to2find the width w of the rectangle. Solvethe equation.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.68 SC StudyText, Course 3 Chapter 2

2-8NAME DATE PERIODStudy GuideSCAS 8-1.1Problem-Solving Investigation: Look for a PatternYou may need to look for a pattern to solve a problem.Understand Determine what information is given in the problem and what you need to fi nd.PlanSelect a strategy including a possible estimate.Solve Solve the problem by carrying out your plan.Check Examine your answer to see if it seems reasonable.ExampleCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Three people board the subway train at the first stop. Five people board the train at thesecond stop. Seven people board the train at the third stop. If this pattern continues and noone gets off the train, how many people are on the subway train when it reaches the seventhand final stop?UnderstandPlanSolveYou know that 3 people boarded the subway train at the first stop. At eachsubsequent stop, 2 more people board the train than at the previous stop.Look for a pattern and use the pattern to find how many people boarded thetrain in all.Complete the information for the first, second, and third stops. Continue thepattern to solve the problem.First Stop Second Stop Third Stop Fourth Stop Fifth Stop Sixth Stop Seventh Stop3 5 7 9 11 13 153 peopleonthe trainCheckExercises3 + 5 = 8people onthe train8 + 7 = 15people onthe train15 + 9 = 24people onthe train24 + 11 = 35people onthe train24 + 11 = 35people onthe train48 + 15 = 63people onthe trainAt the seventh and final stop there were 63 people on the subway train.Check your pattern to make sure the answer is correct.Look for a pattern. Then use the pattern to solve each problem.1. COOKING A muffin recipe calls for 2 1_ 2 cups of flour for every 2_ 3cups of flour should be used when 4 cups of sugar are used?cup of sugar. How many2. FUNDRAISER There were 256 people at a fundraiser. When the event was over, half of thepeople who remained left every 5 minutes. How long after the event ended did the lastperson leave?Chapter 2 SC StudyText, Course 3 69

2-8NAME DATE PERIODSkills PracticeProblem-Solving Investigation: Look for a PatternLook for a pattern. Then use the pattern to solve each problem.SCAS 8-1.11. YARN A knitting shop is having a huge yarn sale. One skein sells for $1.00, 2 skeins sellfor $1.50, and 3 skeins sell for $2.00. If this pattern continues, how many skeins of yarncan you buy for $5.00?2. BIOLOGY Biologists place sensors in 8 concentric circles totrack the movement of grizzly bears throughout YellowstoneNational Park. Four sensors are placed in the inner circle.Eight sensors are placed in the next circle. Sixteen sensorsare placed in the third circle, and so on. If the patterncontinues, how many sensors are needed in all?3. HONOR STUDENTS A local high school displays pictures of the honor students from eachschool year on the office wall. The top row has 9 pictures displayed. The next 3 rowshave 7, 10, and 8 pictures displayed. The pattern continues to the bottom row, whichhas 14 pictures in it. How many rows of pictures are there on the office wall?4. CHEERLEADING The football cheerleaders will arrange themselves in rows to form apattern on the football field at halftime. In the first five rows there are 12, 10, 11, 9,and 10 girls in each row. They will form a total of twelve rows. If the pattern continues,how many girls will be in the back row?5. GEOMETRY Find the perimeters of the next two figures in the pattern. The length ofeach side of each small square is 3 feet.6. HOT TUBS A hot tub holds 630 gallons of water when it is full. A hose fills the tub at arate of 6 gallons every five minutes. How long will it take to fill the hot tub?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.70 SC StudyText, Course 3 Chapter 2

NAME DATE PERIOD2-8 Homework PracticeProblem-Solving Investigation: Look for a PatternMixed Problem SolvingFor Exercises 1 and 2, look for apattern. Then use the pattern to solvethe problem.1. GEOMETRY Draw the next two angles inthe pattern.a.10b.20SCAS 8-1.14. READING Ling read 175 pages by 1:00P.M., 210 pages by 2:00 P.M., and 245pages by 3:00 P.M. If she continuesreading at this rate, how many pageswill Ling have read by 4:00 P.M.?c.d.30 405. MOVIES The land area of Alaska isabout 570 thousand square miles.The land area of Washington, D.C.,is about 0.06 thousand square miles.How many times larger is Alaska thanWashington, D.C.?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2. ANALYZE TABLES A falling objectcontinues to fall faster until it hitsthe ground. How far will an object fallduring the fifth second?Time Period1st second2nd second3rd second4th secondDistance Fallen16 feet48 feet80 feet112 feetUse any strategy to solve Exercises 3–6.Some strategies are shown below.Problem-Solving Strategies• Look for a pattern.• Work backward.3. YARD WORK Denzel can mow 1_ of his8yard every 7 minutes. If he has 40minutes to mow 3_ of the yard, will he4have enough time?6. U.S. PRESIDENTS President Clintonserved 5 two-year terms as governorof Arkansas and 2 four-year terms asPresident of the United States. Howmany total years did he serve in thesetwo government offices?Chapter 2 SC StudyText, Course 3 71

NAME DATE PERIOD2-8 Problem-Solving PracticeProblem-Solving Investigation: Look for a PatternLook for a pattern. Then use the pattern to solve each problem.ENTERTAINMENT For Exercises 1 and 2, use the informationat the right, which shows the ticket prices at a skating rink.SCAS 8-1.1Number ofTotal CostPeople inper GroupGroup1 $1.002 $2.003 $2.904 $3.705 $4.401. Describe the pattern used to calculatethe cost for a group after 2 people.2. If the pattern continues, what wouldthe cost be for a group of 8 skaters?3. SAVINGS Jordan saved $1 the firstweek, $2 the second week, $4 the thirdweek, and $8 the fourth week. If thispattern continues, how much will shesave the eighth week?5. GARDENING Marial was plantingdaisies in her garden. She planted 2white daisies and 5 yellow daisies inthe first row, 4 white daisies and 6yellow daisies in the second row, and6 white daisies and 7 yellow daisiesin the third row. If she continues thepattern, how many white and yellowdaisies will she plant in the sixthrow?4. AGRICULTURE In a vegetable garden,the second row is 8 inches from thefirst row, the third row is 10 inchesfrom the second row, the fourth row is14 inches from the third row, and thefifth row is 20 inches from the fourthrow. If the pattern continues, howfar will the eighth row be from theseventh row?6. BIOLOGY A newborn seal pup weighs4 pounds the first week, 8 poundsthe second week, 16 pounds the thirdweek, and 32 pounds the fourth week.If this growth pattern continues, howmany weeks old will the seal pup bebefore it weighs over 100 pounds?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.72 SC StudyText, Course 3 Chapter 2

NAME DATE PERIOD2-9 Explore Through ReadingPowers and ExponentsGet Ready for the LessonRead the introduction at the top of page 126 in your textbook. Writeyour answers below.1. How many 2s are multiplied to find his savings at Week 4? Week 5?2. How much money will Hector save in Week 8?3. When will he have enough to buy a pair of shoes for $80?SCAS 8-1.6Read the Lesson4. Define the terms base, exponent, and power.For Exercises 5–7, identify the base, exponent, and power in eachexpression.5. 5 4Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6. 7 -27. x 88. Explain in words what 5 4 means.Rewrite each expression using multiplication instead of an exponent.9. 5 4 10. 9 5 11. c 8Evaluate each expression.12. 5 4 13. 9 5 14. 6 3 15. 2 8Remember What You Learned16. Notice that 4 -3 = 1_. A power with a negative exponent is not negative.34Write a true sentence using the terms negative exponent, power, positive, andrational.Chapter 2 SC StudyText, Course 3 73

NAME DATE PERIOD2-9 Study GuidePowers and ExponentsSCAS 8-1.6Expressions containing repeated factors can be written using exponents.Example 1 Write 7 · 7 · 7 · 7 · 7 using exponents.Since 7 is used as a factor 5 times, 7 · 7 · 7 · 7 · 7 = 7 5Example 2Write p · p · p · q · q using exponents.Since p is used as a factor 3 times and q is used as a factor 2 times, p · p · p · q · q = p 3 · q 2 .Any nonzero number to the zero power is 1. Any nonzero number to the negative n power is themultiplicativeinverse of nth power.Example 3 Evaluate 6 2 . Example 4 Evaluate 5 -3 .6 2 = 6 · 6 Defi nition of exponents 5 -3 = 1_Exercises= 36 Simplify. =5 31_125Defi nition of negative exponentsSimplify.Write each expression using exponents.1. 8 · 8 · 8 · 8 · 8 2. 4 · 4 · 4 · 43. a · a · a · a · a · a 4. g · g · g · g · g · g · g5. 5 · 5 · 9 · 9 · 5 · 9 · 5 · 5 6. s · w · w · s · s · sEvaluate each expression.7. 4 2 8. 5 39. 13 2 10. 2 3 · 3 211. 8 -2 12. 2 4 · 5 2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.13. 3 -4 14. 3 4 · 7 274 SC StudyText, Course 3 Chapter 2

NAME DATE PERIOD2-9 Homework PracticePowers and ExponentsWrite each expression using exponents.1. 3 · 3 · m 2. 2 · d · 5 · d · d · 5SCAS 8-1.63. p · 9 · 3 · q · p · 9 4. g · 7 · 7 g · h · 7 · h5. 2 · 5 · r · 7 · s · r · 5 · r · 7 · r · s 6. x · 8 · y · x · 5 · x · 5 · y · 8 · y · y · 5Evaluate each expression.7. 2 4 8. 5 3 9. 2 2 · 6 2 10. 2 3 · 5 211. 3 -4 12. 8 -3 13. 9 -2 14. 5 -315. 7 · 2 2 · 5 2 16. 3 2 · 6 · 10 2 17. 3 -2 · 2 -3 18. 7 · 3 3 · 5 -4Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ALGEBRA Evaluate each expression.19. r 3 · s, if r = 5 and s = 4 20. m 2 · n 3 , if m = 6 and n = 221. f 4 · g 5 , if f = 3 and g = 1 22. x 5 · y, if x = 2 and y = 823. Complete the following pattern.5 4 = 625, 5 3 = 125, 5 2 = 25, 5 1 = 5, 5 0 = ? , 5 -1 = ? , 5 -2 = ?, 5 -3 = ?24. MONEY Suppose $100 is deposited into an account and the amount doublesevery 8 years. How much will be in the account after 40 years?25. EPIDEMICS At the beginning of an epidemic, 50 people are sick. If thenumber of sick people triples every other day, how many people will besick at the end of 2 weeks?Chapter 2 SC StudyText, Course 3 75

2-9NAME DATE PERIODProblem-Solving PracticePowers and ExponentsSCAS 8-1.61. SPORTS In the first round of a localtennis tournament there are 2 5matches. Find the number of matches.2. GEOMETRY The volume of a box can befound by multiplying the length, width,and height of the box. If the length,width, and height of the box are all 5inches, write the volume of the boxusing an exponent.3. MONEY An apartment complex has3 buildings. Each building has 3apartments. There are 3 people livingin each apartment, and each personpays 3 dollars per month for poolmaintenance. The expression 3 4 denotesthe amount paid each month for poolmaintenance. Find this amount.4. ACTIVISM A petition drive is beingheld in 10 cities. In each city, 10 peoplehave collected 10 signatures each. Theexpression 10 3 denotes the number ofsignatures that have been collectedaltogether. Find this number.5. MEASUREMENT There are 10 6millimeters in a kilometer. Write thenumber of millimeters in a kilometer.7. BANKING Suppose that a dollar placedinto an account triples every 12 years.How much will be in the account after60 years?6. NATURE Suppose a certain forest firedoubles in size every 12 hours. If theinitial size of the fire was 1 acre, howmany acres will the fire cover in2 days?8. BIOLOGY Suppose a bacterium splitsinto two bacteria every 15 minutes.How many bacteria will there be in3 hours?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.76 SC StudyText, Course 3 Chapter 2

NameChapter 2 TestMastering the SC StandardsDateCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.1 Which statement below is true?3_ A < 0.60 < 6%5 3_ B = 0.06 = 6%53_ C > 0.60 > 60%5 3_ D5 = 0.60 = 60% 8-2.42 If 5 -1 = 1_5 and 5 -2 = 1_25of 5 -4 ?A1_625B 1_125C1_75D 625, what is the value3 Which symbol will make the numbersentence true when placed in the blank?A -4. −− 58 -4.5 − 88-1.68-2.44 Kuri has to multiply - 3_ 7 by 4_ 5to finish amath problem on her homework sheet.What is the correct answer?A7_12B7_35C12-_35D13-_355 What is the value of y in the equation-7y = 49?A y = -7B y = -6C y = 6D y = 76 Which expression could be used to findhow many times - 1_6A7_8 ÷ - 1_6B7_8 + 1_6C7_8 × - 1_7_6D8 - 1_6goes into7_8 ?8-2.28-3.28-2.2Chapter 2 SC StudyText, Course 3 77

NameDateChapter 2 Test (continued)Mastering the SC Standards7 Which number below is not a rationalnumber?A 0.0056B 0. − 6C 2_3D √ 210 What is the solution to 2 3 × 3 2 ?A 5 5B 6 6C 36D 728-1.68 Robert correctly solves the problem-_912 ÷ 2_ . What is his answer?3A -1_2B -9_8C 9_4D 1_29 What is the value of x in the equation-x + 6 = 18?A x = -13B x = -12C x = 12D x = 138-2.48-2.28-3.211 Ella and her friend Sonia hiked twodifferent trails in Paris Mountain StatePark. Ella hiked 4_ of her trail. Sonia5hiked 2_ of her trail. Which inequality is3equivalent to comparing 4_ and2_5 3 ?ABCD4_30 > 2_3010_15 = 2_310_15 < 12_154_5 = 12_158-2.412 Dimitri is building a bookshelf. On theinstructions, he learns that each shelf of hisbookshelf can hold 40 pounds but the topof his bookshelf can hold no more than20 pounds. Which of the followinginequalities represents the amount ofweight the top can hold?A w < 40B w ≤ 40C w > 40D w ≥ 408-3.2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.78 SC StudyText, Course 3 Chapter 2

3NAME DATE PERIODAnticipation GuideReal Numbers and the Pythagorean TheoremSTEP 1 Before you begin Chapter 3• Read each statement.• Decide whether you Agree (A) or Disagree (D) with the statement.• Write A or D in the first column OR if you are not sure whether you agree or disagree,write NS (Not Sure).STEP 1A, D, or NS1. -4 is a square root of 16.Statement2. To solve an equation when the variable is squared, take thesquare root of each side of the equation.3. The best whole number estimate for the square root of 47is 6.4. A Venn Diagram can contain at most two circles.5. The set of real numbers contains both rational numbers andirrational numbers.6. The set of irrational numbers is the set of all square roots.STEP 2A or DCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.7. The square of the length of the longest side of a triangleequals the sum of the squares of the lengths of the legs istrue only in right triangles.8. 4, 9, 16 is an example of a Pythagorean Triple.9. In the coordinate plane, all ordered pairs in Quadrants IIIand IV have a negative x-coordinates.10. The Pythagorean Theorem can be used to find the distancebetween two points on the coordinate plane.STEP 2 After you complete Chapter 3• Reread each statement and complete the last column by entering an A or a D.• Did any of your opinions about the statements change from the first column?• For those statements that you mark with a D, use a piece of paper to write anexample of why you disagree.Chapter 3 SC StudyText, Course 3 79

NAME DATE PERIOD3Family ActivityState Test PracticeFold the page along the dashed line. Work each problem on anotherpiece of paper. Then unfold the page to check your work.1. Use the array shown below to helpanswer the question.2. Gerri is attempting to install a newwindow for a second floor room. She is notsure how far off the ground the windowis, but she does know that the ladder is20 feet long. She also knows that she isstanding 10 feet from the house.window20 ftWhat is the square root of 121?A 12B 9C 13D 11Fold here.Solution1. The array shows 121 dots in a squarewith 11 rows of 11 dots. The numberof dots in each row shows the squareroot of 121. Since there are 11 dots ineach row, the square root is 11.10 ftWhich equation will allow you to find howfar the window is from the ground (h)?A 20 - 10 = hB 20 2 - 10 = h 2C 20 2 - 10 2 = h 2D h 2 + 10 2 = 20Solution2. Hint: The Pythagorean Theorem canhelp you find the answer to questions ofdistance in cases where a right triangle isformed. The Pythagorean Theorem statesthat the sum of the squares of the legs of aright triangle is equal to the square of thehypotenuse ( a 2 + b 2 = c 2 ). You can usethe rules of mathematics to change the formof this to an equation involving subtractionrather than addition.The ladder, ground, and wall form aright triangle. The ladder represents thehypotenuse or the c value. Let the grounddistance be the b value, and use h torepresent the height, which is the a value.a 2 + b 2 = c 2 becomes h 2 + 10 2 = 20 2If you subtract 10 2 from each side, theequation becomes h 2 = 20 2 - 10 2 . This isthe same as the equation in Choice C.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.The answer is D. The answer is C.80 SC StudyText, Course 3 Chapter 3

NAME DATE PERIOD3-2 Explore Through ReadingEstimating Square RootsGet Ready for the LessonComplete the Mini Lab at the top of page 148 in your textbook.Write your answers below.SCAS1. Place your square on the number line. Between what two consecutive wholenumbers is √ 8 , the side length of the square, located?8-2.6, 8-2.3,8-1.72. Between what two perfect squares is 8 located?3. Estimate the length of a side of the square. Verify your estimate by usinga calculator to compute the value √ 8 .Use grid paper to determine between which two consecutive wholenumbers each value is located.4. √ 23 5. √ 526. √ 27 7. √ 18Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Read the Lesson8. Explain how you can estimate the square root of a number if you knowperfect squares greater than and less than the number.For Exercises 9–12, estimate to the nearest whole number.9. √ 33 10. √ 7111. √ 114 12. √ 21113. Read Example 3 on page 149 of your textbook. What is a “goldenrectangle”?Remember What You Learned14. Draw a triangle and label its sides. (Make sure your triangle is a realtriangle. For example, sides of lengths 2, 2 and 8 do not make a triangle.)Trade triangles with a partner and estimate the area of your trianglesusing Heron’s Formula.Chapter 3 SC StudyText, Course 3 81

3-2NAME DATE PERIODStudy GuideEstimating Square RootsSCAS8-2.6, 8-2.3,8-1.7Most numbers are not perfect squares. You can estimate square roots for these numbers.Example 1Estimate √ 204 to the nearest whole number.• The first perfect square less than 204 is 14.• The first perfect square greater than 204 is 15.196 < 204 < 225 Write an inequality.14 2 < 204 < 15 2 196 = 14 2 and 225 = 15 214 < √ 204 < 15 Take the square root of each number.So, √ 204 is between 14 and 15. Since 204 is closer to 196 than 225, the bestwhole number estimate for √ 204 is 14.Example 2Estimate √ 79.3 to the nearest whole number.• The first perfect square less than 79.3 is 64.• The first perfect square greater than 79.3 is 81.64 < 79.3 < 81 Write an inequality.8 2 < 79.3 < 9 2 64 = 8 2 and 81 = 9 28 < √ 79.3 < 9 Take the square root of each number.So, √ 79.3 is between 8 and 9. Since 79.3 is closer to 81 than 64, the best wholenumber estimate for √ 79.3 is 9.ExercisesEstimate to the nearest whole number.1. √ 8 2. √ 37 3. √ 144. √ 26 5. √ 62 6. √ 487. √ 103 8. √ 141 9. √ 14.3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.10. √ 51.2 11. √ 82.7 12. √ 175.282 SC StudyText, Course 3 Chapter 3

NAME DATE PERIOD3-2 Homework PracticeEstimating Square RootsEstimate to the nearest whole number.SCAS1. √ 38 2. √ 53 3. √ 99 4. √ 2278-2.6, 8-2.3,8-1.75. √ 8.5 6. √ 35.1 7. √ 67.3 8. √ 103.69. √ 86.4 10. √ 45.2 11. √ 57 2_12. √ 27 3_8Order from least to greatest.13. 8, 10, √ 61 , √ 73 14. √ 45 , 9, 6, √ 63 15. √ 50 , 7, √ 44 , 5Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ALGEBRA Estimate the solution of each equation to the nearest integer.16. d 2 = 61 17. z 2 = 85 18. r 2 = 3.719. GEOMETRY The radius of a cylinder with volume V and height 10 centimeters isapproximately √ V_ . If a can that is 10 centimeters tall has a volume of 900 cubic30centimeters, estimate its radius.20. TRAVEL The formula s = √ 18d can be used to find the speed s of a car in miles perhour when the car needs d feet to come to a complete stop after slamming on thebrakes. If it took a car 12 feet to come to a complete stop after slamming on the brakes,estimate the speed of the car.GEOMETRY The formula for the area of a square is A = s 2 , where s isthe length of a side. Estimate the length of a side for each square.21. 22.Area 40 squareinchesArea 97 squarefeetChapter 3 SC StudyText, Course 3 83

NAME DATE PERIOD3-2 Problem-Solving PracticeEstimating Square RootsSCAS8-2.6, 8-2.3,8-1.71. GEOMETRY If the area of a square is29 square inches, estimate the lengthof each side of the square to the nearestwhole number.2. DECORATING Miki has a square rugin her living room that has an area of19 square yards. Estimate the lengthof a side of the rug to the nearestwhole number.3. GARDENING Ruby is planning to put asquare garden with an area of200 square feet in her back yard.Estimate the length of each sideof the garden to the nearest wholenumber.4. ALGEBRA Estimate the solution ofc 2 = 40 to the nearest integer.5. ALGEBRA Estimate the solution ofx 2 = 138.2 to the nearest integer.7. GEOMETRY The radius r of a certaincircle is given by r = √ 71 . Estimate theradius of the circle to the nearest foot.6. ARITHMETIC The geometric meanof two numbers a and b can be foundby evaluating √ a · b . Estimate thegeometric mean of 5 and 10 to thenearest whole number.8. GEOMETRY In a triangle whose baseand height are equal, the base b isgiven by the formula b = √ 2A , whereA is the area of the triangle. Estimateto the nearest whole number the baseof this triangle if the area is 17 squaremeters.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.84 SC StudyText, Course 3 Chapter 3

3ANAME DATE PERIODStudy GuideApproximating Cube RootsSCAS 8-2.6A square root is just one of many kinds of roots. Another kind of root is the cube root. Just as thenumber 9 is a perfect square because it is a square of a whole number, the number 27 is a perfectcube because it is the cube of a whole number.Square RootCube RootThe square root of 9 is 3 The cube root of 27 is 3becausebecause3 × 3 = 9. 3 × 3 × 3 = 27.In symbols, we can write:In symbols, we can write:√ 9 = 3.3√ 27 = 3.Most numbers are not cubes. You can estimate the cube roots for these numbers.Example 1Estimate 3 √ 140 to the nearest whole number.• The first cube less than 140 is 125.• The first cube greater than 140 is 216.125 < 140 < 216 Write an inequality.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5 3 < 140 < 6 3 125 = 5 3 and 216 = 6 35 < 3 √ 140 < 6 Take the cube root of each number.So, √ 3 140 is between 5 and 6. Since 140 is closer to 125 than 216, the best wholenumber estimate for √ 3 140 is 5.Example 2Estimate 3 √ 58.3 to the nearest whole number.• The first cube less than 58.3 is 27.• The first cube greater than 58 is 64.27 < 58.3 < 64 Write an inequality.3 3 < 58.3 < 4 3 27 = 3 3 and 64 = 4 33 < √ 3 58.3 < 4 Take the cube root of each number.So, √ 3 58.3 is between 3 and 4. Since 58.3 is closer to 64 than 27, the best wholenumber estimate for √ 3 58.3 is 4.ExercisesEstimate to the nearest whole number.1.3√ 10 2.3√ 350 3.3√ 214.3√ 289 5.3√ 800 6.3√ 555Chapter 3 SC StudyText, Course 3 85

NAME DATE PERIOD3A Skills PracticeSCAS 8-2.6Approximating Cube RootsEstimate to the nearest whole number.1. √ 3 705 2. √ 3 1200 3. √ 3 28844. √ 3 69 5. √ 3 34 6. √ 3 1927. √ 3 356 8. √ 3 97 9. √ 3 159310. √ 3 4000 11. √ 3 3 12. √ 3 2313. √ 3 56 14. √ 3 2081 15. √ 3 16916. √ 3 227 17. √ 3 3025 18. √ 3 65519. √ 3 788 20. √ 3 1567 21. √ 3 45Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.86 SC StudyText, Course 3 Chapter 3

NAME DATE PERIOD3A Homework PracticeSCAS 8-2.6Approximating Cube RootsEstimate to the nearest whole number.1. √ 3 800 2. √ 3 1776 3. √ 3 77 4. √ 3 95. √ 3 436 6. √ 3 24 7. √ 3 1697 8. √ 3 4559. √ 3 604 10. √ 3 31 11. √ 3 907 12. √ 3 239Order from least to greatest.13. 3 √ 26 , 3, 4, 3 √ 52 14. 7, 8, 3 √ 498 , 3 √ 515 15. 11, 12, 3 √ 1332 , 3 √ 1468Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ALGEBRA Estimate the solution of each equation to the nearest integer.16. a 3 = 130 17. x 3 = 333 18. z 3 = 500GEOMETRY The formula for the volume of a square is A = s 3 , where s isthe length of a side. Estimate the length of a side for each cube.19. 20.Volume = 140 cubic inchesVolume = 1725 cubic inchesChapter 3 SC StudyText, Course 3 87

NAME DATE PERIOD3A Problem-Solving PracticeSCAS 8-2.6Approximating Cube Roots1. SPHERES The formula for the volumeof a sphere is V = 4_3 π r 3 . Suppose asphere has a volume of 258 cm 3 . If yourearrange the formula so that3_4 · V_π = r 3 , what is the approximatevalue of r? Use 3.14 for π.2. BUILDING Jackson is building a box tohold his sports equipment. He wantsthe volume of his box to be 102 cubicfeet. What is the approximate lengthof one side of the box?3. NUMBER THEORY √ 3 -1 = -1 because(-1) (-1) (-1) = -1. Based on this,explain how to find √ 3 -27.4. Look at the list below to answer thequestion.3√ 103√ 10,0003√ 1003√ 1,0003√ 100,0003√ 1,000,000a. Which of the cube roots above is aninteger?b. Explain how you can determine thisby looking.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.88 SC StudyText, Course 3 Chapter 3

NAME DATE PERIOD3-3 Study GuideSCAS 8-1.8Problem-Solving Investigation: Use a Venn DiagramYou may need to use a Venn diagram to solve some problems.Understand • Determine what information is given in the problem and what you need to fi nd.Plan • Select a strategy including a possible estimate.Solve • Solve the problem by carrying out your plan.Check • Examine your answer to see if it seems reasonable.ExampleCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Of the 25 skiers on the ski team, 13 signed up to race in the Slalom race, and8 signed up for the Giant Slalom race. Six skiers signed up to ski in both theSlalom and the Giant Slalom races. How many skiers did not sign up for anyraces?UnderstandPlanSolveCheckExerciseYou know how many skiers signed up for each race and howmany signed up for both races. You need to organize theinformation.You can use a Venn diagram to organize the information.Draw two overlapping circles to represent the two differentraces. Place a 6 in the section that is a part of both circles. Usesubtraction to determine the number for each other section.only the Slalom race: 13 - 6 = 7only the Giant Slalom race: 8 - 6 = 2neither the Slalom or the Giant Slalom race:25 - 7 - 2 - 6 = 10There were 10 skiers who did not sign up foreither race.Check each circle to see if the appropriate number of students is represented.Use a Venn diagram to solve the problem.SPORTS The athletic club took a survey to find out whatsports students might participate in next fall. Of the80 students surveyed, 42 wanted to play football,37 wanted to play soccer, and 15 wanted to play bothfootball and soccer. How many students did not wantto play either sport in the fall?Ski Races10Slalom7 6GiantSlalom2Chapter 3 SC StudyText, Course 3 89

3-3NAME DATE PERIODSkills PracticeProblem-Solving Investigation: Use a Venn DiagramUse a Venn diagram to solve each problem.1. PHONE SERVICE Of the 5,750 residents of Homer,Alaska, 2,330 pay for landline phone service and4,180 pay for cell phone service. One thousand sevenhundred fifty pay for both landline and cell phoneservice. How many residents of Homer do not payfor any type of phone service?SCAS 8-1.82. BIOLOGY Of the 2,890 ducks living in a particularwetland area, scientists find that 1,260 havedeformed beaks, while 1,320 have deformed feet. Sixhundred ninety of the birds have both deformed feetand beaks. How many of the ducks living in thewetland area have no deformities?3. FLU SYMPTOMS The local health agency treated890 people during the flu season. Three hundredfifty of the patients had flu symptoms, 530 had coldsymptoms, and 140 had both cold and flu symptoms.How many of the patients treated by the health agencyhad no cold or flu symptoms?4. HOLIDAY DECORATIONS During the holiday season,13 homes on a certain street displayed lights and8 displayed lawn ornaments. Five of the homesdisplayed both lights and lawn ornaments. If thereare 32 homes on the street, how many had nodecorations at all?5. LUNCHTIME At the local high school, 240 studentsreported they have eaten the cafeteria’s hot lunch,135 said they have eaten the cold lunch, and 82 saidthey have eaten both the hot and cold lunch. If thereare 418 students in the school, how many bringlunch from home?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.90 SC StudyText, Course 3 Chapter 3

NAME DATE PERIOD3-3Homework PracticeSCAS 8-1.8Problem-Solving Investigation: Use a Venn DiagramMixed Problem SolvingUse a Venn diagram to solve Exercises 1and 2.1. SPORTS Of the 25 baseball playerson the Baltimore Orioles 2005 roster,17 threw right handed, 12 were over30 years old, and 9 both threw righthanded and were over 30 years old.How many players on the team neitherthrew right handed nor were over30 years old?4. GEOGRAPHY Of the 50 U.S. states,30 states border a major body of waterand 14 states border a foreign country.Seven states border both a major bodyof water and a foreign country. Howmany states border on just a majorbody of water and how many border onjust a foreign country?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2. GRADES The principal noticed that45 students earned As in English, 49students earned As in math, and 53students earned As in science. Of thosewho earned As in exactly two of thesubjects, 8 earned As in English andmath, 12 earned As in English andscience, and 18 earned As in math andscience. Seventeen earned As in allthree subjects. How many earned As inEnglish only?Use any strategy to solve Exercises3–6. Some strategies are shown below.Problem-Solving Strategies• Look for a pattern.• Use a Venn diagram.• Guess and check.3. NUMBERS What are the next twonumbers in the pattern?486, 162, 54, 18, ___, ___5. LANDSCAPING Three differentlandscaping companies treat lawns forweeds. Company A charges $35 pertreatment and requires 3 treatmentsto get rid of weeds. Company B charges$30 per treatment and requires4 treatments. Company C charges$50 per treatment and requires onlytwo treatments to eliminate weeds.If you want to use the companythat charges the least, whichcompany should youchoose?6. RECEIVING Marc unloaded 7,200 bottlesof water from delivery trucks today. Ifeach truck contained 50 cases and eachcase contained 24 bottles of water, howmany trucks did he unload?Chapter 3 SC StudyText, Course 3 91

NAME DATE PERIOD3-3Problem-Solving PracticeSCAS 8-1.8Problem-Solving Investigation: Use a Venn DiagramUse a Venn diagram to solve each problem.NATIONAL PARKS For Exercises 1 and 2, use the information in the box. Itshows the number of people who visited two National Parks in one year.Number of YearlyNational ParkPasses SoldPass Holders WhoVisited YellowstoneNational ParkPass Holders WhoVisited YosemiteNational ParkPass HoldersWho VisitedBoth Parks4,250,000 1,420,000 2,560,000 770,0001. How many yearly pass holders visitedONLY Yellowstone Park?2. How many yearly pass holders didnot visit either Yosemite Park orYellowstone Park?3. PIZZA At a skating party, 10 skaterssaid they like pepperoni on theirpizza, 12 said they like sausage. Sevenskaters said they like both, and therest like plain cheese. If there were20 skaters having pizza, how manylike plain cheese?5. BOOKS Of the 420 people who visitedthe library, 140 people checked outa nonfiction book, 270 checked out afiction book. Ninety-five of the visitorschecked out both fiction and nonfiction.How many visitors did not check out abook?4. FIELD TRIP Of the 24 students on afieldtrip to the local ski hill, 13 ski and11 snowboard. Four of the students skiand snowboard. How many students donot ski or snowboard?6. SIBLINGS Of the 18 girls on a soccerteam, 10 have a sister, 14 have abrother, and 8 have both a brother anda sister. How many of the girls do nothave a brother or a sister?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.92 SC StudyText, Course 3 Chapter 3

NAME DATE PERIOD3-4Explore Through ReadingThe Real Number SystemGet Ready for the LessonRead the introduction at the top of page 155 in your textbook.Write your answers below.1. The distance from the pitching mound to home plate is 60.5 feet.Is 60.5 a rational number? Explain.SCAS 8-2.3, 8-2.42. The distance from first base to second base is 90 feet. Is 90 a rationalnumber? Explain.3. The distance from home plate to second base is √ 16,200 feet. Can thissquare root be written as a rational number? Explain.Read the Lesson4. What do rational and irrational numbers have in common? What is thedifference between rational numbers and irrational numbers? Give anexample of each.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5. Match the property of real numbers with the algebraic example.Commutative a. (x + y) + z = x + (y + z)AssociativeDistributiveb. pq = qpc. h + 0 = hIdentity d. c + (-c) = 0InverseRemember What You Learnede. x(y + z) = xy + xz6. Think of a way to remember the relationships between the sets ofnumbers in the real number system. For example, think of a rhymethat tells the order of the sets of numbers from smallest to largest.Chapter 3 SC StudyText, Course 3 93

NAME DATE PERIOD3-4 Study GuideSCAS 8-2.3, 8-2.4The Real Number SystemNumbers may be classifi ed by identifying to which of the following sets they belong.Whole Numbers 0, 1, 2, 3, 4, …Integers…, -2, -1, 0, 1, 2, …Rational Numbers numbers that can be expressed in the form a_ , where a and b arebintegers and b ≠ 0Irrational Numbers numbers that cannot be expressed in the form a_ , where a and b arebintegers and b ≠ 0ExamplesName all sets of numbers to which each real number belongs.5 whole number, integer, rational number0.666 … Decimals that terminate or repeat are rational numbers, since they canbe expressed as fractions. 0.666… = 2_ 3-√ 25 Since - √ 25 =-5, it is an integer and a rational number.- √ 11 √ 11 ≈ 3.31662479… Since the decimal does not terminate or repeat, it isan irrational number.To compare real numbers, write each number as a decimal and then compare the decimal values.Example 5 Replace with , or = to make 2 1_4Write each number as a decimal.2 1_4 = 2.25√ 5 ≈ 2.236067…Since 2.25 is greater than 2.236067…, 2 1_4 > √ 5 .ExercisesName all sets of numbers to which each real number belongs.1. 30 2. -113. 5 4_74. √ 215. 0 6. - √ 97. 6_38. - √ 101√ 5 a true sentence.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Replace each9. 2.7 √ 7 10. √ with , or = to make a true sentence.11 3 1_ 11. 4 1_26√ 17 12. 3. − 8 √ 1594 SC StudyText, Course 3 Chapter 3

NAME DATE PERIOD3-4 Homework PracticeThe Real Number SystemName all sets of numbers to which the real number belongs.1. -9 2. √ 144 3. √ 35 4.8_11SCAS 8-2.3, 8-2.45. 9.55 6. 5. − 3 7. 20_58. - √ 44Estimate each square root to the nearest tenth. Then graph the squareroot on a number line.9. √ 7 10. √ 19 11. - √ 33Replace each with , or = to make a true sentence.12. √ 8 2.7 13. √ 15 3.9 14. 5 2_5√ 3015. 2 3_10√ 5.29 16. √ 9.8 3. − 1 17. 8. − 2 8 2_9Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Order each set of numbers from least to greatest.18. √ 10 , √ 8 , 2.75, 2. − 8 19. 5.01, 5.0 − 1 , 5. −− 01 , √ 26 20. - √ 12 , √ 13 , -3.5, 3.521. ALGEBRA The geometric mean of two numbers a and b is √ ab . Find thegeometric mean of 32 and 50.22. ART The area of a square painting is 600 square inches. To the nearest hundredthinch, what is the perimeter of the painting?Chapter 3 SC StudyText, Course 3 95

NAME DATE PERIOD3-4 Problem-Solving PracticeThe Real Number SystemSCAS 8-2.3, 8-2.41. GEOMETRY If the area of a square is33 square inches, estimate the lengthof a side of the square to the nearesttenth of an inch.2. GARDENING Hal has a square gardenin his back yard with an area of210 square feet. Estimate the lengthof a side of the garden to the nearesttenth of a foot.3. ALGEBRA Estimate the solution ofa 2 = 21 to the nearest tenth.4. ALGEBRA Estimate the solution ofb 2 = 67.5 to the nearest tenth.5. ARITHMETIC The geometric meanof two numbers a and b can be foundby evaluating √ a · b . Estimate thegeometric mean of 4 and 11 to thenearest tenth.7. GEOMETRY The length s of a side of acube is related to the surface area A ofthe cube by the formula s = √ A_ . If the6surface area is 27 square inches, whatis the length of a side of the cube tothe nearest tenth of an inch?6. ELECTRICITY In a certain electricalcircuit, the voltage V across a20 ohm resistor is given by the formulaV = √ 20P , where P is the powerdissipated in the resistor, in watts.Estimate to the nearest tenth thevoltage across the resistor if the powerP is 4 watts.8. PETS Alicia and Ella are comparing theweights of their pet dogs. Aliciareports that her dog weighs 11 1_5pounds, while Ella says that her dogweighs √ 125 pounds. Whose dogweighs more?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.96 SC StudyText, Course 3 Chapter 3

3-5NAME DATE PERIODExplore Through ReadingThe Pythagorean TheoremGet Ready for the LessonComplete the Mini Lab at the top of page 162 in your textbook.Write your answers below.1. What is the relationship between the values in the H 2 + B 2 column andthe values in the L column?SCAS8-4.1, 8-1.2,8-1.72. How could you use a value in the H 2 + B 2 column to find a correspondingvalue in the L column?Read the Lesson3. Is it possible to have a right triangle for which the Pythagorean Theoremis not true?4. If you know the lengths of two of the sides of a right triangle, how canyou find the length of the third side?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Use the Pythagorean Theorem to determine whether each of thefollowing measures of the sides of a triangle are the sides of a righttriangle.5. 4, 5, 6 6. 9, 12, 157. 10, 24, 26 8. 5, 7, 9Remember What You Learned9. In everyday language, a leg is a limb used to support the body. How doesthis meaning relate to the legs of a right triangle?Chapter 3 SC StudyText, Course 3 97

NAME DATE PERIOD3-5 Study GuideThe Pythagorean TheoremSCAS8-4.1, 8-1.2,8-1.7The Pythagorean Theorem describes the relationship between the lengths of the legs of any righttriangle. In a right triangle, the square of the length of the hypotenuse is equal to the sum of thesquares of the lengths of the legs. You can use the Pythagorean Theorem to find the length of aside of a right triangle if the lengths of the other two legs are known.Examples Find the missing measure for each right triangle. Roundto the nearest tenth if necessary.24 ftc20 cm15 cm32 ftbc 2 = a 2 + b 2 c 2 = a 2 + b 2c 2 = 24 2 + 32 2 20 2 = 15 2 + b 2c 2 = 576 + 1,024 400 = 225 + b 2c 2 = 1,600 400 - 225 = 225 + b 2 - 225c = ± √ 1,600 175 = b 2c = 40 or -40√ 175 = √ b 213.2 ≈ bLength must be positive, so thelength of the hypotenuse is 40 feet.ExercisesThe length of the other legis about 13.2 centimeters.Write an equation you could use to find the length of the missing sideof each right triangle. Then find the missing length. Round to thenearest tenth if necessary.1.4 ftc5 ft2.c9 m4. a = 7 km, b = 12 km 5. a = 10 yd, c = 25 yd 6. b = 14 ft, c = 20 ft5 m3.25 in.15 in.aCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.98 SC StudyText, Course 3 Chapter 3

3-5NAME DATE PERIODHomework PracticeThe Pythagorean TheoremWrite an equation you could use to find the length of the missing sideof each right triangle. Then find the missing length. Round to thenearest tenth if necessary.1. 2. 3.26 in.a in.8 ft10 ftb ft24 in.c cmSCAS18 cm8-4.1, 8-1.2,8-1.715 cm4. a yd5. 6.14 ydc mm28 yd50 mm50 mmc m64 m45 m7. a, 65 cm; c, 95 cm 8. a, 16 yd; b, 22 ydCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Determine whether each triangle with sides of given lengths is aright triangle.9. 18 ft, 23 ft, 29 ft 10. 7 yd, 24 yd, 25 yd11. The hypotenuse of a right triangle is 15 inches, and one of its legs is11 inches. Find the length of the other leg.12. A leg of a right triangle is 30 meters long, and the hypotenuse is35 meters long. What is the length of the other leg?13. TELEVISIONS The diagonal of a 27-inch television measures 27 inches.If the width of a 27-inch is 22 inches, calculate its height to the nearestinch.Chapter 3 SC StudyText, Course 3 99

NAME DATE PERIOD3-5 Problem-Solving PracticeThe Pythagorean TheoremSCAS8-4.1, 8-1.2,8-1.71. ART What is the length of a diagonal ofa rectangular picture whose sides are12 inches by 17 inches? Round to thenearest tenth of an inch.2. GARDENING Ross has a rectangulargarden in his back yard. He measuresone side of the garden as 22 feet andthe diagonal as 33 feet. What is thelength of the other side of his garden?Round to the nearest tenth ofa foot.3. TRAVEL Troy drove 8 miles due eastand then 5 miles due north. How faris Troy from his starting point? Roundthe answer to the nearest tenth of amile.4. GEOMETRY What is the perimeter of aright triangle if the hypotenuse is15 centimeters and one of the legs is9 centimeters?5. ART Anna is building a rectangularpicture frame. If the sides of the frameare 20 inches by 30 inches, whatshould the diagonal measure? Roundto the nearest tenth of an inch.7. CONSTRUCTION A door frame is80 inches tall and 36 inches wide.What is the length of a diagonal ofthe door frame? Round to the nearesttenth of an inch.6. CONSTRUCTION A 20-foot ladderleaning against a wall is used to reacha window that is 17 feet above theground. How far from the wall is thebottom of the ladder? Round to thenearest tenth of a foot.8. TRAVEL Tina measures the distancesbetween three cities on a map. Thedistances between the three cities are45 miles, 56 miles, and 72 miles. Dothe positions of the three cities form aright triangle?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.100 SC StudyText, Course 3 Chapter 3

NAME DATE PERIOD3-6 Explore Through ReadingSCAS 8-4.1Using the Pythagorean TheoremGet Ready for the LessonRead the introduction at the top of page 167 in your textbook.Write your answers below.1. What type of triangle is formed by the horizontal distance, the verticalheight, and the length of the towrope?2. Write an equation that can be used to find the length of the towrope.Read the LessonDetermine whether each of the following is a Pythagorean triple.3. 13-84-85 4. 11-60-615. 21-23-29 6. 12-25-377. The triple 8-15-17 is a Pythagorean triple. Complete the table to findmore Pythagorean triples.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.a b c Check: c 2 = a 2 + b 2Original 8 15 17 289 = 64 + 225× 2× 3× 5× 108. If the sides of a square are of length s, how can you find the length of adiagonal of the square?Remember What You Learned9. Work with a partner. Write a word problem that can be solved using thePythagorean Theorem, including the art. Exchange problems with yourpartner and solve.Chapter 3 SC StudyText, Course 3 101

NAME DATE PERIOD3-6Study GuideUsing the Pythagorean TheoremSCAS 8-4.1You can use the Pythagorean Theorem to help you solve problems.Example 1A professional ice hockey rink is 200 feetlong and 85 feet wide. What is the lengthof the diagonal of the rink?c85 ftc 2 = a 2 + b 2The Pythagorean Theorem200 ftc 2 = 200 2 + 85 2 Replace a with 200 and b with 85.c 2 = 40,000 + 7,225 Evaluate 200 2 and 85 2 .c 2 = 47,225Simplify.√ c 2 = √ 47,225 Take the square root of each side.c ≈ 217.3Simplify.The length of the diagonal of an ice hockey rink is about 217.3 feet.ExercisesWrite an equation that can be used to answer the question. Then solve.Round to the nearest tenth if necessary.1. What is the length of the diagonal? 2. How long is the kite string?6 in. cc30 m6 in.25 m3. How high is the ramp? 4. How tall is the tree?15 ft10 ftb18 yd7 ydhCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.102 SC StudyText, Course 3 Chapter 3

NAME DATE PERIOD3-6 Homework PracticeSCAS 8-4.1Using The Pythagorean TheoremWrite an equation that can be used to answer the question. Then solve.Round to the nearest tenth if necessary.1. How far is the ship from 2. How long is the wire 3. How far above the water isthe the lighthouse? supporting the sign? the person parasailing?6 mi8 mid1.5 ftw2 ftOpen 24/7100 ydp80 yd4. How wide is the pond? 5. How high is the ramp? 6. How high is the end of theladder against the building?95 ftCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.120 ftwh19 ft21 ft7. GEOGRAPHY Suppose Birmingham, Huntsville, andGadsden, Alabama, form a right triangle. What isthe distance from Huntsville to Gadsden? Round tothe nearest tenth if necessary.8. GEOMETRY Find the diameter d of the circle in the figureat the right. Round to the nearest tenth if necessary.h13 ft4 ftHuntsville98 miGadsden61 miBirmingham18 ftd22 ftChapter 3 SC StudyText, Course 3 103

NAME DATE PERIOD3-6 Problem-Solving PracticeSCAS 8-4.1Using the Pythagorean Theorem1. RECREATION A pool table is 8 feet longand 4 feet wide. How far is it from onecorner pocket to the diagonally oppositecorner pocket? Round to the nearesttenth.2. TRIATHLON The course for a localtriathlon has the shape of a righttriangle. The legs of the triangleconsist of a 4-mile swim and a 10-milerun. The hypotenuse of the triangleis the biking portion of the event.How far is the biking part of thetriathlon? Round to the nearest tenthif necessary.3. LADDER A ladder 17 feet long isleaning against a wall. The bottom ofthe ladder is 8 feet from the base ofthe wall. How far up the wall is thetop of the ladder? Round to the nearesttenth if necessary.4. TRAVEL Tara drives due north for 22miles then east for 11 miles. How far isTara from her starting point? Round tothe nearest tenth if necessary.5. FLAGPOLE A wire 30 feet long isstretched from the top of a flagpoleto the ground at a point 15 feet fromthe base of the pole. How high is theflagpole? Round to the nearest tenth ifnecessary.6. ENTERTAINMENT Isaac’s television is25 inches wide and 18 inches high.What is the diagonal size of Isaac’stelevision? Round to the nearest tenthif necessary.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.104 SC StudyText, Course 3 Chapter 3

NAME DATE PERIOD3-7 Explore Through ReadingSCASDistance on the Coordinate PlaneGet Ready for the LessonRead the introduction at the top of page 173 in your textbook.Write your answers below.1. What does each colored line on the graph represent?8-4.2, 8-4.1,8-1.72. What type of triangle is formed by the lines?3. What are the lengths of the two blue lines?Read the Lesson4. On the coordinate plane, what are the four sections determined by theaxes called?5. Match each term of the coordinate plane with its description.ordinatea. point where number lines meetCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.y-axisoriginabscissax-axisb. x-coordinatec. y-coordinated. vertical number linee. horizontal number line6. To find the distance between two points, draw a right triangle whosehypotenuse is the distance you want to find; find the lengths of the legs,and useto solve the problem.Remember What You Learned7. Think of a way to remember the names of the four quadrants of thecoordinate plane.Chapter 3 SC StudyText, Course 3 105

3-7NAME DATE PERIODStudy GuideDistance on the Coordinate PlaneSCAS8-4.2, 8-4.1,8-1.7You can use the Pythagorean Theorem to find the distance between two points on the coordinateplane.Example 1 Find the distance between points (2, -3) and (5, 4).Graph the points and connect them with a line segment.Draw a horizontal line through (2, -3) and a vertical linethrough (5, 4). The lines intersect at (5, -3).Count units to find the length of each leg of thetriangle. The lengths are 3 units and 7 units. Thenuse the Pythagorean Theorem to find the hypotenuse.c 2 = a 2 + b 2The Pythagorean Theoremc 2 = 3 2 + 7 2 Replace a with 3 and b with 7.c 2 = 9 + 49 Evaluate 3 2 and 7 2 .c 2 = 58Simplify.√ c 2 = √ 58 Take the square root of each side.c ≈ 7.6Simplify.The distance between the points is about 7.6 units.y(5, 4)7 unitsOx(5, 3)(2, 3)3 unitsExercisesFind the distance between each pair of points whose coordinates aregiven. Round to the nearest tenth if necessary.1. yO(1, 1)(6, 3)x2. y( 2, 1)O(4, 3)x3. yGraph each pair of ordered pairs. Then find the distance between thepoints. Round to the nearest tenth if necessary.4. (4, 5), (0, 2) 5. (0, -4), (-3, 0) 6. (-1, 1), (-4, 4)yyO(1, 1)y(3, 2)xCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.OxOxOx106 SC StudyText, Course 3 Chapter 3

3-7NAME DATE PERIODHomework PracticeDistance on the Coordinate PlaneName the ordered pair for each point.1. A 2. BSCASF8-4.2, 8-4.1,8-1.73. C 4. DBEA5. E 6. FHGCD7. G 8. HGraph and label each point.9. J (2 1_4 , 1_2) 10. K (3, -1 2_3)11. M (-3 3_4 , 4 1_4) 12. N (-3 2_5, -23_5)13. P (-2.1, 1.8) 14. Q (1.75, -3.5)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Graph each pair of ordered pairs. Then find the distance between thepoints. Round to the nearest tenth if necessary.15. (4, 3), (1, -1) 16. (3, 2), (0, -4) 17. (-4, 3.5), (2, 1.5)18. Find the distance between points R and S shown atthe right. Round to the nearest tenth.19. GEOMETRY If one point is located at (-6, 2) andanother point is located at (6, -3), find the distancebetween the points.0yRSxChapter 3 SC StudyText, Course 3 107

NAME DATE PERIODMini-Project(Use with Lesson 3-7)Connect the DotsSCAS8-4.2, 8-4.1,8-1.7Graph each point on the coordinate grid. Label each point with its letter.1. A(3, 1) 2. B(9,-4) 3. C(0,-4) 4. D(-6, 6)5. E(7, 5) 6. F(-6,-6) 7. G(-4, 0) 8. H(1, 5)9. I(-9, 1) 10. J(9, 1) 11. K(-6,-2) 12. L(5,-1)13. M(-9,-6) 14. N(2,-4) 15. P(-10, 0) 16. Q(7, 1)17. R(-1, 0) 18. S(6, 4) 19. T(7,-4) 20. U(-9, 6)y21. V(10, 3)22. W(1,-4)23. X(-9,-2)24. Y(-5, 0)25. Z(9, 5)O26. AA(-6, 1)27. BB(10,-1)28. CC(0, 4)29. DD(6,-3)30. EE(5, 1)31. FF(3,-1)32. GG(-7,-1)Follow these directions to create a picture on the coordinate grid:Connect point U to point AA. Connect point I to point D. Connect point P topoint Y. Draw a line from point X to point GG to point K to point M to point F.Connect point G to point R. Connect point A to point EE. Connect point FF topoint L.Draw a line from point CC to point H to point W. Then connect point Cto point N.Connect point Q to point J. Then draw a line from point S to point Eto point Z to point V to point J to point BB to point B to point T to point DD.xCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Write the equation you created: _____________ Solve for x. _____________108 SC StudyText, Course 3 Chapter 3

NameChapter 3 TestMastering the SC StandardsDate1 Between which two whole numbersis √95 ?A 10 and 11B 9 and 10C 8 and 9D 7 and 83 Which subset of real numberscontains √3 ?A irrational numbersB rational numbersC integersD whole numbers8-2.68-2.42 Keiko goes to the South Carolina State fairin Columbia, which has been held since1869. One of the tents she visits has a polethat is braced by a 26-foot rope. The rope isanchored 10 feet from the base of the pole.4 Margo plots part of her hometown on acoordinate grid so that each intersection isan ordered pair. Margo starts at the centerof town, which she plots at the origin. Thenshe moves two blocks north, two blockseast, and two blocks south. Which orderedpair shows her location on the grid?A (2, -2)B (0, 2)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. How tall is the tent pole?A 21.8 ftB 24 ftC 28 ftD 30 ft8-4.1C (2, 0)D (2, 4)8-4.25 In a number game, Long was supposed tofind the square root of a number. Instead,he squared the number and wrote 16.What is the square root of the originalnumber Long had in the number game?A 16B 8C 4D 28-2.6Chapter 3 SC StudyText, Course 3 109

NameDateChapter 3 Test (continued)Mastering the SC Standards6 For which triangle is the relationshipa 2 + b 2 = c 2 true?8 What is the length of the hypotenuse in theright triangle below?Aac3 cmb4 cmBA 2 centimetersabB 5 centimetersC 12 centimetersCcD 14 centimeters8-4.1Dacca7 Between which two whole numbersis √ 117 ?A 8 and 9B 9 and 10C 10 and 11D 11 and 12bb8-4.18-2.69 Which symbol makes the number sentencetrue when placed in the blank?A C =D≥√ 23_28-2.4Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.110 SC StudyText, Course 3 Chapter 3

4NAME DATE PERIODAnticipation GuideAlgebra: IntegersSTEP 1 Before you begin Chapter 4• Read each statement.• Decide whether you Agree (A) or Disagree (D) with the statement.• Write A or D in the first column OR if you are not sure whether youagree or disagree, write NS (Not Sure).STEP 1A, D, or NSStatement1. A ratio is a comparison of two numbers by division.2. $3 per 2 pounds is an example of a unit rate.3. The quantities 4_18 , 6_ , and8_are said to be proportional27 36because they have a constant ratio.4. If the cross products of two ratios are not equal, then theydo not form a proportion.5. Polygons with the same shape and size are called similarpolygons.6. Corresponding angles of similar polygons are congruent.7. A model car could have a scale factor of 1 inch/1 foot.STEP 2A or DCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.8. A negative rate of change means the change is not afavorable one.9. A line with a slope of 0 is a vertical line.STEP 2 After you complete Chapter 4• Reread each statement and complete the last column by entering an A or a D.• Did any of your opinions about the statements change from the first column?• For those statements that you mark with a D, use a piece of paper to write anexample of why you disagree.Chapter 4 SC StudyText, Course 3 111

4NAME DATE PERIODFamily ActivityState Test PracticeFold the page along the dashed line. Work each problem on anotherpiece of paper. Then unfold the page to check your work.1. Determine if the following is aproportional relationship.2. Triangle ABC is similar to triangleDEF.BE!One pair $2.50 or3 for $5.00Is the above relationship proportional?How do you know?A No; 1_$2.50 does not equal 3_$5.00B No; 1_$2.50 does not equal _ $53C Yes; 1_ is equal3_$2.50 $5D This cannot be determined.Fold here.Solution1. Hint: To be proportional, the ratios beingcompared must be equal, or in this case,the cost of each pair of socks must bethe same at regular price and sale price.In order for the relationship to beproportional, the ratio of the number ofpairs of socks for each price must beequal.1_is the ratio of the number$2.50of pairs of socks to the cost at theregular price. If you bought $5 worthof socks at the regular price, you wouldonly get two pair. Since you can get3 pair for $5 at the sale price, theratios are not equal, and therefore therelationship is not proportional.A?If the area of triangle ABC is 67.5square millimeters, what is the heightof triangle DEF?CDA 5 millimetersB 5 square millimetersC 3 millimetersD 3 square millimetersSolution2. Hint: Use the area of triangle ABC tofind the height (A = 1_2 bh).When triangles are similar, their sides areproportional.A = 1_2 bh67.5 = 1_ (15)h A = 67.5, b = 15267.5 = 7.5h Multiply.9 = h Divide each side by 7.5The linear measures in the two trianglesare proportional.__ 5 mm15 mm = h_height of ∆DEF9height of ∆ABCh = 3?FCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.PasssThe answer is A. The answer is C.112 SC StudyText, Course 3 Chapter 4

4-1NAME DATE PERIODExplore Through ReadingRatios and RatesGet Ready for the LessonRead the introduction at the top of page 190 in your textbook.Write your answers below.1. To make a smaller amount of orange paint, how much red paint should youuse for every drop of yellow paint? Explain your reasoning.SCAS 8-2.7PDFRead the Lesson2. What does it mean if the ratio of red marbles to blue marbles is 3 to 5?3. What is another way to write the ratio 3 to 5?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.4. What must you do before you can simplify the ratio 30 minutes to8 hours? What is the simplified ratio?Remember What You Learned5. When you go to a bank to exchange money of one currency for another, thebank uses a conversion rate to calculate the amount of money in the newcurrency. Find out what the current conversion rate is to exchange U.S.dollars to Canadian dollars at a local bank. Then write the rate as a ratioof one currency compared to the other.Chapter 4 SC StudyText, Course 3 113

NAME DATE PERIOD4-1 Study GuideSCAS 8-2.7Ratios and RatesA ratio is a comparison of two numbers by quantities. Since a ratio can be written as a fraction, itcan be simplifi ed.Example 135_42 = 5_ 6The ratio in simplest form is 5_ 6Express 35 wins to 42 losses in simplest form.Divide the numerator and denominator by the greatest common factor, 7.or 5:6.Example 2Express 1 foot to 3 inches in simplest form.To simplify a ratio involving measurements, both quantities must have the sameunit of measure.__ 1 foot= __ 12 inchesConvert 1 foot to 12 inches.3 inches 3 inches= __ 4 inches Divide the numerator and denominator by 3.1 inchThe ratio in simplest form is 4_ or 4:1.1PasssA rate is a ratio that compares two quanitities with different types of units. A unit rate is a rate with adenominator of 1.Example 3__ 309 miles6 hours= __ 51.5 miles1 hourExpress 309 miles in 6 hours as a unit rate.The unit rate is 51.5 miles per hour.ExercisesExpress each ratio in simplest form.Divide the numerator and denominator by 6 to get a denominator of 1.1. 3 out of 9 students 2. 8 passengers:2 cars3. 5 out of 10 dentists 4. 35 boys:60 girls5. 18 red apples to 42 green apples 6. 50 millimeters to 1 meterExpress each rate as a unit rate.7. 12 waves in 2 hours 8. 200 miles in 4 hoursCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.9. 21 gallons in 2.4 minutes 10. $12 for 4.8 pounds114 SC StudyText, Course 3 Chapter 4

NAME DATE PERIOD4-1 Homework PracticeRatios and RatesSCAS 8-2.7Express each ratio in simplest form.1. 32 out of 200 adults like opera 2. 20 picked out of 65 who tried out3. 48 robins to 21 blackbirds seen 4. 10 rock musicians to 22 classicalmusicians in the concert5. 2 feet long to 64 inches wide 6. 45 millimeters out of 10 centimetersPDF7. 10 ounces sugar for 1 pound apples 8. 2 quarts out of 4 gallons leaked outExpress each rate as a unit rate.9. 110 inches of snow in 8 days 10. 38 feet in 25 secondsCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.11. 594 cars crossing the bridge in 3 hours 12. 366 miles on 12 gallons13. SHOPPING An 8-ounce box of Crispy Crackers costs $1.59 and a2-pound box costs $6.79. Which box is the better buy? Explain yourreasoning.14. ANIMALS Which animal listed in thetable consumes the least amount of foodcompared to its body weight? Explainyour reasoning.AnimalBodyWeight(lb)Amount ofFood perDay (lb)African Elephant 12,000 500Blue Whale 286,000 8,000Koala 22 2Komodo Dragon 300 240Source: Scholastic Book of World RecordsChapter 4 SC StudyText, Course 3 115

NAME DATE PERIOD4-1 Problem-Solving PracticeRatios and RatesSCAS 8-2.71. COOKING In a bread dough recipe,there are 3 eggs for every 9 cups offlour. Express this ratio in simplestform.2. WILDLIFE Dena counted 14 robins out of150 birds. Express this ratio insimplest form.3. INVESTMENTS Josh earned dividends of$2.16 on 54 shares of stock. Find thedividends per share.4. TRANSPORTATION When Denise boughtgasoline, she paid $27.44 for 11.2gallons. Find the price of gasoline pergallon.Passs5. WATER FLOW Jacob filled his 60-gallonbathtub in 5 minutes. How fast wasthe water flowing?7. HOUSING Mr. and Mrs. Romero boughta 1,200 square-foot house for $111,600.How much did they pay per squarefoot?6. TRAVEL On her vacation, Charmaine’sflight lasted 4.5 hours. She traveled954 miles. Find the average speed ofthe plane.8. SHOPPING A breakfast cereal comes intwo different sized packages. The8-ounce box costs $2.88, while the12-ounce box costs $3.60. Whichbox is the better buy? Explain yourreasoning.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.116 SC StudyText, Course 3 Chapter 4

4-2NAME DATE PERIODExplore Through ReadingProportional and Nonproportional RelationshipsGet Ready for the LessonRead the introduction at the top of page 194 in your textbook.Write your answers below.1. Copy and complete the table to determine the cost for different numbersof pizzas ordered.Cost of Order ($) 8Pizzas Ordered 1 2 3 42. For each number of pizzas, write the relationship of the cost and numberof pizzas as a ratio in simplest form. What do you notice?SCAS 8-2.7, 8-1.7PDFCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Read the Lesson3. At Better Shirts, an order of 10 printed T-shirts is $45 and an order of250 printed T-shirts is $875. What must you do before you can comparethe ratios to see if they are proportional?4. What must be true in order for the ratios to be proportional?5. What are the simplified ratios for the T-shirt orders? Are the ratiosproportional or nonproportional?Remember What You Learned6. A delivery service charges $7 per package delivered locally. There is also a $2 servicecharge for registering an order of packages for any number of packages. Create atable to show what the costs of sending 1, 2, 3, and 4 packages are, using the service.Is the relationship between total cost and number of packages proportional ornonproportional? Explain your reasoning.Chapter 4 SC StudyText, Course 3 117

4-2NAME DATE PERIODStudy GuideProportional and Nonproportional RelationshipsSCAS 8-2.7, 8-1.7Two related quantities are proportional if they have a constant ratio between them. If two relatedquantities do not have a constant ratio, then they are nonproportional.Example 1 The cost of one CD at a record store is $12. Create a table to showthe total cost for different numbers of CDs. Is the total cost proportional to thenumber of CDs purchased?Number of CDs 1 2 3 4Total Cost $12 $24 $36 $48___Total CostNumber of CDs = 12_1 = 24_2 = 36_3 = 48_Divide the total cost for each by the number= $12 per CD4 of CDs to find a ratio. Compare the ratios.Since the ratios are the same, the total cost is proportional to the number of CDs purchased.Example 2 The cost to rent a lane at a bowling alley is $9 per hour plus $4 forshoe rental. Create a table to show the total cost for each hour a bowling lane isrented if one person rents shoes. Is the total cost proportional to the number ofhours rented?Number of Hours 1 2 3 4Total Cost $13 $22 $31 $40___Total Cost→13_Number of Hours 1 or 13 22_2 or 11 31_3 or 10.34 40_or 104Since the ratios are not the same, the total cost is nonproportional tothe number of hours rented with shoes.ExercisesUse a table of values to explain your reasoning.Divide each cost by thenumber of hours.1. PICTURES A photo developer charges $0.25 per photo developed. Is the total costproportional to the number of photos developed?2. SOCCER A soccer club has 15 players for every team, with the exception of two teamsthat have 16 players each. Is the number of players proportional to the number ofteams?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Passs118 SC StudyText, Course 3 Chapter 4

NAME DATE PERIOD4-2 Homework PracticeSCAS 8-2.7, 8-1.7Proportional and Nonproportional RelationshipsFor Exercises 1–3, use a table of values to explain your reasoning.1. ANIMALS The world’s fastest fish, a sailfish, swims at a rate of 69 miles per hour.Is the distance a sailfish swims proportional to the number of hours it swims?PDFFOSSILS For Exercises 2 and 3, use the following information.In July, a paleontologist found 368 fossils at a dig. In August, she found about14 fossils per day.2. Is the number of fossils the paleontologist found in August proportional tothe number of days she spent looking for fossils that month?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.3. Is the total number of fossils found during July and August proportional tothe number of days the paleontologist spent looking for fossils in August?Chapter 4 SC StudyText, Course 3 119

NAME DATE PERIOD4-2 Problem-Solving PracticeProportional and Nonproportional RelationshipsFor Exercises 1–8, use a table of values when appropriate to explainyour reasoning.SCAS 8-2.7, 8-1.71. SPORTS A touchdown is worth 6 points.Additionally you score an extra pointif you can kick a field goal. Is the totalnumber of points scored equal to thenumber of touchdowns?2. DRIVING Gasoline costs $2.79 pergallon. Is the number of gallonsproportional to the total cost?3. JOBS Michael earns $3.90 per hour asa server at a restaurant. In addition,he earns an average of 18% tips on hisfood sales. Is the amount of money thathe earns proportional to the number ofhours that he works?4. RECREATION A outdoor swimming poolcosts $8 per day to visit during thesummer. There is also a $25 yearlyregistration fee. Is the total costproportional to the total number ofdays visited?Passs5. SCHOOL At a certain middle school,there are 26 students per teacher inevery homeroom. Is the total numberof students proportional to the numberof teachers?7. MONEY At the beginning of thesummer, Roger had $180 in the bank.Each week he deposits another $64that he earns mowing lawns. Is hisaccount balance proportional to thenumber of weeks since he startedmowing lawns?6. TEAMS A baseball club has 18 playersfor every team, with the exception offour teams that have 19 players each.Is the number of players proportionalto the number of teams?8. SHELVES A bookshelf holds 43 books oneach shelf. Is the total number of booksproportional to the number of shelvesin the bookshelf?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.120 SC StudyText, Course 3 Chapter 4

NAME DATE PERIOD4-3 Explore Through ReadingRate of ChangeGet Ready for the LessonRead the introduction at the top of page 198 in your textbook.Write your answers below.1. What is the change in the number of entries from 2004 to 2006?SCAS 8-2.7, 8-1.72. Over what number of years did this change take place?3. Write a rate that compares the change in the number of entries to thechange in the number of years. Express your answer as a unit rate andexplain its meaning.PDFRead the Lesson4. What does a rate of change measure on a graph?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5. On a graph, what does it mean when a rate of change is negative?6. Complete the sentence: When a quantity does not change over a period oftime, it is said to have a __________ rate of change.Remember What You Learned7. Write out in words the formula for finding a rate of change between twodata points (x 1, y 1) and (x 2, y 2).Chapter 4 SC StudyText, Course 3 121

NAME DATE PERIOD4-3 Study GuideRate of changeSCAS 8-2.7, 8-1.7To fi nd the rate of change between two data points, divide the difference of the y-coordinates by the__difference of the x-coordinates. The rate of change between ( x 1 , y 1 ) and ( x 2 , y 2 ) is y 2 - y 1x 2 - x .1Example INCOME The graph shows Mr. Jackson’sannual income between 1998 and 2006. Find the rate ofchange in Mr. Jackson’s income between 1998 and 2001.Use the formula for the rate of change.Let (x 1, y 1) = (1998, 48,500) and (x 2, y 2) = (2001, 53,000).__ y 2- y 1x 2- x 1= ___53,00 - 48, 5002001 - 1998=_ 4,5003=_ 1,5001Write the formula for rate of change.Simplify.Express this rate as a unit rate.Between 1998 and 2001, Mr. Jackson’s income increased anaverage of $1,500 per year.Annual Income ($)65,000y60,00055,00050,00045,000Mr. Jackson's Income2006, 57,0002001, 53,0001998, 48,500x0'98 '00 '02 '04 '06YearPasssExercisesSURF For Exercises 1–3, use the graph thatshows the average daily wave height asmeasured by an ocean buoy over a nine-dayperiod.1. Find the rate of change in the average dailywave height between day 1 and day 3.2. Find the rate of change in the average dailywave height between day 3 and day 7.3. Find the rate of change in the average dailywave height between day 7 and day 9.Wave Height151311970yWave Height(7, 14)(3, 12)(9, 11)(1, 8)x1 3 5 7 9DayCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.122 SC StudyText, Course 3 Chapter 4

NAME DATE PERIOD4-3 Homework PracticeRate of ChangeSNOWFALL For Exercises 1–3, use the following information.The amount of snow that fell during five time periods is shown in the table.Time (P.M.) 2:00 2:10 2:20 2:30 2:40Snowfall (in.) 3.8 5.1 5.5 7.8 8.3SCAS 8-2.7, 8-1.7PDF1. Find the rate of change in inches ofsnow that fell per minute between2:00 P.M. and 2:10 P.M.2. Find the rate of change in inches ofsnow that fell per minute between2:30 P.M. and 2:40 P.M.3. Make a graph of the data. Duringwhich time period did the rate ofsnowfall increase the greatest? Explain yourreasoning.Snowfall (in.)1098765432102:00 2:10 2:20 2:30 2:40Time (P.M.)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.POPULATION For Exercises 4 –7, use the the information below and at the right.The graph shows the population of Washington,D.C., every ten years from 1950 to 2000.4. Find the rate of change in populationbetween 1950 and 1970.5. Between which two 10-year periods didthe population decrease at the fastestrate?6. Find the rate of change in populationbetween 1950 and 2000.Population of Washington, D.C.7. If the rate of change in population between 1950 and 2000 were to continue,what would you expect the population to be in 2010? Explain your reasoning.Population (thousands)850(1950, 802)800750(1960, 764)700(1970, 757)650(1990, 607)600(1980, 638)550500(2000, 572)45040001950 1960 1970 19801990 2000 2010YearSource: U.S. Census BureauChapter 4 SC StudyText, Course 3 123

PasssNAME DATE PERIOD4-3 Problem-Solving PracticeSCAS 8-2.7, 8-1.7Rate of ChangeELECTIONS For Exercises 1–3, use the table that shows the total numberof people who had voted in District 5 at various times on election day.Time 8:00 A.M. 10:00 A.M. 1:00 P.M. 4:30 P.M. 7:00 P.M.Number of Voters 141 351 798 1,008 1,7531. Find the rate of change in the numberof voters between 8:00 A.M. and10:00 A.M. Then interpret its meaning.2. Find the rate of change in the numberof voters between 10:00 A.M. and1:00 P.M. Then interpret its meaning.3. During which of these two time periodsdid the number of people who hadvoted so far increase faster? Explainyour reasoning.5. FITNESS In 1998, the price of an annualmembership at Mr. Jensen’s healthclub was $225. In 2008, the price of thesame membership was $319.50. Findthe rate of change in the price of theannual membership between 1998 and2008.4. MUSIC At the end of 2005, Candace had47 CDs in her music collection. At theend of 2008, she had 134 CDs. Find therate of change in the number of CDs inCandace’s collection between 2005 and2008.6. HIKING Last Saturday Fumio and Kishiwent hiking in the mountains. Whenthey started back at 2:00 P.M., theirelevation was 3,560 feet above sealevel. At 6:00 P.M., their elevationwas 2,390 feet. Find the rate ofchange of their elevation between2:00 P.M. and 6:00 P.M. Then interpretits meaning.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.124 SC StudyText, Course 3 Chapter 4

NAME DATE PERIOD4-5 Explore Through ReadingSolving ProportionsGet Ready for the LessonRead the introduction at the top of page 210 in your textbook. Writeyour answers below.1. Write a ratio in simplest form that compares the cost to the number ofbottles of nail polish.SCAS 8-2.72. Suppose you and some friends wanted to buy 6 bottles of polish. Write aratio comparing the cost to the number of bottles of polish.PDF3. Is the cost proportional to the number of bottles of polish purchased?Explain.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Read the Lesson4. Complete the sentence: If two ratios form a proportion, then the ratios aresaid to be .5. Do the ratios a_bandc_dalways form a proportion? Why or why not?6. Explain how you can use cross products to solve proportions in which one ofthe terms is not known.Remember What You Learned7. For the proportion a_bcalled cross products?andc_, why do you think the products ad and bc aredChapter 4 SC StudyText, Course 3 125

NAME DATE PERIOD4-5 Study GuideSolving ProportionsSCAS 8-2.7A proportion is an equation that states that two ratios are equivalent. To determine whether a pair ofratios forms a proportion, use cross products. You can also use cross products to solve proportions._ _ Example 1 Determine whether each pair of ratios 20 12and forms a proportion.24 18Find the cross products._ 2024 _ 12 → 24 · 12 = 28818 → 20 · 18 = 360Since the cross products are not equal, the ratios do not form a proportion.Example 2 Solve 12_ 1230 = k_ 70_ 30 = k_ 70 .Write the equation.12 · 70 = 30 · k Find the cross products.840 = 30k Multiply._ 84030 = 30k30Divide each side by 30.28 = k Simplify. The solution is 28.PasssExercisesDetermine whether each pair of ratios forms a proportion.1.17_10 , _ 122.6_59 , 12_ 3.184.7.7_15 , 13_324_7 , _ 1271Solve each proportion.10.13.x_5 = 15_ 25_ 1624 = z_ 155.8.11.14.7_9 , 49_ 6320_35 , 30_ 456.9.3_4 = 12_ c 12.5_8 = s_ 1215.8_12 , 10_ 158_24 , 12_ 2818_24 , 3_ 46_9 = 10_ r14_t= 10_ 11Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.16.w_6 = _ 2.8717.5_y = 7_ 16.818.x_18 = 7_ 36126 SC StudyText, Course 3 Chapter 4

NAME DATE PERIOD4-5 Homework PracticeSolve each Proportion.1. b_5 = 8_16Solving Proportions2. 18_x = 6_103. t_5 = 12_80SCAS 8-2.74. _ 1110 = n_145. _ 2.535 = 2_d6. _ 3.518 = z_36PDF7. _ 0.454.2 = _ p148. _ 2.46 = _ 2.8s3.69. _k = _ 0.20.510. CLASSES For every girl taking classes at the martial arts school, there are3 boys who are taking classes at the school. If there are 236 students takingclasses, write and solve a proportion to predict the number of boys takingclasses at the school.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.11. BICYCLES An assembly line worker at Rob’s Bicycle factory adds a seat toa bicycle at a rate of 2 seats in 11 minutes. Write an equation relating thenumber of seats s to the number of minutes m. At this rate, how long will ittake to add 16 seats? 19 seats?12. PAINTING Lisa is painting a fence that is 26 feet long and 7 feet tall. Agallon of paint will cover 350 square feet. Write and solve a proportion todetermine how many gallons of paint Lisa will need.Chapter 4 SC StudyText, Course 3 127

NAME DATE PERIOD4-5 Problem-Solving PracticeSCAS 8-2.7Solving Proportions1. USAGE A 12-ounce bottle of shampoolasts Enrique 16 weeks. How longwould you expect an 18-ounce bottleof the same brand to last him?2. COMPUTERS About 13 out of 20homes have a personal computer. Ona street with 60 homes, how manywould you expect to have a personalcomputer?3. SNACKS A 6-ounce package of fruitsnacks contains 45 pieces. How manypieces would you expect in a 10-ouncepackage?4. TYPING Ingrid types 3 pages in thesame amount of time that Tanya types4.5 pages. If Ingrid and Tanya starttyping at the same time, how manypages will Tanya have typed whenIngrid has typed 11 pages?Passs5. SCHOOL A grading machine can grade48 multiple-choice tests in 1 minute.How long will it take the machine tograde 300 tests?7. PRODUCTION A shop produces 39wetsuits every 2 weeks. How long willit take the shop to produce429 wetsuits?6. AMUSEMENT PARKS The waiting timeto ride a roller coaster is 20 minuteswhen 150 people are in line. How longis the waiting time when 240 peopleare in line?8. FISH Of the 50 fish that Jim caughtfrom the lake, 14 were trout. Theestimated population of the lake is7,500 fish. About how many troutwould you expect to be in thelake?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.128 SC StudyText, Course 3 Chapter 4

NAME DATE PERIOD4-6 Study GuideSCAS 8-1.8Problem-Solving Investigation: Draw a DiagramPDFExample It takes a worker 4 minutes to stack 2 rows of 8 boxes in awarehouse. How long will it take to stack 8 rows of 8 boxes? Use the draw adiagram strategy to solve the problem.UnderstandPlanSolveCheckAfter 4 minutes, a worker has stacked a 2 rows of 8 boxes. At this rate, howlong would it take to stack 8 rows of boxes?Draw a diagram showing the level ofboxes after 4 minutes.2 rows of 8 boxes = 4 minutes8 rows = 4 × 2 rows, so multiply the time by 4.4 × 4 minutes = 16 minutes8 boxes × 2 rows of boxes = 16 boxes Multiply to find the total number of boxes in the stack.4 minutes ÷ 16 boxes = 0.25 min. per box Divide the number of minutes by the number of boxes.8 boxes × 8 rows of boxes = 64 boxes Multiply to find the number of boxes in the new stack.64 boxes × 0.25 min. = 16 minutes Multiply the number of boxes by the time per box.It will take 16 minutes to stack an 8 × 8 wall of boxes.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ExercisesFor Exercises 1–4, use the draw a diagram strategy to solve the problem.1. GAS A car’s gas tank holds 16 gallons. After filling it for 20 seconds, the tankcontains 2.5 gallons. How many more seconds will it take to fill the tank?2. TILING It takes 96 tiles to fill a 2-foot by 3-foot rectangle. How many tileswould it take to fill a 4-foot by 6-foot rectangle?3. BEVERAGES Four juice cartons can fill 36 glasses of juice equally. How manyjuice cartons are needed to fill 126 glasses equally?4. PACKAGING It takes 5 large shipping boxes to hold 120 boxes of an actionfigure. How many action figures would 8 large shipping boxes hold?Chapter 4 SC StudyText, Course 3 129

NAME DATE PERIOD4-6 Skills PracticeSCAS 8-1.8Problem-Solving Investigation: Draw a DiagramFor Exercises 1–5, use the draw a diagram strategy to solve theproblem.1. AQUARIUM An aquarium holds 60 gallons of water. After 6 minutes, thetank has 15 gallons of water in it. How many more minutes will it take tofill the tank?2. TILING Meredith has a set of ninety 1-inch tiles. If she starts with one tile,then surrounds it with a ring of tiles to create a larger square, how manysurrounding rings can she make before she runs out of tiles?Passs3. SEWING Judith has a 30-yard by 1-yard roll of fabric. She needs to use 1.5 squareyards to create one costume. How many costumes can she create?4. DRIVING It takes 3 gallons of gas to drive 102 miles. How many miles canbe driven on 16 gallons of gas?5. PACKING Hector can fit 75 compact discs into 5 boxes. How many compactdiscs can he fit into 14 boxes?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.130 SC StudyText, Course 3 Chapter 4

NAME DATE PERIOD4-6 Homework PracticeSCAS 8-1.8Problem-Solving Investigation: Draw a DiagramMixed Problem SolvingUse the draw a diagram strategy tosolve Exercises 1 and 2.1. SWIMMING Jon is separating the widthof the swimming pool into equal-sizedlanes with rope. It took him 30 minutesto create 6 equal-sized lanes. How longwould it take him to create 4 equalsizedlanes in a similar swimming pool?4. LETTERS Suppose you have three stripsof paper as shown. How many capitalletters of the alphabet could you formusing one or more of these three stripsfor each letter? List them according tothe number of strips.PDFCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2. TRAVEL Two planes are flying fromSan Francisco to Chicago, a distance of1,800 miles. They leave San Franciscoat the same time. After 30 minutes,one plane has traveled 25 more milesthan the other plane. How much longerwill it take the slower plane to get toChicago than the faster plane if thefaster plane is traveling at 500 milesper hour?Use any strategy to solve Exercises 3–6.Some strategies are shown below.Problem-Solving Strategies• Work backward.• Look for a pattern.• Use a Venn diagram.• Draw a diagram.3. TALENT SHOW In a solo singing andpiano playing show, 18 people sang and14 played piano. Six people both sangand played piano. How many peoplewere in the singing and piano playingshow?5. CLOTHING A store has 255 wool ponchosto sell. There are 112 adult-sizedponchos that sell for $45 each. The restare kid-sized and sell for $32 each. Ifthe store sells all the ponchos, howmuch money will the store receive?6. DINOSAURS Brad mad a model ofa Stegosaurus. If you multiply themodel's length by 8 and subtract 4,you will find the length of an averageStegosaurus. If the actual Stegosaurusis 30 ft long, how long is Brad’smodel.Chapter 4 SC StudyText, Course 3 131

PasssNAME DATE PERIOD4-6 Problem-Solving PracticeFor Exercises 1–6, use the draw a diagram strategy to solve the problem.SCAS 8-1.8Problem-Solving Investigation: Draw a Diagram1. TILING Kelly is using 3-inch square tilesto cover a 4-foot by 2-foot area. Thetiles are 0.5 inches tall. If the tiles werestacked on top of each other to create atower, how many inches tall would thetower be?2. AQUARIUM An aquarium holds 42gallons of water. After 2 minutes, theaquarium has 3 gallons of water in it.How many more minutes will it take tocompletely fill the aquarium?3. FABRIC It takes Lucy 7 minutes to cuta 20-yard by 1-yard roll of fabric into14 equal pieces. How many minuteswould it take her to cut the fabric into25 equal pieces?4. SPORTS The width of a soccer field is12 feet more than 2_ of its length. If3the field is 96 feet long, what is itsperimeter?5. BEVERAGES It requires 4 gallon jugs ofwater to fill 104 glasses equally. Howmany gallons jugs are required to fill338 glasses equally?6. GAS It takes Richard 48 seconds to fillhis gas tank with 3 gallons of gas. Ifthe tank holds 14 gallons, how manymore seconds will it take to fill itcompletely?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.132 SC StudyText, Course 3 Chapter 4

NAME DATE PERIOD4-7 Explore Through ReadingSimilar PolygonsGet Ready for the LessonComplete the Mini Lab at the top of page 218 in your textbook. Writeyour answers below.1. Compare the angles of the triangles by matching them up. Identify theangle pairs that have equal measure.2. Express the ratio _ DF_LK , EFJK, and _ DE to the nearest tenth.LJ3. What do you notice about the ratios of the matching sides of matchingtriangles?SCAS 8-5.1, 8-2.7PDFRead the Lesson4. Complete the sentence: If two polygons are similar, then theircorresponding angles are, and their corresponding sides are.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5. If two polygons have corresponding angles that are congruent, does thatmean that the polygons are similar? Why or why not?6. If the sides of one square are 3 centimeters and the sides of another squareare 9 centimeters, what is the ratio of corresponding sides fromthe first square to the second square?Remember What You Learned7. Look up the everyday definition of the word similar in a dictionary. Howdoes the definition relate to what you learned in this lesson?Chapter 4 SC StudyText, Course 3 133

4-7NAME DATE PERIODStudy GuideSimilar PolygonsSCAS 8-5.1, 8-2.7Two polygons are similar if their corresponding angles are congruent and their corresponding sidemeasures are proportional.Example 1 Determine whether △ABC is similar to△DEF. Explain your reasoning.∠A ∠D, ∠B ∠E, ∠C ∠F,AB_DE = 4_ or2_6_EF = 6_93 , BCor2_3 , AC_DF = 8_ or2_12 3The corresponding angles are congruent, and the corresponding sides areproportional.Thus, △ABC is similar to △DEF.Example 2 Given that polygon KLMN ∼ polygon PQRS, write aproportion to find the measure of PQ −−− . Then solve.The ratio of corresponding sides from polygon KLMN topolygon PQRS is 4_ . Write a proportion with this scale3factor. Let x represent the measure of PQ −−− ._ KLPQ = 4_35_x = 4_−− KL corresponds to−−−PQ . The scale factor is 4_3 .KL = 5 and PQ = x35 · 3 = x · 4 Find the cross products.__154 = 4x43.75 = x Simplify.ExercisesMultiply. Then divide each side by 4.1. Determine whether the polygons 2. The triangles below are similar. Write abelow are similar. Explain yourproportion to find each missing measure.reasoning.Then solve.1254116 4121548BA 8CD 12F4xKN656LMEP3S9xQRCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Passs134 SC StudyText, Course 3 Chapter 4

NAME DATE PERIOD4-7 Homework PracticeSimilar PolygonsDetermine whether each pair of polygons is similar. Explain.1. 52. 151522.87.612248135SCAS 8-5.1, 8-2.71517458PDFEach pair of polygons is similar. Write and solve a proportion to findeach missing measure.3. 445.6x104.3 186 9x18126Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5.46644.5x7. TILES A blue rectangular tile and a red rectangular tile are similar. Theblue tile has a length of 10 inches and a perimeter of 30 inches. The redtile has a length of 6 inches. What is the perimeter of the red tile?6.x53.520814Chapter 4 SC StudyText, Course 3 135

NAME DATE PERIOD4-7 Problem-Solving PracticeSCAS 8-5.1, 8-2.7Similar Polygons1. JOURNALISM The editor of the schoolnewspaper must reduce the size ofa graph to fit in one column. Theoriginal graph is 2 inches by 2 inches,and the scale factor from the originalto the reduced graph is 8:3. Find thedimensions of the graph as it willappear in one column of the newspaper.2. PHOTOCOPIES Lydia plans to use aphotocopy machine to increase the sizeof a small chart that she has made aspart of her science project. The originalchart is 4 inches by 5 inches. If sheuses a scale factor of 5:11, will thechart fit on a sheet of paper 8 1_2 inchesby 11 inches? Explain.3. MICROCHIPS The image of a microchipin a projection microscope measures8 inches by 10 inches. The width of theactual chip is 4 millimeters. Howlong is the chip?4. PROJECTIONS A drawing on atransparency is 11.25 centimeters wideby 23.5 centimeters tall. The widthof the image of the drawing projectedonto a screen is 2.7 meters. How tall isthe drawing on the screen?Passs5. GEOMETRY Polygon ABCD is similarto polygon FGHI. Each side of polygonABCD is 3 1_ times longer than the4corresponding side of polygon FGHI.Find the perimeter of polygon ABCD.ABDC3 in.F3 in.2 in.G HI5 in.6. KITES A toy company produces twokites whose shapes are geometricallysimilar. Find the length of the missingside of the smaller kite.30 in.25 in.25 in.30 in.x22.5 in.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.136 SC StudyText, Course 3 Chapter 4

NAME DATE PERIOD4-8 Explore Through ReadingDilationsGet Ready for the LessonSCAS8-4.3, 8-4.4,8-4.2Complete the Mini Lab at the top of page 225 in your textbook. Writeyour answers below.1. Measure and compare corresponding lengths on the original figure and thenew figure. Describe the relationship between these measurements? Howdoes this relate to the change in grid size?PDF2. MAKE A CONJECTURE What size squares should you use to create a versionof the original figure with dimensions that are four times the correspondinglengths on the original? Explain.Read the LessonCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.3. If you are given the coordinates of a figure and the scale factor of adilation of that figure, how can you find the coordinates of the newfigure?4. When you graph a figure and its image after a dilation, how can you checkyour work?Remember What You Learned5. Complete the table below to help you remember the effects of different scalefactors.If the scale factor isbetween 0 and 1greater than 1equal to 1Then the dilation isChapter 4 SC StudyText, Course 3 137

4-8NAME DATE PERIODStudy GuideDilationsSCAS8-4.3, 8-4.4,8-4.2The image produced by enlarging or reducing a fi gure is called a dilation.Example 1 Graph △ABC with vertices A(-2, -1),B(2, 3), and C(2, -1). Then graph itsimage △A′B′C′after a dilation with ascale factor of 3_2 .A(-2, -1) → (-2 · 3_ , -1 ·3_2 2) → A′ (-3, -1 1_B(2, 3) → (2 · 3_2 , 3 · 3_2) → B′ (3, 4 1_2)C(2, 3) → (2 · 3_2 , 3 · 3_2) → C′ (3, -1 1_2)Example 2 Segment M′N′ is a dilation of segment MN. Find the scale factorof the dilation, and classify it as an enlargement or a reduction.Write the ratio of the x- or y-coordinate of one vertex of thedilated figure to the x- or y-coordinate of the correspondingvertex of the original figure. Use the x-coordinates of N(1,-2)and N′(2,-4).x-coordinate ____ of point N′x-coordinate of point N = 2_1 or 2The scale factor is 2. Since the image is larger than the originalfigure, the dilation is an enlargement.Exercises1. Polygon ABCD has vertices A(2, 4), B(-1, 5), C(-3, -5), andD(3, -4). Find the coordinates of its image after a dilationwith a scale factor of 1_ . Then graph polygon ABCD and its2dilation.2. Segment P′Q′ is a dilation of segment PQ. Find the scalefactor of the dilation, and classify it as an enlargement ora reduction.2)'' ''OO'OOyyyy''''''xxxxCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Passs138 SC StudyText, Course 3 Chapter 4

NAME DATE PERIOD4-8 Homework PracticeDilationsDraw the image of the figure after the dilation with the given centerand scale factor.1. center: C, scale factor: 2 2. center: N, scale factor: 1_2SCAS8-4.3, 8-4.4,8-4.2LABPMCONPDFFind the coordinates of the vertices of polygon F G H J after polygonFGHJ is dilated using the given scale factor. Then graph polygon FGHJand polygon F G H J .3. F(-2, 2), G(2, 3), H(3, -2), J(-1, -3); 4. F(-2, 2), G(2, 4), H(3, -3), J(-4, -4);scale factor 3_4scale factor 2yy84Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.In the exercises below, figure R S T is a dilation of figure RST andfigure A B C D is a dilation of figure ABCD. Find the scale factor of eachdilation and classify it as an enlargement or as a reduction.5.‘R‘TRTySO‘Sxx-86. AD-4A‘‘DO 4-4-8yO‘C‘BC8xBx7. GLASS BLOWING The diameter of a vase is now 4 centimeters. If the diameter increasesby a factor of 7_ , what will be the diameter then?3Chapter 4 SC StudyText, Course 3 139

NAME DATE PERIOD4-8 Problem-Solving PracticeDilationsSCAS8-4.3, 8-4.4,8-4.21. EYES Dave’s optometrist used medicineto dilate his eyes. Before dilation,his pupils had a diameter of4.1 millimeters. After dilation,his pupils had a diameter of8.2 millimeters. What was thescale factor of the dilation?2. BIOLOGY A microscope increasesthe size of objects by a factor of 8.How large will a 0.006 millimeterparamecium appear?3. PHOTOGRAPHY A photograph wasenlarged to a width of 15 inches. If thescale factor was 3_ , what was the width2of the original photograph?4. MOVIES Film with a width of35 millimeters is projected onto a screenwhere the width is 5 meters. What isthe scale factor of this enlargement?Passs5. PHOTOCOPYING A 10-inch long copy ofa 2.5-inch long figure needs to be madewith a copying machine. What is theappropriate scale factor?7. MODELS An architectural model is30 inches tall. If the scale used to buildthe model is1_, what is the height of120the actual building?6. MODELS A scale model of a boat isgoing to be made using a scale of 1_50 .If the original length of the boat is20 meters, what is the length of themodel?8. ADVERTISING An advertiser needs a4-inch picture of a 14-foot automobile.What is the scale factor of thereduction?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.140 SC StudyText, Course 3 Chapter 4

4-9NAME DATE PERIODExplore Through ReadingIndirect MeasurementGet Ready for the LessonRead the introduction at the top of page 232 in your textbook. Writeyour answers below.1. What appears to be true about the corresponding angles in the twotriangles?SCAS 8-5.1, 8-2.72. If the corresponding sides are proportional, what could you conclude aboutthe triangles?PDFRead the Lesson3. Complete the following sentence.When you solve a problem using shadow reckoning, the objects beingcompared and their shadows form two sides of .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.4. Suppose that you are standing near a building and you see the shadowscast by you and the building. If you know the length of each of theseshadows and you know how tall you are, write a proportion in words thatyou can use to find the height of the building.5. STATUE If a statue casts a 6-foot shadow and a 5-foot mailbox casts a4-foot shadow, how tall is the statue?Remember What You Learned6. Work with a partner. Have your partner draw two triangles that are similarwith the lengths of two corresponding sides labeled and the length of oneadditional side labeled. Tell your partner how to write a proportion to solvefor the length of the side corresponding to the additional side labeled.Chapter 4 SC StudyText, Course 3 141

4-9NAME DATE PERIODStudy GuideIndirect MeasurementSCAS 8-5.1, 8-2.7Indirect measurement allows you to find distances or lengths that are difficult to measure directlyusing the properties of similar polygons.ExampleWrite a proportion and solve.George’s shadow → _ 1.5lightpole’s shadow →LIGHTING George is standing next to alightpole in the middle of the day. George’sshadow is 1.5 feet long, and the lightpole’sshadow is 4.5 feet long. If George is 6 feettall, how tall is the lightpole?4.5 = 6_ hThe lightpole is 18 feet tall.← George’s height← lightpole’s height1.5 · h = 4.5 · 6 Find the cross products.1.5h = 27 Multiply._ 1.5h1.5 = 27_Divide each side by 1.5.1.5h = 18Simplify.h ft6 ft4.5 ft 1.5 ftPasssExercisesFor Exercises 1–4, use the draw a diagram strategy to solve the problem.1. MONUMENTS A statue casts a shadow 30 feetlong. At the same time, a person who is 5 feettall casts a shadow that is 6 feet long. Howtall is the statue?2. BUILDINGS A building casts a shadow 72 meterslong. At the same time, a parking meter that is1.2 meters tall casts a shadow that is 0.8 meterlong. How tall is the building?3. SURVEYING The twotriangles shown in thefigure are similar. Findthe distance d acrossRed River.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.142 SC StudyText, Course 3 Chapter 4

NAME DATE PERIOD4-9Homework PracticeIndirect MeasurementSCAS 8-5.1, 8-2.7In Exercises 1-4, the triangles are similar. Write a proportion and solvethe problem.1. TREES How tall is Yori? 2. TREASURE HUNT How far is it from thehut to the gold coins?Shovel25 ft18 yd20 fth5 ftSilver CoinsHut15 ydx ydGoldCoins12 ydPDFJewels3. LAKE How deep is the water 31.5 feet 4. SURVEYING How far is it across thefrom the shore? (Hint: ∆ABC ˜ ∆ADE) pond? (Hint: ∆RST ˜ ∆RUV)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A6 ft31.5 ftB2 ftCDEd ft162.5 mT325 mFor Exercise 5, draw a diagram of the situation.Then write a proportion and solve the problem.5. ARCH The Gateway Arch in St. Louis,Missouri, is 630 feet tall. Suppose a12-foot tall pole that is near the Archcasts a 5-foot shadow. How long is theArch’s shadow?VR156 mSd mUChapter 4 SC StudyText, Course 3 143

NAME DATE PERIOD4-9 Problem-Solving PracticeSCAS 8-5.1, 8-2.7Indirect Measurement1. HEIGHT Paco is 6 feet tall and casts a12-foot shadow. At the same time,Diane casts an 11-foot shadow. How tallis Diane?2. LIGHTING If a 25-foot-tall house casts a75-foot shadow at the same time that astreetlight casts a 60-foot shadow, howtall is the streetlight?3. FLAGPOLE Lena is 5 1_feet tall and2casts an 8-foot shadow. At the sametime, a flagpole casts a 48-foot shadow.How tall is the flagpole?4. LANDMARKS A woman who is 5 feet5 inches tall is standing near the SpaceNeedle in Seattle, Washington. Shecasts a 13-inch shadow at the sametime that the Space Needle casts a121-foot shadow. How tall is the SpaceNeedle?Passs5. NATIONAL MONUMENTS A 42-footflagpole near the WashingtonMonument casts a shadow that is14 feet long. At the same time, theWashington Monument casts a shadowthat is 185 feet long. How tall is theWashington Monument?6. ACCESSIBILITY A ramp slopes upwardfrom the sidewalk to the entrance ofa building at a constant incline. If theramp is 2 feet high when it is5 feet from the sidewalk, how highis the ramp when it is 7 feet fromthe sidewalk?5 ft2 ftCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.144 SC StudyText, Course 3 Chapter 4

NAME DATE PERIOD4-10 Explore Through ReadingSCAS 8-2.7, 8-1.1Scale Drawings and ModelsGet Ready for the LessonRead the introduction at the top of page 236 in your textbook.Write your answers below.1. How many inches tall is the photo of the statue?2. The actual height of the statue is 19 feet. Write a ratio comparing the photoheight to the actual height.PDF3. Simplify the ratio you found and compare it to the scale shown below thephoto.Read the Lesson4. Give another example of a scale drawing or scale model that is differentfrom the examples of scale drawings and scale models given on page 236 inyour textbook.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5. Complete the sentence: distances on a scale model areto distances in real life.6. What is the scale factor for a model if part of the model that is 4 inchescorresponds to a real-life object that is 16 inches?Remember What You Learned7. Make a scale drawing of a room, such as your classroom or your bedroom.Select an appropriate scale so that your drawing is a reasonable size. Besure to indicate your scale on your drawing. Use another piece of paper ifnecessary.Chapter 4 SC StudyText, Course 3 145

4-10NAME DATE PERIODStudy GuideScale Drawings and ModelsSCAS 8-2.7, 8-1.1Distances on a scale drawing or model are proportional to real-life distances. The scale is determinedby the ratio of a given length on a drawing or model to its corresponding actual length.Example 1 INTERIOR DESIGN A designer has madea scale drawing of a living room for one of her1_ clients. The scale of the drawing is 1 inch = 13feet. On the drawing, the sofa is 6 inches long.Find the actual length of the sofa.Let x represent the actual length of the sofa. Write and solvea proportion.Sofa11 in. = 1 3ft1 in. 6 in.=11 ft x ft311 · x = 1 · 63x = 8PasssThe actual length of the sofa is 8 feet.To fi nd the scale factor for scale drawings and models, write the ratio given by the scale in simplestform.Example 2 Find the scale factor for the drawing in Example 1.Write the ratio of 1 inch to 1 1_ feet in simplest form.3_ 1 in1 1_ = _1_1 in. Convert 1 feet to inches.3 ft 16 in.3The scale factor is 1_ or 1:16. This means that each distance on the drawing16is 1_ the actual distance.16ExercisesLANDSCAPING Yutaka has made a scale drawingof his yard. The scale of the drawing is1 centimeter = 0.5 meter.1. The length of the patio is 4.5 centimeters in thedrawing. Find the actual length.2. The actual distance between the water faucet andthe pear tree is 11.2 meters. Find the correspondingdistance on the drawing.3. Find the scale factor for the drawing.PatioPearTreePathWater FaucetPondGarden1 cm = 0.5 mCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.146 SC StudyText, Course 3 Chapter 4

NAME DATE PERIOD4-10 Homework PracticeScale Drawings and ModelsLANDSCAPE PLANS In Exercises 1–4, use the drawing and an inch ruler tofind the actual length and width of each section of the park.Measure to the nearest eighth of an inch.1. PlaygroundSCAS 8-2.7, 8-1.12. RestroomsKey1 in. 68 ftLawnPDF3. Picnic AreaPicnicAreaDogRunPlayground4. What is the scale factor of thepark plan? Explain its meaning.RestroomsCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5. SPIDERS The smallest spider, the Patu marples of Samoa, is 0.43 millimeter long.A scale model of this spider is 8 centimeters long. What is the scale of the model?What is the scale factor of the model?6. ANIMALS An average adult giraffe is 18 feet tall. A newborn giraffe is about 6 feet tall.Kayla is building a model of a mother giraffe and her newborn. She wants the model tobe no more than 17 inches high. Choose an appropriate scale for a model of the giraffes.Then use it to find the height of the mother and the height of the newborn giraffe.7. TRAVEL On a map, the distance between Charleston and Columbia, South Carolina,is 5 inches. If the scale of the map is 7_ inch = 20 miles, about how long would it take8the Garcia family to drive from Charleston to Columbia if they drove 60 miles perhour?Chapter 4 SC StudyText, Course 3 147

NAME DATE PERIODMini-ProjectSCAS 8-2.7, 8-1.1Scale Drawings and ModelsMaterialsrulermeasuring tapeyardstick(Use with Lesson 4-10)Make a scale drawing of a room.1. Measure and record the perimeter of the room: .2. Sketch the perimeter on the grid below. Use the scale 1_ in. = 1 ft.43. Show all doors, windows, and any other permanent objects within the room.4. Draw the furniture in the room.PasssExtension5. On another sheet of paper, draw a map of your neighborhood. Choosea reasonable scale to represent 1 block. Show such places as yourhouse, friends’ houses, parks, schools, the library, the post office,and stores. Label the streets. Remember that the direction north isat the top of the map.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.148 SC StudyText, Course 3 Chapter 4

NameChapter 4 TestMastering the SC StandardsDatePDF1 A supermarket surveillance camera counts524 customers entering the store over a6-hour period. If customers continue toenter the store at the same rate, whichproportion can be used to find x, thenumber of people who enter the store overa 9-hour period?A6_524 = 9_ x_6 = 9_xB 524x_ C524 = 6_9D6_x = 9_5248-2.74 Timothy’s hiking club takes a long walkevery Saturday. If the club members hike ata constant speed, which graph shows therelationship between the distance they walkand the time it takes them to hike thatdistance?AB2 The two quadrilaterals shown below aresimilar. What is the value of x?CCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.8 ٍّ12 21.6A 12.8 C 14.4B 14.2 D 15.68-5.13 South Carolina’s state animal, the whitetaileddeer, can run at speeds up to 40 milesper hour. At this rate, how far can a whitetaileddeer run in 3 hours?A 43 milesB 80 milesC 120 milesD 150 milesD8-2.78-2.7Chapter 4 SC StudyText, Course 3 149

NameDateChapter 4 Test (continued)Mastering the SC Standards5 For a history project, Enrico builds areplica of the South Carolina State Capitolbuilding in Columbia. His model has ascale factor of 1_ . If the height of the50Capitol building is 165 feet, how high is itin Enrico’s replica?A 33 in.B 2.3 ftC 3.3 ftD 33 ft8-2.76 Triangle ABC was dilated to form triangleA′B′C′.y14 cm21 cm 18 cm12 cmWhich fraction represents the scale factorused to change △ABC into △A′B′C′?A1_2B 5_8C3_4D 3_2x8-4.47 Maya fills a 60-gallon aquarium in14 minutes. What is the approximatefill rate?A About 4.1 gal/minB About 4.3 gal/minC About 4.6 gal/minD About 4.9 gal/min8 What value of x would make the twotrapezoids similar?8 cm12 cm9 cm 9 cm11 cm 16.5 cmA 4 cmB 6 cmC 7 cmD 8 cm8-2.78-5.19 Shawna hikes the Island trail at HuntingtonIsland State Park. The scale on her map ofthe park is 1 inch = 2.5 miles. If the lengthof the trail is 3.2 inches on the map, howlong is the actual trail?A 5 milesB 3.2 milesC 8 milesD 32 miles8-2.7Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Pass150 SC StudyText, Course 3 Chapter 4

5NAME DATE PERIODAnticipation GuidePercentSTEP 1 Before you begin Chapter 5• Read each statement.• Decide whether you Agree (A) or Disagree (D) with the statement.• Write A or D in the first column OR if you are not sure whether you agree or disagree,write NS (Not Sure).Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.STEP 1A, D, or NSStatement1. To write a fraction as a percent, rewrite the fraction with adenominator of 100.2. To write a fraction as a decimal, divide the numerator by thedenominator.3. Dividing by 100 will move the decimal point two places tothe right.4. The proportion 22_ could be used to find what percent25 = x_100of 25 is 22.5. 30% is equivalent to 1_3 .6. To find 25% of any number, divide that number by 4.7. Two numbers are considered compatible if their quotient is 1.8. 35 is 62% of what number could be solved by the equation35 = 62p.9. A percent of change is a ratio comparing a change in quantityto the original amount.10. The interest earned on an account can be calculated when theoriginal amount borrowed and the rate of interest are known.STEP 2 After you complete Chapter 5• Reread each statement and complete the last column by entering an A or a D.• Did any of your opinions about the statements change from the first column?• For those statements that you mark with a D, use a piece of paper to write anexample of why you disagree.STEP 2A or DChapter 5 SC StudyText, Course 3 151

5NAME DATE PERIODFamily ActivityState Test PracticeFold the page along the dashed line. Work each problem on another piece ofpaper. Then unfold the page to check your work.1. Mr. Kirker was grading his class’ mathtests. He stopped and started severaltimes. He ended up with grades infraction form, percent form, and decimalform. On the list below are the scores ofthe top three tests in the pile. Put thesein order from best to worst scores.14Jimmy_20Andrea 75.00%Billy 0.85Which choice shows the test scores inthe proper order?A 0.85, 14_20B 75%, 0.85, 14_202. Use the model below to estimate thevalue of 85% of 60.60 unitsWhat number would be about 85%of 60?A 30B 20, 75% C 0.85, 75%, _ 14 C 4520D _D 501420 , 0.85, 75%Fold here.Solution1. Hint: First change the numbers so thatthey are all in the same from beforecomparing them.Jimmy’s grade is in fraction form.Changing the fraction to a decimal, hisscore is 14 ÷ 20, or 0.70.Andrea’s grade is in percent form. Inorder to change a percent to a decimal,you divide by 100. Her score in decimalform is 75 ÷ 100, or 0.75.Billy’s grade is already in decimal form.Putting the grades in descending order(best to worst), we have: 0.85, 0.75, 0.70.Replacing the grades with their originalforms, it becomes: 0.85, 75%, 14_20 . Solution2. Hint: Eliminate the unreasonable answersand then evaluate the ones left.30 is 50% of 60, so Options A and B canbe eliminated immediately, since bothare less than 85%.75% is halfway between 50% and 100%,and 45 is halfway between 30 and 60,so Option C can be eliminated.Through the process of elimination,85% of 60 is about 50. Checking theassumption on the number line above,it makes sense that 50 wouldapproximately correspond with 85%.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.The answer is C. The answer is D.152 SC StudyText, Course 3 Chapter 5

5-3NAME DATE PERIODExplore Through ReadingAlgebra: The Percent ProportionGet Ready for the LessonComplete the Mini Lab at the top of page 263 in your textbook.Write your answers below.1. What is 40% of 5?2. 4 is 80% of what number?3. Draw a model and find what percent 7 is of 20.Read the Lesson4. Look at page 263 in your textbook. Fill in theblanks to complete the percent proportion.SCAS 8-2.70 0part2 104 20percent6 308 4010 5012 6014 70whole16 8018 90100%20 1005. Complete the table for each statement or problem. For a quantity thatneeds to be found, put a question mark in the appropriate column.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.a. 14 is 20% of 70.b. 6% of 40 is 2.4c. 13 out of 25 is 52%d. What is 30% of 65?e. Find 41% of 250.f. What percent of 25 is 18?Remember What You Learnedpart whole percent6. Use a clean sheet of paper and Examples 1 –3 on pages 263 and 264 inyour textbook. Starting with Example 1, cover up everything in theexample with your paper except the title and its question. Now try towork the problem without looking at the book. Then compare your workto the work in the book. Repeat this with the other two examples.Chapter 5 SC StudyText, Course 3 153

5-3NAME DATE PERIODStudy GuideAlgebra: The Percent ProportionSCAS 8-2.7You can use a percent proportion to fi nd a missing part, whole, or percent._ partwhole = percentExample 1 12 is what percent of 60?__ partwhole→_→ 12_ p_60 = 100⎫⎬⎭percent Replace a with 12 and b with 60.12 · 100 = 60 · p Find the cross products.1,200 = 60p Multiply._ 1,200=_ 60pDivide each side by 60.60 6020 = p 12 is 20% of 60.Example 2 What number is 40% of 55?__ part →_ a_whole → 55 = 40_ ⎫ ⎬ percent Replace p with 40 and b with 55.100 ⎭a · 100 = 55 · 40Find the cross products.a = 22 Use similar steps to solve for a.So, 22 is 40% of 55.ExercisesWrite a percent proportion and solve each problem.Round to the nearest tenth if necessary.1. 3 is what percent of 10? 2. What number is 15% of 40?3. 24 is 75% of what number? 4. 86 is what percent of 200?5. What number is 65% of 120? 6. 52 is 13% of what number?7. 35 is what percent of 56? 8. What number is 12.5% of 88?9. 161 is 92% of what number? 10. 45 is what percent of 66?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.11. What number is 31.5% of 200? 12. 81 is 54% of what number?154 SC StudyText, Course 3 Chapter 5

5-3NAME DATE PERIODHomework PracticeAlgebra: The Percent ProportionWrite a percent proportion and solve each problem. Round to thenearest tenth if necessary.1. 6 is what percent of 24? 2. 125 is what percent of 375?SCAS 8-2.73. What is 20% of 80? 4. What is 14% of 440?5. 28 is 35% of what number? 6. 63 is 63% of what number?7. 16.24 is what percent of 14? 8. Find 350% of 49.9. What percent of 120 is 24? 10. What percent of 84 is 6?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.11. What is 7.5% of 225? 12. 9 is what percent of 660?13. 110 is 21.1% of what number? 14. Find 6.4% of 72.15. What percent of 160 is 1? 16. 83 is 12.5% of what number?17. GAMES Before discarding, Carolee has 4 green cards, 3 red cards, 3 orangecards, and 1 gold card. If she discards the gold card, what percent of herremaining cards are red?Chapter 5 SC StudyText, Course 3 155

NAME DATE PERIOD5-3 Problem-Solving PracticeAlgebra: The Percent ProportionSCAS 8-2.71. COMMUTING On his trip across town,Mark was stopped by a red light at 9out of 15 intersections. At what percentof intersections was Mark stopped by ared light?2. CLIMATE In Las Vegas, Nevada, theskies are clear on 92% of the days.How many days in the month of Junewould you expect the skies to be clearin Las Vegas? Round the answer to thenearest day.3. POLLING A recent poll shows that 65%of adults are in favor of increasedfunding for education. The number ofadults surveyed for the poll was 140.How many of the adults surveyedwere in favor of increased funding foreducation?4. FLOWERS Mika’s rosebush had 24blooms in the first week of May. Thiswas 80% as many blooms as Tammy’srosebush had during the same period.How many blooms did Tammy’srosebush have?5. SPORTS In a recent season, the SanFrancisco Giants won 75 out of162 games. What percent of theirgames did they win? Round to thenearest tenth if necessary.7. DRIVING TEST On the written portionof her driving test, Sara answered84% of the questions correctly. If Saraanswered 42 questions correctly, howmany questions were on the drivingtest?6. GOLF On a recent round of golf, Shanamade par on 15 out of 18 holes. Onwhat percent of holes did Shana makepar? Round to the nearest tenth ifnecessary.8. EDUCATION In a certain small, town,65% of the adults are college graduates.How many of the 240 adults living inthe town are college graduates?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.156 SC StudyText, Course 3 Chapter 5

NAME DATE PERIOD5-5 Study GuideSCAS 8-1.1Problem-Solving Investigation: Reasonable AnswersIn the four-step problem-solving plan, remember that the last step is to check forreasonable answers.UnderstandPlanSolveCheck• Determine what information is given in the problem and what you need to fi nd.• Select a strategy including a possible estimate.• Solve the problem by carrying out your plan.• Examine your answer to see if it seems reasonable.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Example 1 The cost of a guitar is $300. Margaret works at the musicstore and can buy the guitar for 65% of the price. Will she have to pay moreor less than $200?Understand You know the cost of the guitar. Margaret can buy the guitar for 65% of theprice. You want to know if the guitar will cost more or less than $200.Plan Find a close estimate. 65% is close to 66.66% or 2_ . Multiply the cost by the3estimate.$300 × 2_3 = $200Solve Think. $300 × 2_ = $200. 65% is less than 66.66%, so she will have to pay3less than $200.Check Find 65% of $300. $300.00 × .65 = $195.Exercises$195 < $200.00 The answer is reasonable.For Exercises 1–5, determine a reasonable answer.1. JOBS Maxine is paid $9.25 an hour to work at the bookstore. If she is saving to buy anew video game system that costs $360, will she have to work 30, 40, or 50 hours?2. MONEY Jeff brings $120 to purchase winter clothes. He buys a coat for $57.36. Hewants to purchase a pair of jeans for $28.95 and a pair of boots for $54.98. Doeshe have enough money with him to make these two purchases?3. SURVEY In a recent survey, 56% of students at Trenton Middle School work atpart-time jobs during the school year. If there are 1,378 students in the school,is 550, 650, or 750 a reasonable estimate for the number of students who workpart time during the school year?4. SHOPPING Byron took $80 to the mall to buy gifts. He spent $28.73 on a video game.He wants to purchase a book for $13.89 and a laptop bag for $39.99. Does he haveenough money with him to make these two purchases?5. ATTENDANCE There are 1,200 students at Hillsboro Middle School. If 43% of thestudents attend an exhibit given by the art department, would the number of studentswho attended be 924, 516, or 430?Chapter 5 SC StudyText, Course 3 157

NAME DATE PERIOD5-5 Skills PracticeSCAS 8-1.1Problem-Solving Investigation: Reasonable AnswersFor Exercises 1–12, estimate and rewrite the problem to determine a reasonableanswer.1. 53% of 813 2. 27% of 4563. 87% of 1,978 4. 11% of 1765. 67% of 543 6. 8% of 6977. 81% of 2,211 8. 48% of 7629. 4% of 4,874 10. 23% of 58411. 45% of 1,252 12. 32% of 620For Exercises 13–24, estimate and rewrite the problem to determine areasonable answer.13. $54.87 + $28.97 14. $22.38 + $46.1215. $94.67 + $17.78 16. $88.88 + $36.3217. $7.87 + $48.31 18. $74.78 + $75.1819. $37.42 + $85.01 20. $28.69 + $35.0921. $108.24 + $127.95 22. $89.99 + $79.99Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.23. $217.87 + $186.65 24. $46.22 + $86.86158 SC StudyText, Course 3 Chapter 5

NAME DATE PERIOD5-5 Homework PracticeSCAS 8-1.1Problem-Solving Investigation: Reasonable AnswersMixed Problem SolvingUse the reasonable answer strategy tosolve Exercises 1 and 2.1. POPULATION About 9.5% of thepopulation of New Mexico is NativeAmerican. If the population of NewMexico is 1,874,614, would the numberof Native Americans living in NewMexico be about 180,000, 360,000, or900,000?4. MONEY After Latoya gave 35% of herallowance to her brother and 25% ofher allowance to her sister, she had$12 left. How much was Latoya’sallowance?2. HOMES Mr. and Mrs. Whatley wantto buy a new home for $245,000. Thebank requires 20% of the price ofthe home as a down payment for theloan. Should the Whatleys plan to pay$5,000, $25,000, or $50,000 as the downpayment?5. ELECTIONS A county with 31,500registered voters is buying new votingmachines. State law requires that thecounty have one polling place for every750 registered voters and 4 votingmachines per polling place. How manynew voting machines should the countyorder?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Use any strategy to solve Exercises 3–6.Some strategies are shown below.Problem-Solving Strategies• Work backward.• Look for a pattern.• Draw a diagram.3. SPORTS Three teams participating ina track meet have 25 members, 29members, and 33 members. The coachof the hosting team wants to have threebottles of water for each athlete. Ifeach case of water contains 24 bottles,should the coach buy 4, 12, or 20 casesof water?6. GEOMETRY Brandon is drawing arectangle similar to the one belowexcept that each side of his rectangleis 2 1_ times longer. Find the area of2Brandon’s rectangle.8 cm2.4 cmChapter 5 SC StudyText, Course 3 159

NAME DATE PERIOD5-5 Problem-Solving PracticeSCAS 8-1.1Problem-Solving Investigation: Reasonable AnswersFor Exercises 1 –8, determine a reasonable answer.1. SHOPPING A coat that normally costs$90 is on sale at 45% off. If Jared brings$45 with him, will he have enoughto purchase the coat? Explain.2. MONEY Helen took $100 to the store.She spent $44.56 on a video game. Shewants to buy a CD for $18.79 and a bookfor $32.89. Does she have enough moneywith her to make these two purchases?Explain.3. SCHOOL There are 438 students atNewton Middle School. If 38% of thestudents participate in after-schoolsports, would the number of studentsinvolved in sports be about 110, 170,or 220? Explain.4. JOBS Fredrick is paid $12.35 per hourat his part-time job at a landscapingcompany. If he is saving to buy a newMP3 player that costs $289, will he haveto work 20, 25, or 30 hours? Explain.5. INTEREST A savings account earns5.23% interest in one year. If theaccount holds $4,978 for the entire year,about how much will it earn in interest?Explain.7. CARS Maryanne is saving to buy a car.She wants to have a down payment of10% for a car that costs $11,783. So far,she has saved $487. If she saves $125each week for the down payment, howsoon can she buy the car?6. SURVEY In a recent survey, 22% ofstudents at Belletown Middle Schoolparticipate in music programs at theschool. If there are 1,417 studentsin the school, is 280, 420, or 560 areasonable estimate for the numberof students who participate in musicprograms? Explain.8. GAS Lucie’s car averages about34.7 miles per gallon. If a full tankholds 14.3 gallons of gas, about how farcan she drive on a full tank of gas?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.160 SC StudyText, Course 3 Chapter 5

NAME DATE PERIOD5-6 Explore Through ReadingPercent and EstimationGet Ready for the LessonRead the introduction at the top of page 275 in your textbook.Write your answers below.1. Round the distance from Jupiter to the sun to the nearest hundred millionkilometers.SCAS 8-2.72. Round 19% percent to the nearest ten percent.3. Use mental math to estimate the distance from Earth to the sun.Read the Lesson4. What are compatible numbers?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5. Are 1_86. Are 6_7and 56 compatible numbers? Explain.and 32 compatible numbers? Explain.Remember What You LearnedDescribe how to estimate the following using compatible numbers.7. 65% of 648. 18 out of 59 is what percentChapter 5 SC StudyText, Course 3 161

5-6NAME DATE PERIODStudy GuidePercent and EstimationSCAS 8-2.7You can use compatible numbers to estimate a percent of a number. Compatible numbers are twonumbers that are easy to divide mentally.Example 1 Estimate 35% of 60.35% is about 33 1_31_of 60 is 20.3So, 35% of 60 is about 20.% or1_3 . 1_and 60 are compatible numbers.3Example 2 Estimate what percent corresponds to 23 out of 59.23_59 ≈ _ 24 or2_23 is about 24, and 59 is about 60.60 52_5 = 40%So, 23 out of 59 is about 40%.ExercisesEstimate.1. 11% of 60 2. 24% of 363. 81% of 25 4. 19% of 415. 32% of 66 6. 67% of 44Estimate each percent.7. 7 out of 15 8. 6 out of 239. 5 out of 51 10. 8 out of 3511. 13 out of 17 12. 17 out of 26Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.162 SC StudyText, Course 3 Chapter 5

NAME DATE PERIOD5-6 Homework PracticeSCAS 8-2.7Percent and EstimationEstimate.1. 39% of 80 2. 66% of 72 3. 40% of 89 4. 75% of 355. 19% of 79 6. 72% of 51 7. 53% of 199 8. 23% of 1629. 48.5% of 151 10. 76.5% of 303 11. 148% of 69 12. 226% of 81Estimate each percent.13. 8 out of 37 14. 4 out of 19 15. 10 out of 21 16. 29 out of 90Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.17. 7 out of 9 18. 29 out of 40 19. 9 out of 31 20. 11 out of 5921. ANALYZE TABLES The table gives the land area of one county in eachstate and the land area of the entire state. Estimate the percent of theland area of each state that is in the county. Then determine whichcounty has the greatest percent of its state’s land area. Round to thenearest tenth if necessary.CountyLand Area ofCounty(square miles)Land Area ofEntire Estate(square miles)Kent County, MD 279 9,774Marion County, SC 489 30,109Newport County, RI 104 1,045Source: U.S. Census BureauChapter 5 SC StudyText, Course 3 163

NAME DATE PERIOD5-6 Problem-Solving PracticePercent and EstimationSCAS 8-2.71. FITNESS At the office where Michaelworks, 8 out of 17 employees work outat-least twice a week. Estimate thepercent of employees that work out atleast twice a week.2. PETS Niki asked 25 of her classmatesabout what pets they have at home.Eleven of the 25 said they had both acat and a dog. Estimate the percent ofNiki’s classmates that have both a catand a dog.3. BOOKS Jorge has read 19 novelsthis year, 4 of which were sciencefiction. Estimate the percent of novelsthat were science fiction.4. PARKS The students in Kara’s eighthgrade science class determined that 9out of 33 trees at a local park are pinetrees. Estimate the percent of pinetrees at the park.5. BAND The marching band at DurangoHigh School has 120 members. Ofthese, 18% are ninth-grade students.Estimate the number of ninth-gradegrade students in the marching band.7. HOTELS At the Westward Inn hotel,48% of the rooms face the courtyard.The hotel has 91 rooms. Estimate thenumber of rooms that face thecourtyard.6. RESTAURANTS In one east-coast city,35% of the restaurants in the cityare on the bay. The city has 180restaurants. Estimate the number ofrestaurants that are on the bay.8. FARMING Roy has planted soybeans on68% of his farm this year. Roy’s farmhas 598 acres of land. Estimate thenumber of acres of soybeans that Royhas this year.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.164 SC StudyText, Course 3 Chapter 5

NameChapter 5 TestMastering the SC StandardsDateCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.This chapter includes a review of some Grade 7Number and Operations Standards.1 A large bag of marbles contains 14% greenmarbles, 35% red marbles, 18% yellowmarbles, 24% white marbles, and 9%purple marbles. Kristen puts 400 of thesemarbles in a jar. Which proportion can beused to find y, the total number of yellowmarbles that Kristen would expect to findin the jar?A _ 400y = 18_100B _ y400 = 18_18_100Cy_400 = 100Dy_18 = _ 1004008-2.72 Players on the Tigers basketball team make15 out of 24 free throws in a game. What isthe best estimate for the team’s successfulcompletion rate?A about 60%B about 70%C about 75%D about 80%3 What is 130% of 90?A 90B 108C 117D 1258-2.74 Last year there were 16 students in themath club. This year there are 20 students.What was the percent increase in the sizeof the math club?A 20%B 25%C 30%D 35%Review of 7-2.55 How much simple interest is earned on adeposit of $800 at an annual rate of 5%after 2 years?A $40B $60C $75D $80Review of 7-2.56 Inez buys a jacket that regularly sells for$42. What is the best estimate for the priceof the jacket if it is on sale for 20% off?A $25B $32C $34D $408-2.7Review of 7-2.1Chapter 5 SC StudyText, Course 3 165

NameDateChapter 5 Test (continued)Mastering the SC Standards7 Emily and her dad went bird watching.They wanted to see if they could spot SouthCarolina’s state bird, the Carolina wren.At the end of the day, they saw 4 bluebirds,6 Carolina wrens, and 3 woodpeckers.Which equation can be used to find c, thepercent of Carolina wrens they saw?A4_6 = c_100B6_3 = _ 1006_cC _13 = 100c6_ D13 = c_1008-2.710 Emily reads an article that states that onaverage 15% of men are left-handed and9% of women are left-handed. Emilygathers her own data by surveying adults ata basketball game. She finds that 5 out ofthe 26 women are left-handed. What is thedifference in percentage between thestudy’s findings and Emily’s experimentalresults?A 4.2%B 6.2%C 10.2%D 19.2%Review of 7-2.58 If 0.2 < x < 30%, what could be thevalue of x?A1_4B 1_3C 1_2D 3Review of 7-2.39 Mr. Davis buys a gallon of paint for $20.95,two paintbrushes for $2.95 each, a painttray for $0.99, and a paint scraper for$4.15. The tax is 8%. What is a goodestimate of the amount of tax he pays?A $1.50B $2.00C $2.50D $3.0011 Which number is the best estimate for% of 268?1_2A 0.5B 1C 2D 4Review of 7-2.1Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.8-2.7166 SC StudyText, Course 3 Chapter 5

6NAME DATE PERIODAnticipation GuideGeometry and Spatial ReasoningSTEP 1 Before you begin Chapter 6• Read each statement.• Decide whether you Agree (A) or Disagree (D) with the statement.• Write A or D in the first column OR if you are not sure whether you agreeor disagree, write NS (Not Sure).STEP 1A, D, or NSStatement1. Adjacent angles share a common side and are alwayscongruent.2. Two angles whose measures have a sum of 180° aresupplementary angles.3. All obtuse angles have measures less than 90°.4. The strategy of problem solving which uses an existing ruleto make a decision is called deductive reasoning.5. The sum of the measures of the angles of a polygon is 180°.STEP 2A or DCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6. If two polygons are congruent they are the same shape butnot necessarily the same size.7. The letter D has one line of symmetry.8. All corresponding points on a figure and its reflection are thesame distance from the line of reflection.9. The vertex (3, -5) of a square would have coordinates(-1, -3) after a translation 4 units to the left and 2 unitsdown.10. The image of a figure after a translation is either smalleror larger than the original figure.STEP 2 After you complete Chapter 6• Reread each statement and complete the last column by entering an A or a D.• Did any of your opinions about the statements change from the first column?• For those statements that you mark with a D, use a piece of paper to writean example of why you disagree.Chapter 6 SC StudyText, Course 3 167

NAME DATE PERIOD6Family ActivityState Test PracticeFold the page along the dashed line. Work each problem on another piece ofpaper. Then unfold the page to check your work.1. The figure shown below has beentranslated 4 units down and 5 unitsto the right from its original location.Oyx2. The following shape is to be reflectedover the y-axis.y''''OxWhere was the original quadrilateral?A A(-4, -3); B(-4, -6); C(0, -6); D(-1, -3)B A(-5, -4); B(-4, -4); C(0, -7); D(-1, -7)C A(-5, -3); B(-4, -6); C(0, -6); D(-1, -3)D A (-4,-4); B(0, -4); C(1, -7); D(-3, -7)Fold here.Solution1. Hint: Moving an object to the right or upis a positive translation. Moving an objectdown or left is a negative translation.Do the opposite movement to find theoriginal location. That is, move 4 units upand 5 units left.4 units up means add 4 to they-coordinate and 5 units left means tosubtract 5 units from the x-coordinate.Look at point A.(0, -7) → (0 - 5, -7 + 4)(-5, -3)Check the other vertices, but choiceC is the only one with these coordinatesfor A.Where will the vertices of the reflectionbe located?A X′(2, 3); Y′(6, 8); Z′(6, 3)B X′(2, 3); Y′(6, 3);Z′ (6, 8)C X′(-2, -3); Y′(-6, -8); Z′(-6, -3)D X′(-2, -8); Y′(-6, -3); Z′(-6, -8)Solution2. Hint: A reflection should look like themirror image of the original. The twoimages (the original and the reflected)should be equally spaced from the lineof reflection.Since we are reflecting over the y-axis,the y-coordinates will not change(The image will not move up or down).The x-coordinates will be the opposite(or negative) of their current value sothat they are on the other side of they-axis.Point X′: (2, 3)Point Y′: (6, 8)Point Z′: (6, 3)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.The answer is C. The answer is A.168 SC StudyText, Course 3 Chapter 6

NAME DATE PERIOD6-2 Study GuideProblem-Solving Investigation: Use Logical ReasoningYou may need to use logical reasoning to solve some problems.SCAS 8-1.3, 8-1.5UnderstandPlanSolveCheck• Determine what information is given in the problem and what you need to fi nd.• Select a strategy including a possible estimate.• Solve the problem by carrying out your plan.• Examine your answer to see if it seems reasonable.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ExampleA plane figure has four sides. The figure has only two congruentsides and two pairs of congruent angles. Is the figure a square,rectangle, parallelogram, rhombus, or trapezoid? Did you usedeductive or inductive reasoning?Understand We know that a plane figure has four sides and the figure has only twocongruent sides and two pairs of congruent angles. We need to see if thefigure is a square, rectangle, parallelogram, rhombus, or trapezoid.PlanSolveCheckExercisesLet’s look at the characteristics of these different figures.A square or rhombus has four congruent sides.The figure is not a square or a rhombus.A rectangle or parallelogram has two pairs ofcongruent sides. The figure is not a rectangleor a parallelogram.An isosceles trapezoid can have two congruent sidesand two pairs of congruent angles. The figure could be a trapezoid.Since all choices but the trapezoid were eliminated, the figure is a trapezoid.Because you used existing rules about four-sided figures to make a decision,you used deductive reasoning.For Exercises 1–3, solve each problem using logical reasoning.1. GEOMETRY Jennifer draws a square on a piece of paper and uses a ruler to draw oneline through the square to create two shapes. What is the maximum number of sidesthat either of these shapes can have, and how would the line have to be drawn to createit?2. MODELS You have 30 toothpicks. You can create two adjacent squares using 7 toothpicksif the adjacent square shares a toothpick for the side between them. How many totalsquares could be created this way with 30 toothpicks, if the squares are formed ina row?3. AGES You and your grandfather have a combined age of 84 years. If your grandfatheris 6 times as old as you are, how old are you? Explain.Chapter 6 SC StudyText, Course 3 169

6-2NAME DATE PERIODSkills PracticeProblem-Solving Investigation: Use Logical ReasoningFor Exercises 1–6, state whether the example uses deductive reasoningor inductive reasoning.1. After checking the house numbers on several streets in yourneighborhood, you discover that houses that face north always have anodd house number.2. You determine the type of shape that a sticker is by examining its sidesand angles.3. You use a set of clues about how received higher or lower scores on amath test as compared with other students to place the students in orderfrom lowest grade to highest grade.4. You roll a number cube 1,000 times and discover that it lands on thenumber 4 twice as many times as the number 1.5. You find a way to use 2 larger containers to measure out the exactamount for a smaller container.6. You determine what types of shapes will be created by connecting thecorners of a regular hexagon.SCAS 8-1.3, 8-1.5For Exercises 7–10, solve each problem using logical reasoning.7. Use a 5-liter container and a 3-liter container to measure out 4 liters ofwater into a third container.8. How can you create two right triangles and an isosceles trapezoid bydrawing two straight lines through a square?9. How can you arrange four squares with 6-inch sides to create a figurewith a perimeter of 48 inches?10. Use a 7-inch-long craft stick and a 4-inch-long eraser to draw a 10-inchline.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.170 SC StudyText, Course 3 Chapter 6

6-2NAME DATE PERIODHomework PracticeProblem-Solving Investigation: Use Logical ReasoningMixed Problem SolvingFor Exercises 1 and 2, solve eachproblem using logical reasoning.1. NUMBER SENSE Simplify each product ofpowers. Then use logical reasoning tosimplify 1 0 4 × 0. 1 4 , 1 0 5 × 0. 1 5 , and10 4 × 0. 1 12 .Product ofPowers10 2 × 0. 1 21 0 3 × 0. 1 31 0 7 × 0. 1 7SimplifiedFormSCAS 8-1.3, 8-1.54. SHOPPING Brittany bought five items atthe grocery store for her mother. Fromthe given clues, list the items fromleast expensive to most expensive.• The peanut butter cost less than thesliced turkey.• The sliced turkey cost half as muchas the birthday cake.• The peanut butter cost $0.20 morethan the milk.• The price of the lettuce was 40%of the price of the milk.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2. MEASUREMENT You have a pen that is 6inches long and a pencil that is 7 incheslong. Explain how you can use the penand pencil to draw a line segment thatis 3 inches long.Use any strategy to solve Exercises 3–6.Some strategies are shown below.Problem-Solving Strategies• Look for a pattern.• Draw a diagram.• Use logical reasoning.3. SPORTS At the end of a baseball game,the winning team had three more runsthan their opponents. If they had scored1 more run, they would have had twiceas many as their opponents. How manyruns did each team have?5. SOLAR SYSTEM Jupiter is the largestplanet in the solar system witha diameter of 88,736 miles. Saturnis the second largest planet witha diameter of 74,978 miles. How muchgreater is the diameter of Jupiter thanthe diameter of Saturn?6. TRAVEL Mr. Bradley often flies fromChicago to San Francisco and backagain, a total distance of 3,716 miles.If he made this trip 25 times last year,find the total distance Mr. Bradleytraveled on these trips.Chapter 6 SC StudyText, Course 3 171

NAME DATE PERIOD6-2 Problem-Solving PracticeProblem-Solving Investigation: Use Logical ReasoningSolve each problem using logical reasoning.SCAS 8-1.3, 8-1.51. GEOMETRY A solid figure has twotriangular faces and three square faces.Is the figure a pyramid, a triangularprism, or a cube? Explain.2. MEASUREMENT Can you use a 4-pintcontainer and a 9-pint container to filla 10-pint container? Explain.3. MONEY After a visit to the mall, Rayand Mary counted their money to seehow much they had left. Ray said,“If I had $8 more, I would have as muchas you.” Mary replied, “If I had $8 more,I would have twice as much as you.”Explain.5. NUMBER SENSE The sum of twonumbers is equal to 15. The productof the numbers is 44. What are the twonumbers?4. SPORTS Mark, Rich, Sue, Matt, andTracey were the first five finishersof a race. From the given clues, statethe order in which they finished: Richfinished behind Matt, Sue was fifth,Tracey finished ahead of Mark, andMatt finished behind Mark.6. GEOMETRY A regular hexagon has6 hexagons surrounding it. Each ofthe 6 hexagons shares a side with themiddle hexagon and with the hexagonnext to it. If each of the hexagons has2-inch sides, what is the perimeter ofthe figure?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.172 SC StudyText, Course 3 Chapter 6

NameChapter 6 TestMastering the SC StandardsDateThis chapter includes a review of some Grade 7Geometry Standards.3 If ∠7 in the figure below measures 143º,what is the measure of ∠4?1 If △ABC is translated 5 units to the leftand 3 units up, what are the newcoordinates of point A?y12345678A 33ºB 37ºOBxC 110ºD 143ºReview of 7-4.5ACCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A (-4, -1) C (-1, -4)B (-2, 1) D (0, 5)2 Consider the two triangles below.2 cm1.5 cm2 cm8-4.2What other information is needed to provethat the triangles are congruent?A The length of side xB The measure of angle BC The length of side aD The measure of angle F4 What will the coordinates of point L′ be ifthe triangle is reflected across the y-axis?y44321543 211 2 3 4 5 x12 L3 M45NA L′ (-3, -3)B L′ (3, -3)C L′ (-3, 3)D L′ (3, 3)8-4.2Review of 7-4.1Chapter 6 SC StudyText, Course 3 173

NameDateChapter 6 Test (continued)Mastering the SC Standards5 How many lines of symmetry does therectangle below have?7 The sum of the interior angles of a triangleis 180º. The sum of the interior angles of arectangle is 360º. The sum of the interiorangles of a hexagon is 720º. What is thesum of the interior angles of an octagon?A 0B 1C 2D 4A 630ºB 720ºC 900ºD 1,080ºReview of 7-4.10Review of 7-4.16 Two rectangles forming the roof of thehouse below are congruent. A roofingcompany charges $1.50 per square foot toshingle a roof.8 If △ABC is translated 3 units down and2 units to the left, what are the newcoordinates of point B?yWhat will be the cost for shingling the roofof the house?A $1,200B $1,800C $2,400D $3,600 Review of 7-4.1A (0, 1)B (4, -5)C (4, 1)D (0, -5)Ox8-4.2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.174 SC StudyText, Course 3 Chapter 6

7NAME DATE PERIODAnticipation GuideMeasurement: Area and VolumeSTEP 1 Before you begin Chapter 7• Read each statement.• Decide whether you Agree (A) or Disagree (D) with the statement.• Write A or D in the first column OR if you are not sure whether you agreeor disagree, write NS (Not Sure).STEP 1A, D, or NSStatement1. The distance from the center of a circle to any point on thecircle is called the radius.2. The diameter of a circle equals two times the radius.3. The formula for the area of a circle is A = 2πr or πd.4. The area of a composite figure can be found by separating it intoshapes whose areas you know how to find.5. A rectangular prism has six edges, six faces, and eight vertices.STEP 2A or DCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6. A rectangular pyramid has a rectangular base and fourtriangular faces.7. Measurements of volume are given in cubic units.8. The volume of any prism can be found by the formula V = lwh.9. The volume of a rectangular prism with the same base andheight as a rectangular pyramid will be 1_ that of the pyramid.310. The surface area of three-dimensional solids is given in squareunits.11. The height and slant height of a pyramid are the same.12. If two rectangular prisms are similar with a scale factor of 2,then the volume of the larger prism will be 6 times the volumeof the smaller prism.STEP 2 After you complete Chapter 7• Reread each statement and complete the last column by entering an A or a D.• Did any of your opinions about the statements change from the first column?• For those statements that you mark with a D, use a piece of paper to write anexample of why you disagree.Chapter 7 SC StudyText, Course 3 175

NAME DATE PERIOD7Family ActivityState Test PracticeFold the page along the dashed line. Work each problem on another piece ofpaper. Then unfold the page to check your work.1. Alexandria wants to know how wide herroom is. She knows the area is 156square feet and that the length is 12feet.2. Chaz is sending his brother (who is inthe army) a package to let him knowthat he is thinking of him. Thedimensions of the package are shownbelow.A 156 ft 2w14 cm12 ftWhat is the width of the room shownabove?A 12 feetB 13 feetC 14 feetD 15 feet15 cm12 cmWhat is the surface area of the boxChaz is sending to his brother?A 2,520 cubic centimetersB 2,520 square centimetersC 1,116 cubic centimetersD 1,116 square centimetersFold here.Solution1. Hint: The area of a rectangle is A = lw.The area of a rectangle is the lengthmultiplied by the width. In this case,we know the area and the length of theroom, so we will use the area formula tocalculate the width.A = lw156 ft 2 = 12 ft × ww = 156 ÷ 12w = 13 ftSolution2. Hint: The surface area of a prism is thesum of the surface areas of all of itsfaces.A rectangular prism has 6 faces. Theopposite sides are identical. The surfacearea is the sum of the surface areas ofthe 3 pairs of faces.Front and back:2 × 14 cm × 15 cm = 420 cm 2Ends:2 × 14 cm × 12 cm = 336 cm 2Top and bottom:2 × 12 cm × 15 cm = 360 cm 2Now add the areas(420 + 336 + 360) = 1,116 cm 2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.The answer is B. The answer is D.176 SC StudyText, Course 3 Chapter 7

7-1NAME DATE PERIODExplore Through ReadingCircumference and Area of CirclesGet Ready for the LessonComplete the Mini Lab at the top of page 352 in your textbook.Write your answers below.1. What distance does C represent?2. Find the ratio C_ for this object.d3. Repeat the steps above for at least two other circular objects and comparethe ratios of C to d. What do you observe?SCAS 8-5.44. Graph the data you collected as ordered pairs, (d, C). Then describe thegraph.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Circumference (cm)12963CdO 1 2 3 4 5Diameter (cm)Read the Lesson5. Explain the difference between the radius and the diameter of a circle.6. What is the ratio of the circumference of a circle to its diameter?7. Explain how you find the circumference of a circle given its radius is4 inches.Remember What You Learned8. One way to help you remember a formula or concept is to make up asaying. For example, to remember the formula for the area of a circle youmight use, “Fuzzy Wuzzy was a bear; area equals π (pi) r squared.” Makeup your own sayings to help you remember the formulas for thecircumference and area of circles.Chapter 7 SC StudyText, Course 3 177

7-1NAME DATE PERIODStudy GuideCircumference and Area of CirclesSCAS 8-5.4The circumference C of a circle is equal to its diameter d times π or 2 times theradius r times π, or C = πd or C = 2πr.The area A of a circle is equal to π times the square of the radius r,or A = π r 2 .drCExamples Find the circumference of each circle. Use 3.14 for π. Round to thenearest tenth.4 in.C = πdCircumference of a circleC = π · 4 Replace d with 4.C = 4πThis is the exact circumference.C ≈ 4 · 3.14 or 12.6 Replace π with 3.14 and multiply.The circumference is about 12.6 inches.5.4 mC = 2πrCircumference of a circleC ≈ 2 · 3.14 · 5.4 Replace r with 5.4.C ≈ 33.9Replace π with 3.14 and multiply.The circumference is about 33.9 inches.Example 3 Find the area of the circle. Use 3.14 for π. Round to the nearesttenth.A = π r 2Area of a circleA ≈ 3.14 (1.5) 2 Replace π with 3.14 and r with half of 3 or 1.5.A ≈ 3.14 · 2.25 Evaluate (1.5) 2 .A ≈ 7.1Multiply.The area is about 7.1 square feet.ExercisesFind the circumference and area of each circle. Use 3.14 for π. Round to thenearest tenth.1.3 ft1 cm4. The diameter is 9.3 meters.2.11 yd3.4.2 mCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5. The radius is 6.9 millimeters.6. The diameter is 15.7 inches.178 SC StudyText, Course 3 Chapter 7

NAME DATE PERIOD7-1 Homework PracticeCircumference and Area of CirclesSCAS 8-5.4Find the circumference of each circle. Use 3.14 for π. Round to the nearest tenth.1.2.3.4.14 mm10 in.22 yd25 mFind the area of each circle. Use 3.14 for π. Round to the nearest tenth.5.6.7.8.8.5 ft5.25 cm25 m6.75 miCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Find the circumference and area of each circle. Round to the nearest tenth.9. The diameter is 8 centimeters. 10. The radius is 4.7 inches.11. The radius is 0.9 feet. 12. The diameter is 6.8 kilometers._Another approximate value for π is 22 . Use this value to find the circumference7and area of each circle.13. The diameter is 14 yards. 14. The radius is 1 1_6 millimeters.15. WINDMILL Each sail on a windmill is 5 meters in length.How much area do the wings cover as they turn from theforce of the wind?16. ALGEBRA Find the radius of a circle if its area is314 square miles.Chapter 7 SC StudyText, Course 3 179

NAME DATE PERIOD7-1 Problem-Solving PracticeCircumference and Area of CirclesSCAS 8-5.41. FOUNTAINS The circular fountain infront of the courthouse has a radius of9.4 feet. What is the circumference ofthe fountain? Round to the nearesttenth.2. PETS A dog is leashed to a point in thecenter of a large yard, so the areathe dog is able to explore is circular.The leash is 20 feet long. What is thearea of the region the dog is able toexplore? Round to the nearest tenth.3. GARDENING A flowerpot has a circularbase with a diameter of 27 centimeters.Find the circumference of the base ofthe flowerpot. Round to the nearesttenth.4. WINDOWS Find the area of the windowshown below. Round to the nearesttenth.5. BICYCLES A bicycle tire has a radius of13 1_ inches. How far will the bicycle4travel in 40 rotations of the tire? Roundto the nearest tenth.1413 in.36 in.6. LANDSCAPING Joni has a circulargarden with a diameter of 14 1_ feet. If2she uses 2 teaspoons of fertilizer forevery 25 square feet of garden, howmuch fertilizer will Joni need for herentire garden? Round to the nearesttenth.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.180 SC StudyText, Course 3 Chapter 7

NAME DATE PERIOD7-2 Study GuideExample 1 Gift cards come in packages of 12 and envelopes come in packagesof 15. Meagan needs to send 600 cards in envelopes. How manypackages of each kind should she buy?Understand Meagan needs that same number of cards and envelopes.PlanFind out how many packages are needed for 300 cards in envelopes.Solve 12c = 300 15e = 300c = 25 e = 20Multiply the answers by 2.Check 2 × 25 = 50 packages of cards 2 × 20 = 40 packages of envelopesMeagan should buy 50 packages of cards and 40 packages of envelopes.Example 2 How many triangles of any size arein the figure at the right?UnderstandPlanWe need to find how many triangles are in the figure.Draw a simpler diagram.SCAS 8-1.8Problem-Solving Investigation: Solve a Simpler ProblemCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Solve 9 Count the smallest triangles, which have 1 triangle per side.3 Count the next largest triangles, which have 2 triangles per side.__ 1 Count the largest triangle, which has 3 triangles per side.13 Add together to fi nd the total triangles of any size.CheckExercisesNow repeat the steps for the original problem.16 Count the smallest triangles, which have 1 triangle per side.7 Count the next largest triangles, which have 2 triangles per side.3 Count the next largest triangles, which have 3 triangles per side.__ 1 Count the largest triangle, which has 4 triangles per side.27 Add together to fi nd the total triangles of any size.For Exercises 1–3, solve a simpler problem.1. Hot dogs come in packages of 10 and buns come in packages of 8. How many packagesof each will Mindy need to provide 640 hot dogs for a street fair?2. Mark can plant 3 tree saplings in an hour and Randy can plant 5 tree saplings inan hour. Working together, how long will it take them to plant 80 tree saplings?3. A restaurant has 18 square tables that can be pushed together to form one long tablefor large parties. Each square table can seat 2 people per side. How many people can beseated at the combined tables?Chapter 7 SC StudyText, Course 3 181

NAME DATE PERIOD7-2 Skills PracticeProblem-Solving Investigation: Solve a Simpler ProblemFor Exercises 1–3, rewrite the problem as a simpler problem.SCAS 8-1.81. Jerry has a square-shaped deep-dish pizza. What is the maximum number of piecesthat can be made by using 6 cuts?2. CDs come in packages of 25 and CD cases come in packages of 16. How many of eachtype of package will Lilly need to buy in order to make print 400 CDs and put them incases with none left of either?3. A restaurant has 10 triangular tables that can be pushed together in an alternating upand-downpattern as shown below to form one long table for large parties. Eachtriangular table can seat 3 people per side. How many people can be seated at thecombined tables?For Exercises 4–15, rewrite to solve a simpler problem and solve.Find a reasonable answer.4. 13 × 29 5. 48 + 32 + 876. 74 × (18 - 9) 7. 33 ÷ 98. 57_1139. 55 + 44 + 3310. 63 × 17 11. 532 - 38912. 78 × 41 - 276 13. 52 + 39 + 11114. 452 - 377 15. 67 × 34 × 12Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.182 SC StudyText, Course 3 Chapter 7

NAME DATE PERIOD7-2Homework PracticeSCAS 8-1.8Problem-Solving Investigation: Solve a Simpler ProblemMixed Problem SolvingUse the solve a simpler problemstrategy to solve Exercises 1 and 2.1. ASSEMBLY A computer company hastwo locations that assemble computers.One location assembles 13 computers inan hour and the other locationassembles 12 computers in an hour.Working together, how long will it takeboth locations to assemble 80computers?4. ANALYZE TABLES Mr. Brown has $1,050to spend on computer equipment. DoesMr. Brown have enough money to buythe computer, scanner, and software if a20% discount is given and the sales taxis 5%? Explain.ItemCostComputer $899Scanner $54Software $2782. AREA Determine the area of theshaded region if the radii of the sixcircles are 1, 2, 3, 4, 5, and 10centimeters. Use 3.14 for π. Round tothe nearest tenth if necessary.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Use any strategy to solve Exercises 3–6.Some strategies are shown below.Problem-Solving Strategies• Look for a pattern.• Use a Venn diagram.• Solve a simpler problem.3. NUMBER SENSE Find the sum of all theeven numbers from 2 to 50, inclusive.5. COPIER The counter on a businesscopier read 18,678 at the beginning ofthe week and read 20,438 at the end ofthe week. If the business was inoperation 40 hours that week, what wasthe average number of copies made eachhour?6. HUMMINGBIRD In normal flight ahummingbird can flap its wings 75times each second. At this rate, howmany times does a hummingbird flap itwings in a 20-minute flight?Chapter 7 SC StudyText, Course 3 183

NAME DATE PERIOD7-2 Problem-Solving PracticeProblem-Solving Investigation: Solve a Simpler ProblemFor Exercises 1 –6, use the solve a simpler problem strategy.SCAS 8-1.81. GEOMETRY Mark has a large pizza.What is the maximum number ofpieces that can be made by using 12cuts?2. TABLES A picnic area has 21 squaretables that can be pushed together toform one long table for large group.Each square table can seat 4 people perside. How many people can be seated atthe combined tables?3. PACKAGES Postcards come in packagesof 12 and stamps come in packages of20. How many of each type of packagewill Jessica need to buy in order tosend 300 postcards with no stamps orpostcards left over?5. BUILDING Jason can lay 40 bricks inone hour. Mark can lay 30 bricks in onehour. Jesse can lay 20 bricks in onehour. About how long will it them tobuild a wall that uses 900 bricks?4. JOBS Larry can stuff 150 envelopes inone hour. Harold can stuff 225envelopes in one hour. About how longwill it take them to stuff 10,000envelopes?6. GEOMETRY How many squares of anysize are in the figure?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.184 SC StudyText, Course 3 Chapter 7

NAME DATE PERIOD7-3 Explore Through ReadingSCASArea of Composite FiguresGet Ready for the LessonRead the introduction at the top of page 363 in your textbook.Write your answers below.1. Identify some of the polygons that make up the infield of the speedway.8-5.4, 8-5.5,8-1.62. How can the polygons be used to find the total area of the infield?Read the Lesson3. What is a composite figure?4. What is the first step in finding the area of a composite figure?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5. Explain how to divide up the figure shown.Remember What You Learned6. Look up the everyday definition of the word composite in a dictionary.How does the definition relate to what you learned in the lesson?Chapter 7 SC StudyText, Course 3 185

NAME DATE PERIOD7-3 Study GuideArea of Composite FiguresSCAS8-5.4, 8-5.5,8-1.6To fi nd the area of a composite fi gure, separate the fi gure into shapes whose areas you know how tofi nd. Then fi nd the sum of these areas.Example Find the area of the composite figure.The figure can be separated into a semicircle and trapezoid.Area of semicircleA = 1_A = 1_2 π r 2 A = 1_2 · 3.14 · (7) 2 A = 1_2Area of trapezoid2 h(b 1 + b 2 )· 10 · (14 + 18)A ≈ 77.0 A = 160The area of the figure is about 77.0 + 160 or 237 square inches.14 in.10 in.18 in.ExercisesFind the area of each figure. Use 3.14 for π. Round to the nearest tenth ifnecessary.1.8 mm5 mm6 mm2.9 ft6 ft9 ft3. 7 mi4. What is the area of a figure formed using a triangle with a base of6 meters and a height of 11 meters and a parallelogram with a base of6 meters and a height of 11 meters?5. What is the area of a figure formed using a semicircle with a diameter of8 yards and a square with sides of a length of 6 yards?6. What is the area of a figure formed using a rectangle with a length of9 inches and a width of 3 inches and a triangle with a base of 4 inchesand a height of 13 inches?7 mi14 mi5 mi5 miCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.186 SC StudyText, Course 3 Chapter 7

NAME DATE PERIOD7-3 Homework PracticeSCASArea of Composite FiguresFind the area of each figure. Use 3.14 for π. Round to the nearest tenth ifnecessary.1. 12 mi2. 3.8-5.4, 8-5.5,8-1.65 mi18 mi8 mi4.8 cm3.6 cm5 ft4 ft1.1 cm5.9 cm4.8 m6 m10 m 6 m5.9 yd 6.8 yd7 in.12 in.9 in.4 in.20 mIn each diagram, one square unit represents 10 square centimeters.Find the area of each figure. Round to the nearest tenth if necessary.7. 8.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.9. GAZEBO The Parks and Recreation departmentis building a gazebo in the local park with thedimensions shown in the figure. What is the areaof the floor?10. DECK The Pueyo family wants to paint the deckaround their swimming pool with the dimensionsshown in the figure. If a gallon covers 200 squarefeet, how many gallons of paint are needed to applytwo coats of paint?5 m11 m24 ft12 ft30 ft18 ft4 m24 ft36 ftChapter 7 SC StudyText, Course 3 187

NAME DATE PERIOD7-3 Problem-Solving PracticeSCASArea of Composite Figures8-5.4, 8-5.5,8-1.6LANDSCAPING For Exercises 1 and 2 use the diagram of ayard and the following information. The figure showsthe measurements of Marcus’ yard which he intendsto sod.15 ft20 ft30 ft1. Find the area of the yard. 2. One pallet of sod covers 400 squarefeet. How many full pallets of sod willMarcus need to buy to have enough forhis entire yard?50 ft3. ICE CREAM Leeor was asked to repaintthe sign for his mother’s ice creamshop, so he needs to figure out howmuch paint he will need. Find the areaof the ice cream cone on the sign.Round to the nearest tenth.6 in.12 in.5. SCHOOL PRIDE Cindy has a jacket withthe first letter of her school’s name onit. Find the area of the letter on Cindy’sjacket.10 in.2 in.2 in.2 in.6 in.6 in.4. HOME IMPROVEMENT Jim is planning toinstall a new countertop in his kitchen,as shown in the figure. Find the area ofthe countertop.2 ft2.5 ft6 ft2 ft3 ft3 ft 3 ft 2 ft2.5 ft6. SWIMMING POOLS The Cruz family isbuying a custom-made cover for theirswimming pool, shown below. The covercosts $2.95 per square foot. How muchwill the cover cost? Round to thenearest cent.15 ft25 ftCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.188 SC StudyText, Course 3 Chapter 7

7ANAME DATE PERIODStudy GuideSCAS 8-5.5Area and Perimeter of Triangles and TrapezoidsThe area A of a triangle equals half the product of its base b and its height h.A = 1_2 bh The base of atriangle can beany of its sides.bhThe height is thedistance from a baseto the opposite vertex.A trapezoid has two bases, b 1 and b 2 . The height of a trapezoid is thedistance between the two bases. The area A of a trapezoid equals halfthe product of the height h and the sum of the bases b 1 and b 2 .A = 1_2 h( b 1 + b 2 )The perimeter of any fi gure is the sum of the lengths of its sides.hb 1b 2Example 1Estimate 1_ (6)(5) = 152Find the area of triangle.A 1_ = bh Area of a triangle2· 6 · 4.52Replace b with 6 and h with 4.5.A = 13.5Multiply.A = 1_4.5 in.6 in.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.The area of the triangle is 13.5 square inches. This is close to the estimate.Example 2Find the area of the trapezoid.A 1_ =2 h( b 1 + b 2) Area of a trapezoidA 1_ =2 (4)(3 + 6) Replace h with 4, b 1 with 3, and b 2 with 6.A = 18Simplify.The area of the trapezoid is 18 square centimeters.ExercisesFind the area and perimeter of each figure. Round to the nearest tenth ifnecessary.1.8.6 ft 7 ft 8 ft12 ft2.9 mm13 mm9.4 mm7 mm3 cm4 cm6 cm3. 14 in. 4.8 cm6.1 in. 5 in.6.1 in.7 in.15 cm 13.5 cm13.6 cm18 cmChapter 7 SC StudyText, Course 3 189

NAME DATE PERIOD7ASkills Practice14. trapezoid: bases 5 ft and 3 1_2 ft, height 7 ft SCAS 8-5.5Area and Perimeter of Triangles and TrapezoidsFind the area and perimeter of each figure. Round to the nearest tenth ifnecessary.1.2.2.4 ft 2 ft 2.9 ft10 cm 13.45 cm3 ft9 cm3.4.3 ft4.3 ft 4 ft 4.3 ft6.5 ft5. 9.2 cm6.27 mm22 mm8.75 cm 7 cm 7.5 cm20.7 mm2 cm24 mm7.20.1 ft8.12.3 ft12 ft 12.3 ft10 in.6.9 in.25 ft7.2 in.5.6 in.9.10.12.8 cm12.2 cm7.5 cmFind the area of each figure. Round to the nearest tenth if necessary.11. triangle: base = 16 cm, height = 9.4 cm12. triangle: base = 13.5 in., height = 6.4 in.13. trapezoid: bases 22.8 mm and 19.7 mm, height 36 mm11.7 mm12 mm18 mm10 mm3.8 mm14 mm15.3 mm 18.4 mmCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.190 SC StudyText, Course 3 Chapter 7

7ANAME DATE PERIODHomework PracticeArea and Perimeter of Triangles and TrapezoidsFind the area and perimeter of each figure. Round to the nearest tenth ifnecessary.1.11 ft 2.3.SCAS 8-5.56.3 m7.3 ft7 ft 7.3 ft10 in.6 in.35 4 in.4 m 4.8 m5 in.3.6 m7 ft4.14.3 cm12 cm16.7 cm5.5 yd13 2 yd4 yd5 yd6.12.3 mm7 mm18.4 cm9 yd10.1 mmCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.7. GEOGRAPHY The shape of Arkansas is roughlytrapezoidal with bases of 150 miles and 250 milesand a height of 260 miles. What is the approximatearea and perimeter of Arkansas?ALGEBRA Find the height of each figure.8. Area = 23,000 m 2 9. Area = 6,460 i n 2x m125 m275 mDraw and label each figure. Then find the area.250 miArkansas260 mi 278.6 mi196 in.136 in.150 mi10. a trapezoid with a height less than 11. a right triangle with a base greater5 feet and an area greater than than 10 meters and an area greater50 square feet than 75 square metersx in.Chapter 7 SC StudyText, Course 3 191

7ANAME DATE PERIODProblem-Solving PracticeSCAS 8-5.5Area and Perimeter of Triangles and Trapezoids1. GEOGRAPHY North Dakota has a shapethat is similar to a trapezoid with basesof about 323 miles and 354 miles and aheight of about 211 miles. What is theapproximate area of the state.2. PATIOS Greta is making a patio withthe dimensions given in the figure.What is the area and perimeter of thepatio?15 ft15 ft 16.5 ft8 ft3. FLAGS Malila wants to make theInternational Marine Signal flagshown which represents the numbersix. What is the area of the flag?4. SIGNS Estimate the area of the yieldsign.30 in.30 in.100 in.5 in.5. TILING A ceramics company wants toproduce tiles in the shape shown. Whatis the area of the surface of each tile?8.5 cm8.5 cm26 in.6. GARDENING Kinu wants to buy topsoilfor a section of her garden that has thedimensions shown in the figure. Whatis the area of this section of Kinu’sgarden?3.5 yd4 ydCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.192 SC StudyText, Course 3 Chapter 7

7-6NAME DATE PERIODExplore Through ReadingVolume of Pyramids and ConesGet Ready for the LessonComplete the Mini Lab at the top of page 380 in your textbook.Write your answers below.1. Compare the base areas and the heights of the two solids.SCAS 8-5.3, 8-5.22. Fill the pyramid with rice, sliding a ruler across the top to level theamount. Pour the rice into the cube. Repeat until the prism is filled. Howmany times did you fill the pyramid in order to fill the cube?3. What fraction of the cube’s volume does one pyramid fill?Read the Lesson4. How is the volume of a cone related to that of a cylinder?5. How is the volume of a pyramid related to that of a prism?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6. Fill in the table about what you know from the diagram. Then compute thevolume of the pyramid.6 in.11 in. length of rectangle8 in.Remember What You Learnedwidth of rectanglearea of baseheight of pyramidvolume of pyramid7. Explain why the radius and height of cones and pyramids always forma right angle.Chapter 7 SC StudyText, Course 3 193

NAME DATE PERIOD7-6 Study GuideVolume of Pyramids and ConesSCAS 8-5.3, 8-5.2PyramidV = 1_3 BhV = volume, h = height,B = area of the base or lwVolume FormulasConeV = 1_3 BhV = volume, h = height,B = area of the base or π r 2Example 1Find the volume of the pyramid.V = 1_ Bh Volume of a pyramid3V = 1_3 s 2 h The base is a square, so B = s 2 .V = 1_3 · (3.6) 2 · 9 s = 3.6, h = 9V = 38.88Simplify.The volume is 38.88 cubic meters.9 m3.6 m3.6 mExample 2 Find the volume of the cone. Use 3.14 for π.V = 1_3 π r 2 h Volume of a coneV = 1_3 · 3.14 · 52 · 10 π ≈ 3.14, r = 5, h = 10V ≈ 261.7SimplifyThe volume is about 261.7 cubic feet.ExercisesFind the volume of each solid. Use 3.14 for π. Round to the nearesttenth if necessary.1.4.3 yd 2.4 yd6 ft5.5 cm 3.8 cm10 m7 m5 cm6.5 in.6 in.7m10 ft5 ft5 m4 in.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.4 ft4 ft194 SC StudyText, Course 3 Chapter 7

7-6NAME DATE PERIODHomework PracticeVolume of Pyramids and ConesFind the volume of each pyramid. Use 3.14 for π. Round to the nearest tenth ifnecessary.1.5 ft2.2.1 cm3.22yd3SCAS 8-5.3, 8-5.23ft3 ft1.2 cm1.6 cm3 yd413ydFind the volume of each cone. Use 3.14 for π. Round to the nearest tenth ifnecessary.4.5.20 mm 6.5 in.3 in.18 mm10 in.2 in.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Find the volume of each solid. Use 3.14 for π. Round to the nearest tenth ifnecessary.2 ft7.6 mm 8. 4 ft9.1.5 yd2 mm8 mm8 mm5 ft10. PYRAMIDS The Great Pyramid has an astounding volume of about84,375,000 cubic feet above ground. At ground level the area of the baseis about 562,500 square feet. What is the approximate height of the GreatPyramid?3 ft2 yd0.9 ydChapter 7 SC StudyText, Course 3 195

NAME DATE PERIODMini-Project(Use with Lesson 7-6)Volume of SolidsSCAS 8-5.3, 8-5.2Trace the patterns on paper, cut them out, and tape their edges together tocreate a rectangular prism, triangular prism, pyramid, cone, and cylinder.1. Which solid do you think has the greatest volume?the least?2. Arrange the solids from greatest volume to least volume.Make an opening in each solid so you can fill it with rice. Compare theamount of rice it takes to fill each solid.3. Which solid holds the most rice? the least rice?4. Record the solids in order from most rice to least rice.5. Did the order change from Exercise 2 to Exercise 4?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6. Name something you learned about the volume of solids.196 SC StudyText, Course 3 Chapter 7

7BNAME DATE PERIODStudy GuideVolume of Pyramids, Cones, and SpheresSCAS 8-5.3Volume of a Sphere To fi nd the volume V of a sphere, use the formula V = 4_3 π r 3 , where r is theradius.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Example 1Find the volume of the sphere. Round to the nearest tenth.V 4_ =3 π r 3 Volume of a sphereV 4_ =3 π (5) 3 Replace r with 5.V ≈ 523.6 i n 3 Simplify.The volume is about 523.6 i n 3 .Example 2SOCCER A giant soccer ball has a diameter of 40 inches.Find the volume of the soccer ball. Then find how long it willtake the ball to deflate if it leaks at a rate of 100 cubic inchesper hour.UnderstandPlan5 in.You know the diameter of the soccer ball.You know the rate at which it is losing air.Find the volume of the ball.Find how long it will take to deflate.Solve V = 4_3 π r 3 Volume of a sphere= 4_3 π · 20 3 Since d = 40, replace r with 20.≈ 33,493.3 in 3Use a proportion._____100 i n 31 hour = 33,493.3 i n 3x hour100x = 33,493.3Simplify.x ≈ 334.9So, it will take approximately 335 hours for the ball to deflate.ExercisesFind the volume of each sphere. Round to the nearest tenth.1.3 cm2.14 ft3.8 m4. Sphere: radius 5.2 miles 5. Sphere: diameter 11.6 feetChapter 7 SC StudyText, Course 3 197

NAME DATE PERIOD7B Skills PracticeVolume of Pyramids, Cones, and SpheresFind the volume of each figure. Round to the nearest tenth, if necessary.1.2.3.16 m4 ft4 in.SCAS 8-5.37.5 m4.5 in.7.5 m4.5.5 ft 6.7 yd7 yd12 ft12 ft15 in.2 yd7. 20 ft23 ft8.9.5 mm15 cm10. Rectangular pyramid: length 7 feet, width 2.5 feet, height 8 feet11. Cone: radius 20 centimeters, height 30 centimeters14 cmCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.12. Sphere: radius 2 inches198 SC StudyText, Course 3 Chapter 7

NAME DATE PERIOD7B Homework PracticeVolume of Pyramids, Cones, and SpheresFind the volume of each figure. Round to the nearest tenth, if necessary.1.17 in.2.3.3 yd7 ftSCAS 8-5.312 in.3 yd12 in.4.10 m5.4.5 cm6.10 m12 m11 m38 mCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.7. Find the volume of rectangular pyramid with a length of 14 feet, a width of 12 feet,and a height of 9 feet.8. Find the radius of a sphere with a volume of 972π c m 3 .9. Find the height of a cone with a radius of 12 in. and a volume of 408π i n 3 .10. CONTAINERS A cone with a diameter of 3 inches has a height of 4 inches. A 2-inchsquare pyramid is being designed to hold nearly the same amount of ice cream. Whatwill be the height of the square pyramid? Round to the nearest tenth.Chapter 7 SC StudyText, Course 3 199

7BNAME DATE PERIODProblem-Solving PracticeVolume of Pyramids, Cones, and Spheres1. ARCHITECTURE Although the EiffelTower in Paris is not a solid pyramid,its shape approximates that of apyramid with a square base measuring120 feet on a side and a height of980 feet. If it were a solid pyramid,what would be the Eiffel Tower’svolume, in cubic feet?2. WEATHER After a snow storm, you anda friend decide to build a snowman.You use three spheres of snow to buildthe snowman. The bottom sphere hasa diameter of 4 feet, the middle has adiameter of 2 feet, and the head hasa diameter of 18 inches. What is thevolume of the snowman? Round youranswer to the nearest cubic foot.5. FARMING Mr. Mills has just finishedhis corn harvest. He filled 12 truckswith corn and needs to move thecorn to one of the two silos on hisfarm. Each truck bed is shaped like arectangular prism having dimensions10 feet wide, 20 feet long, and 6 feettall. Mr. Mills needs to fit all the cornin the same silo.40 ft8 ft25 ftSilo ASCAS 8-5.3Silo B8 ft15 ft50 ft3. ICE CREAM A spherical scoop of icecream is placed on a waffle cone. Thediameter of the ice cream scoop is6.4 centimeters. The waffle cone has adiameter of 5 centimeters and a heightof 9 centimeters. If all the ice creammelts before you eat any, how much ofthe melted ice cream will overflow thewaffle cone? Round your answer to thenearest tenth.4. HISTORY The Great Pyramid of Khufuin Egypt has a square base measuring756 feet on a side and a height of481 feet. The stones used to build theGreat Pyramid were limestone blockswith an average volume of 40 cubicfeet. How many of these blocks wereneeded to construct the Great Pyramid?Round your answer to the nearestwhole number.a. How much corn has Mr. Millsharvested?b. How much corn will each silo hold?c. Which silo should Mr. Mills put all ofhis corn in? How many more fulltruckloads of corn could he store in thelarger silo?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.200 SC StudyText, Course 3 Chapter 7

NAME DATE PERIOD7-9 Explore Through ReadingSCAS 8-5.1, 8-5.2Similar SolidsGet Ready for the LessonRead the introduction at the top of page 399 in your textbook.Write your answers below.1. If the model car is 4.2 inches long, 1.6 inches wide, and 1.3 inches tall,what are the dimensions of the original car?2. Make a conjecture about the radius of the wheel of the original carcompared to the model.Read the Lesson3. What is the scale factor for two similar solids?4. If a 6-meter high pyramid is a model of an actual Egyptian pyramid andthe scale factor is 1_ , what is the height of the actual pyramid?8Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5. A cube has a volume of 216 cubic feet. A smaller cube is similar by a scalefactor of 2. What is the length of a side of the smaller cube?Remember What You Learned6. You can calculate the slant height of either pyramid on page 399 usingthe Pythagorean Theorem by creating a right triangle with the pyramid’sheight, its slant height, and 1_ of the side of the square base. The slant2height is the hypotenuse. The slant height of the larger pyramid is about8.4 meters. How can you find the slant height of the smaller pyramidwithout using the Pythagorean Theorem?Chapter 7 SC StudyText, Course 3 201

NAME DATE PERIOD7-9 Study GuideSimilar SolidsSCAS 8-5.1, 8-5.2Similar solids have the same shape, their corresponding linear measures are proportional, and theircorresponding faces are similar polygons.Example 1 The cones at the right are similar. Find the height of cone A.8_x = 4_34x = 24x = 6Write a ratio.Find the cross products.8 in.4 in.Simplify.3 in.The height of the smaller cone is 6 inches.cone Acone BExample 2 The pyramids at the right are similar.Find the total surface area of pyramid B.The scale factor a_bis6_or3_4 2 .surface _____area of pyramid Asurface area of pyramid B = ( a_b ) 2Write a proportion._ 98.4S = ( 3__ 98.4S = 9_4( 3_2) 2 = 3_2 · 3_22) 2 Substitute the known values. Let S represent the surface area.or9_498.4 · 4 = 9S Find the cross products._ 393.6= 9S_9 9Divide each side by 9.43.7 ≈ S Simplify.The surface area of pyramid B is approximately 43.7 square centimeters.ExercisesFor Exercises 1 and 2, the solids in each pairare similar. Find the surface area of solid B.1. solid A solid B2.S 24 units 2scale factor 5For Exercises 3 and 4, find the value of x.3.x624164.xsolid B1.5Pyramid AS 98.4 cm 231.53solid APyramid BS 6 cm 4 cm1266S 180 units 2515Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.202 SC StudyText, Course 3 Chapter 7

NAME DATE PERIOD7-9 Homework PracticeSimilar SolidsFind the missing measure for each pair of similar solids. Round tothe nearest tenth if necessary.1.?3 ft9 ft15 ft2.?4 cm6 cmSCAS 8-5.1, 8-5.21 cm3.2.9 mm8.7 mm5.8 mm4.2 in.1 in.3 in.S = ?S = 288 mm2S = 10 in2S = ?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5.3 m5 m3V = 9 mV = ?7. MODEL TRAINS The caboose of an N scale model train is 4 1_1 inch represents 13 1_26.8 yd3V = 88 yd V = ?inches long. In the N scale,2feet. What is the length of the original caboose?8. ALGEBRA The volumes of two similar cylinders are 7 cubic meters and 56 cubic meters.Find their scale factor.For Exercises 9–11, use the similar prisms shown.9. Write the ratio of the surface areas and the ratioof the volumes of Prism B to Prism A.4 cmPrism AS = 144 cm24 yd2 cmPrism BV = 14 cm310. Find the surface area of prism B.11. Find the volume of prism A.Chapter 7 SC StudyText, Course 3 203

NAME DATE PERIOD7-9 Problem-Solving PracticeSimilar SolidsFor Exercises 1–6, find the missing measure for each pair of similarsolids. Round to the nearest tenth if necessary.SCAS 8-5.1, 8-5.21. ARCHITECTURE A model of a cylindricalgrain silo is 14 inches tall. On themodel 2 inches represents 5 feet. Whatis the height of the actual grain silo?2. AQUARIUMS A pet store has three sizesof aquariums. The dimensions of thesmallest aquarium are 12 in. × 16 in.× 10 in. If other sizes of aquariums are2 times and 2.5 times as large, whatare the dimensions of the otheraquariums?3. BUILDING A room has dimensions thatare 12 ft × 14 ft × 9 ft. A larger roomis 1.5 times as large in each dimension.What is the scale factor of the rooms'volumes? (Hint: the scale factor of thethree-dimensional volumes is not thesame as the scale factor in onedimension)14 ft5. MODELS An architectural model of askyscraper is shaped like a very tallpyramid. The length of the sides of thesquare base on the model are 6 inchesand the slant height is 24 inches. Ifthe scale factor of the model is12 ft1_400 ,what is the slant height of the actualbuilding?9 ft4. ART Ray takes a photo of a sculpturehe has just finished. In the photograph,the sculpture is 4 inches wide. If eachinch in the photograph represents2.5 feet, how wide is the sculpture?6. CARS Sam has a picture of his favoritetype of car. In the photo, the car is12 inches wide by 6 inches tall. If theactual height of the car is 54 inchestall, what is the actual length of thecar?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.204 SC StudyText, Course 3 Chapter 7

7CNAME DATE PERIODStudy GuidePrecision and AccuracySCAS 8-5.6Real world measurements are all approximations. The greater care in which a measurement is taken,the more accurate it will be.Accuracy is the degree to which a measurement is close to its exact value.The precision of a measurement depends on the smallest unit available on the measuring tool.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Look at the acorn at the right. You can measure thewidth of the acorn to the nearest inch, half-inch,quarter-inch, and eighth-inch.• To the nearest inch, its length is 1 inch.• To the nearest half-inch, its length is1 1_2 inches.• To the nearest quarter-inch, its length is1 1_4 inches.• To the nearest eighth-inch, its length is1 3_8 inches.The actual length of the acorn above is closer to its measuredvalue to the nearest eighth-inch than to the nearest quarter- orhalf-inch. You can measure objects to an appropriate degree ofaccuracy.Exercisesin.1 2Choose the correct term to determine the necessary level of precisionin each measurement situation.1. The weight of a child taken at a sports physical would be given to thenearest (tenth of a pound, tenth of an ounce).2. The amount of time needed to cook a batch of cookies would be described in(minutes, seconds).3. A person building a house measures the beams to the nearest (inch, eighthof an inch).Chapter 7 SC StudyText, Course 3 205

7CNAME DATE PERIODSkills PracticePrecision and AccuracyMeasure the length of each object below to an appropriate degree of accuracy.Choose from inch, half-inch, quarter-inch, or eighth-inch. Justify your response.1. 2.SCAS 8-5.63. 4.5. 6.7. 8.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.206 SC StudyText, Course 3 Chapter 7

NAME DATE PERIOD7C Homework PracticeSCAS 8-5.6Precision and AccuracyMeasure the length of each object below to an appropriate degree ofaccuracy. Choose from inch, half-inch, quarter-inch, or eighth-inch.1. 2.3. 4.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5.Choose the correct term to determine the necessary precision in eachmeasurement situation.6. A person making curtains measures the fabric to the nearest (inch, eighthof an inch).7. The time of an airport layover is described in (minutes, hours).8. In a pharmacy, medicine is measured to the nearest 0.01 (gram, kilogram).Chapter 7 SC StudyText, Course 3 207

NAME DATE PERIOD7C Problem-Solving PracticeSCAS 8-5.6Precision and Accuracy1. Look at the peapod below.2. Look at the eraser below.Is the length of the peapod measured tothe nearest eighth-inch more accuratethan when measured to the nearestquarter-inch? Justify your response.Is the length of the eraser measuredto the nearest inch more accurate thanmeasured to the nearest half-inch?Justify your response.3. Look at the ear below.4. Look at the egg below.Is the height of the ear measured to thenearest eighth-inch more accurate thanwhen measured to the nearest quarterinch?Justify your response.Is the length of the egg measured tothe nearest quarter-inch more accuratethan when measured to nearest halfinch?Justify your response.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.208 SC StudyText, Course 3 Chapter 7

NAME DATE PERIOD7D Study GuideSCAS 8-5.7Relating Customary and Metric UnitsBoth customary and metric measurements are used in the United States. Therefore, it is agood idea to develop some sense of the relationships between the two systems. The tablesshow the approximate equivalents between customary and metric units.Units of LengthCustomary Metric Metric Customary1 in. ≈ 2.5 cm 1 cm ≈ 0.4 in.1 yd ≈ 0.9 m 1 m ≈ 1.1 yd1 mi ≈ 1.6 km 1 km ≈ 0.6 miExample 1Complete each sentence.a. 42 in. ≈ cm b. 6 m ≈ ydThere are approximatelyThere are approximately2.5 cm in an inch. 1.1 yards in a meter.42 in. × 2.5 = 105 cm 6 m × 1.1 = 6.6 ydExample 2Converting Between Metric and Customary UnitsUnits of CapacityCustomary Metric Metric Customary1 qt ≈ 0.9 L 1 L ≈ 1.1 qt1 pt ≈ 0.5 L 1 L ≈ 2.1 ptCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Amber is using a recipe to make soup. The recipe calls for 3 quarts of chickenbroth. How many liters of chicken broth will Amber need?There is approximately 0.9 liter in a quart. 3 qt × 0.9 = 2.7 LThe table below shows the approximate equivalents between customary andmetric units of weights and mass.Units of Weight/MassCustomary Metric Metric Customary1 oz ≈ 28.3 g 1 g ≈ 0.04 oz1 lb ≈ 0.5 kg 1 kg ≈ 2.2 lbExample 3Complete: 500 oz =kgThere are approximately 28.3 grams in an ounce. First find the number ofgrams in 500 ounces.500 oz × 28.3 = 14,150 gThen change grams to kilograms. There are 1,000 grams in a kilogram.14,150 g ÷ 1,000 = 14.15 kgExercisesComplete each sentence.1. 17 oz ≈ g 2. 90 km ≈ mi 3. 7 L ≈ pt4. 1.5 mi ≈ m 5. 67 kg ≈ lb 6. 12 pt ≈ LChapter 7 SC StudyText, Course 3 209

7DNAME DATE PERIODSkills PracticeRecall what you know about metric and customary equivalents.Tell whether each statement is true or false.1. A length of 4 meters is longer than 4 yards.SCAS 8-5.7Converting Between Metric and Customary Units2. A weight of 10 pounds is more than 5 kilograms.3. A capacity of 1 gallon is more than 4 liters.4. A length of 1 foot is about the same as 30 centimeters.5. A kilometer is more than half a mile.6. A pound is a little more than half a kilogram.7. On a road in Canada, the posted speed 8. Sean has a recipe that calls for 0.25 L oflimit is 45 kilometers per hour. Aimee milk. He has a one-cup container of milkis driving at a speed of 40 miles per in the refrigerator. Is this enough milkhour. Is this above or below the speed for the recipe?limit?9. The posted load limit for a bridge is 10. Leah is pouring paint from a 5-gallon5 tons. The mass of Darryl’s truck is can into some jars. She has twelve jars1,500 kilograms and it is holding cargo that each hold 1 liter and six jars thatthat weighs a half ton. Can Darryl drive each hold 1.25 liters. Does she havehis truck across the bridge?enough jars for all the paint?Choose the better estimate for each measure.11. the height of a palmetto tree: 10 yards or 10 kilometers12. the amount of water in a cooler: 8 pints or 8 litersCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.13. the weight of a bag of sugar: 4 pounds or 4 kilograms210 SC StudyText, Course 3 Chapter 7

7DNAME DATE PERIODHomework PracticeConverting Between Metric and Customary UnitsComplete each conversion. Round to the nearest hundredth ifnecessary.1. 10 cm ≈ in 2. 300 gal ≈ LSCAS 8-5.73. 250 g ≈ oz 4. 5.5 kg ≈ lb5. 145 m ≈ mi 6. 9.5 L ≈ pt7. 13 yd ≈ m 8. 1.095 mi ≈ km9. 23 pt ≈ L 10. 12 g ≈ oz11. 44 m ≈ yd 12. 504 L ≈ qt13. 118 oz ≈ g 14. 3,000 cm ≈ in.15. 4 mi ≈ m 16. 7 km ≈ ydCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Convert each rate using dimensional analysis. Round to the nearesthundredth if necessary.17. 88 mi/h ≈ km/min 18. 10 ft/min ≈ m/h19. 165 L/h ≈ qt/min 20. 26 yd/s ≈ km/h21. 474 gal/day ≈ L/week 22. 33.6 m/s ≈ ft/min23. 22 fl oz/min ≈ mL/s 24. 229 km/h ≈ mi/min25. TRAVEL Lisa is traveling to Europe. The information from the airlines saidthat she is only allowed to check 25 kilograms worth of baggage. How manypounds is this?26. SPACE SHUTTLE The space shuttle travels at an orbital speed of about17,240 miles per hour. How many meters per minute is this?Chapter 7 SC StudyText, Course 3 211

7DNAME DATE PERIODProblem-Solving PracticeSCAS 8-5.7Converting Between Metric and Customary Units1. COOKING Ty enters a chili cook-off.If he uses 2 pounds of ground beef inhis recipe, how many kilograms ofground beef does he use?2. GIFTS Jayda brought 27 bottles offlavored water to give her class. If eachbottle holds 1 pint of water, how manyliters of water did Jayda bring?3. BUILDING Davis built a shelf thatholds a maximum of 30 kilograms.If Davis has a set of books that eachweigh 1_ pound, how many books can2Davis put on his shelf? Explain.4. DECORATING Maya is cutting streamersfor the school dance. Each streamershe cuts is 1 meter long. If the rollof streamers is 81 inches, how many1 meter streamers can Maya get fromeach roll?5. PETS Andrew has a 20-pound bag ofdry dog food. Each day he feeds hisdog 150 grams of dry dog food. Forapproximately how many days will thebag of dog food be enough to feed hisdog? Explain.6. COOKING Bri needs 1 quart of halfand-halffor each batch of homemadeice cream she makes. If Bri has10 liters of half-and-half, how manybatches of ice cream can she make?Explain.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.212 SC StudyText, Course 3 Chapter 7

NameChapter 7 TestMastering the SC StandardsDate1 Which of the following choices is closest tothe volume of the cone below?3 The dimensions of two cylinders are shownbelow.r = 4 ftr = 2 ft10 cmh = 4 fth = 8 ft6 cmA 31 cm 3B 94 cm 3C 283 cm 3D 377 cm 38-5.3The volume of the smaller cylinder is16π cubic feet. What is the volume of thelarger cylinder?A 32π ft 3 C 96π ft 3B 64π ft3 D 128π ft 3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2 Mr. Garcia made a circular stained-glasswindow for the entryway of his house.24 in.What is the approximate area of thestained-glass window?A 75π in 2B 144π in 2C 165π in 2D 1,808π in 28-5.48-5.24 The dimensions of a small granola box areshown in the diagram below. Its volume is192 cubic inches.64What is the volume of a large granolabox similar to the one shown abovewhose dimensions are dilated by a scalefactor of 1.5?A 384 in 3 C 648 in 3B 576 in 3 D 768 in 388-5.2Chapter 7 SC StudyText, Course 3 213

NameDateChapter 7 Test (continued)Mastering the SC Standards5 Kenesha and her family rode the antiquecarousel at the Family Kingdom Park inMyrtle Beach. If a horse on the carousel is8 feet from the center, about how far willthe horse travel in 8 revolutions? 7 Stacy has a garden in the shape of thetrapezoid below.8 cm4 cm 8 cm16 cm What procedure can she use to find the areaof her garden?A 50 ftB 100 ftC 200 ftD 400 ft6 The dimensions of two cubes are shownbelow.n cm3n cmThe volume of the smaller cube is125 cubic centimeters. What is thevolume of the larger cube?A 375 cm 3B 1,125 cm 3C 3,375 cm 38-5.4A Add 8 and 16, multiply by 4, and thendivide the result by 2.B Add 8 and 16, and then multiply theresult by 4.C Add 4 and 8, and then multiply theresult by 16.D Add 4 and 8, multiply by 4, and thendivide the result by 2.8-5.58 Suppose a pizza has a circumference of 43inches. What is the smallest size box thepizza will fit in?A 12 in.B 13 in.C = 43 in.C 14 in.D 15 in.8-5.4Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.D 15,625 cm 38-5.2214 SC StudyText, Course 3 Chapter 7

8NAME DATE PERIODAnticipation GuideAlgebra: More Equations and InequalitiesSTEP 1 Before you begin Chapter 8• Read each statement.• Decide whether you Agree (A) or Disagree (D) with the statement.• Write A or D in the first column OR if you are not sure whether you agree or disagree,write NS (Not Sure).STEP 1A, D, or NSStatement1. The expression 6y + 3(x - 2) is in simplest form because ithas no like terms.2. The expressions 4(x + 3) and 4x + 12 are equivalent.3. When solving equations, undo each operation in the sameorder as the order of operations.4. To solve the equation 4 - 2x = 10, first subtract 4 from eachside, and then divide each side by 2.5. Three times a number decreased by 1 is 11 and 11 equals 1 lessthan three times a number are equivalent statements.STEP 2A or DCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6. A variable can be added to or subtracted from both sides ofan equation with the equation remaining true.7. The phrase a minimum of $25 can be written as m ≤ 25.8. If t = 8, then the inequality 3t - 6 ≤ 20 is false.STEP 2 After you complete Chapter 8• Reread each statement and complete the last column by entering an A or a D.• Did any of your opinions about the statements change from the first column?• For those statements that you mark with a D, use a piece of paper to write anexample of why you disagree.Chapter 8 SC StudyText, Course 3 215

8NAME DATE PERIODFamily ActivityState Test PracticeFold the page along the dashed line. Work each problem on another piece ofpaper. Then unfold the page to check your work.1. Suppose that one pyramid balances twocubes and one cylinder balances threecubes as shown in the figure.2. The model represents the equation2x + 4 = 4y + 4.xx1 11 1y y yy1 11 1Which statement is not true?A One pyramid and one cube balancethree cubes.B One pyramid and one cube balanceone cylinder.C One cylinder and one pyramidbalance four cubes.D One cylinder and one cube balancetwo pyramids.Fold here.Solution1. Hint: Remember you can add or subtractequivalent items from each side of thescale to maintain the balance. You canalso substitute equivalent items.A You can add one cube to each side ofthe left scale. This is true.B You can add one cube to each side ofthe left scale. So, one pyramid andone cube balance three cubes. In thetop scale, three cubes balance onecylinder. This is true.C You can add the items on the leftpart of the scales and items onthe right side of the scales. So, onecylinder and one pyramid balancefive cubes. This is not true.D You can add one cube to each side ofthe right scale. So, one cylinder andone cube balance four cubes. Thebottom scale shows that one pyramidbalances two cubes. So, two pyramidswill balance four cubes. This is true.What is the value of x?A 2yB 4yC 2y + 4D 4y + 8Solution2. Hint: Make equivalent changes to bothsides of the balance.Since there are four 1’s on each side ofthe balance, they can be removed,resulting in a balance between 2x and4y. Since both are multiples of two, youcan divide each side into two groups, orone x for 2y, so the value of x is 2y.The answer is C. The answer is A.216 SC StudyText, Course 3 Chapter 8Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

8-1NAME DATE PERIODExplore Through ReadingSimplifying Algebraic ExpressionsGet Ready for the LessonDo the Mini Lab at the top of page 416 in your textbook. Write youranswers below.1. Choose two positive and one negative value for x. Then evaluate 2(x + 3)and 2x + 6 for each of these values. What do you notice?SCAS 8-3.3, 8-1.42. Use algebra tiles to rewrite the expression 3(x - 2). (Hint: Use one greenx-tile and 2 red -1-tiles to represent x - 2.)Read the Lesson3. When is the Distributive Property used to simplify an algebraicexpression?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.4. Explain how to simplify the expression 5(x - 3).5. Explain what it means for two expressions to be equivalent.6. Give an example of an expression containing three terms, one of which isa constant.Remember What You Learned7. One of your classmates was absent from school today and has not studiedthe lesson. Write a letter to your classmate explaining how to simplify anexpression and how to identify terms and constants.Chapter 8 SC StudyText, Course 3 217

8-1NAME DATE PERIODStudy GuideSimplifying Algebraic ExpressionsSCAS 8-3.3, 8-1.4The Distributive Property can be used to simplify algebraic expressions.Examples Use the Distributive Property to rewrite each expression.3(a + 5) -2(d - 3)3(a + 5) = 3(a) + 3(5) Distributive Property -2(d - 3) = -2[d + (-3)] Rewrite d - 3 as= 3a + 15 Simplify. d + (-3).= -2(d) + (-2) (-3) Distributive Property= -2(d) + 6 Simplify.When a plus sign separates an algebraic expression into parts, each part is called a term. In termsthat contain a variable, the numerical part of the term is called the coefficient of the variable. A termwithout a variable is called a constant. Like terms contain the same variables, such as 3x and 2x.Example 3 Identify the terms, like terms, coefficients, and constants in theexpression 7x - 5 + x - 3x.7x - 5 + x - 3x = 7x + (-5) + x + (-3x) Defi nition of subtraction= 7x + (-5) + 1x + (-3x) Identity Property; x = 1xThe terms are 7x, -5, x, and -3x. The like terms are 7x, x, and -3x. The coefficients are7, 1, and -3. The constant is -5.An algebraic expression is in simplest form if it has no like terms and no parentheses.Example 4 Simplify the expression -2m + 5 + 6m - 3.-2m and 6m are like terms. 5 and -3 are also like terms.-2m + 5 + 6m - 3 = -2m + 5 + 6m + (-3) Defi nition of subtraction= -2m + 6m + 5 + (-3) Commutative Property= (-2 + 6)m + 5 + (-3) Distributive Property= 4m + 2 Simplify.ExercisesUse the Distributive Property to rewrite each expression.1. 2(c + 6) 2. -4(w + 6) 3. (b - 4)(-3)4. Identify the terms, like terms, coefficients, and constants in theexpression 4m - 2 + 3m + 5.Simplify each expression.5. 3d + 6d 6. 2 + 5s - 4 7. 2z + 3 + 9z - 8Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.218 SC StudyText, Course 3 Chapter 8

NAME DATE PERIOD8-1 Homework PracticeSimplifying Algebraic ExpressionsSCAS 8-3.3, 8-1.4Use the Distributive Property to rewrite each expression.1. 6(z + 4) 2. -7(c + 2) 3. (d + 5)9 4. (h + 8)(-3)5. 5(y - 2) 6. 3(6 - n) 7. -4(s - 4) 8. -9(2 - p)9. 2(3x + 1) 10. -5(4n - 5) 11. 8(u - 2v) 12. 3a(7b + 6c)Identify the terms, like terms, coefficients, and constants in each expression.13. 4b + 7b + 5 14. 8 + 6t - 3t + t 15. -5x + 4 - x - 1Simplify each expression.16. h + 6h 17. 10k - k 18. 3b + 8 + 2bCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.19. 4 + 5v + v 20. -2f + 3 - 2f - 8 21. -7s - 5 - 7s + 922. -3_4 x - 1_3 + 7_8 x - 1_223. 5c - 3d - 12c + d 24. -y + 9z - 16y - 25zWrite two equivalent expressions for the area of each figure.25.x +6826.9x 5 27.28. PAINTING Mr. Torres paid $43 for supplies to paint his office. He paid one person $8per hour to prepare the office to be painted and another person $10 per hour to paintthe office. If both people worked h hours, write two expressions that you could use torepresent the total cost of painting the office.x + 120Chapter 8 SC StudyText, Course 3 219

NAME DATE PERIOD8-1 Problem-Solving PracticeSCAS 8-3.3, 8-1.4Simplifying Algebraic Expressions1. GAMES At the Beltway Outlet store, youbuy x computer games for $13 each anda magazine for $4. Write an expressionin simplest form that represents thetotal amount of money you spend.2. TENNIS Two weeks ago, James bought3 cans of tennis balls. Last week, hebought 4 cans of tennis balls. Thisweek, he bought 2 cans of tennis balls.The tennis balls cost d dollars per can.Write an expression in simplest formthat represents the total amount thatJames spent.3. AMUSEMENT PARKS Sari and herfriends are going to play miniaturegolf. There are p people in the group.Each person pays $5 for a round of golfand together they spend $9 on snacks.Write an expression in simplest formthat represents the total amount thatSari and her friends spent.5. GEOMETRY Write an expression insimplest form for the perimeter of thetriangle below.2x4x 22x 34. BICYCLING The bicycle path at thepark is a loop that covers a distance ofm miles. Jorge biked 2 loops each onMonday and Wednesday and 3 loopson Friday. On Sunday, Jorge biked 10miles. Write an expression in simplestform that represents the total distancethat Jorge biked this week.6. SIBLINGS Mala is y years old. Hersister is 4 years older than Mala.Write an expression in simplest formthat represents the sum of the agesof the sisters.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.220 SC StudyText, Course 3 Chapter 8

NAME DATE PERIOD8-2 Explore Through ReadingSolving Two-Step EquationsGet Ready for the LessonRead the introduction at the top of page 422 in your textbook.Write your answers below.1. Explain how you could use the work backward strategy to find the cost ofeach bag of dog treats. Find the cost.SCAS 8-3.42. Find the cost of each bag.Read the Lesson3. Define two-step equation.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Determine whether each equation is a two-step equation. Explain.4. n + 8 = 21 5. 2x + 1 = 15 6. c_4 = 6.5What is the first step in solving each equation?7. 3y - 2 = 16 8. 5 - 6x = -19 9. -2p + 11 = 7Remember What You Learned10. Draw a diagram that shows how the equation 2x + 3 = 8 can be modeledusing algebra tiles.Chapter 8 SC StudyText, Course 3 221

NAME DATE PERIOD8-2 Study GuideSolving Two-Step EquationsSCAS 8-3.4A two-step equation contains two operations. To solve a two-step equation, undo each operation inreverse order.Example 1Method 1 Vertical MethodSolve -2a + 6 = 14. Check your solution.Method 2 Horizontal Method-2a + 6 = 14 Write the equation. -2a + 6 = 14_______ -6 = -6 Subtract 6 from each side. -2a + 6 - 6 = 14 - 6-2a = 8 Simplify. -2a = 8_-2a-2 = 8_Divide each side by -2._-2a-2-2 = 8_-2a = -4 Simplify. a = -4Check -2a + 6 = 14 Write the equation.-2(-4) + 6 14 Replace a with -4 to see if the sentence is true.The solution is -4.14 = 14 ✓ The sentence is true.Sometimes it is necessary to combine like terms before solving an equation.Example 2 Solve 5 = 8x - 2x - 7. Check your solution.5 = 8x - 2x - 7 Write the equation.5 = 6x - 7 Combine like terms.5 + 7 = 6x - 7 + 7 Add 7 to each side.12 = 6x Simplify.__126 = 6x6Divide each side by 6.2 = x Simplify.The solution is 2.Check this solution.ExercisesSolve each equation. Check your solution.1. 2d + 7 = 9 2. 11 = 3z + 5 3. 2s - 4 = 64. -12 = 5r + 8 5. -6p - 3 = 9 6. -14 = 3x + x - 27. 5c + 2 - 3c = 10 8. 3 + 7n + 2n = 21 9. 21 = 6r + 5 - 7rCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.10. 8 - 5b = -7 11. -10 = 6 - 4m 12. -3t + 4 = 1913. 2 + a_6= 5 14. -1_q - 7 = -3 15. 4 -v_3 5 = 0222 SC StudyText, Course 3 Chapter 8

NAME DATE PERIOD8-2 Homework PracticeSolving Two-Step EquationsSolve each equation. Check your solution.1. 3g + 5 = 17 2. 9 = 4a + 13 3. 13 = 5m - 2SCAS 8-3.44. -15 = 2t - 11 5. 7k - 5 = -19 6. 13 = 4x - 117. 10 = z_2+ 7 8. 6 +n_5= -4 9. 4 - 3y = 3110. 15 - 2b = -9 11. -1_y - 6 = -11 12. 16 -r_3 7 = 2113. 30 = 5d - 8d 14. w + 3w = 20 15. 5 - 7m + 9m = 1116. -18 = 8x - 9 - 5x 17. 25 = s + 13 - 4s 18. 6a + 7 - a = -1819. 3(y + 5) = 21 20. 7(p - 3) = 35 21. -48 = 6(v + 2)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.22. _ k - 34= 10 23._ z + 57= -3 24._ 9 + t12 = -325. SHOPPING Mrs. Williams shops at a store that has an annual membershipfee of $30. Today she paid her annual membership and bought several fruitbaskets costing $15 each as gifts for her coworkers. Her total was $105.Solve the equation 15b + 30 = 105 to find the number of fruit basketsMrs. Williams purchased.26. GAMES A card game has 50 cards. After dealing 7 cards to each player,Tupi has 15 cards left over. Solve the equation 50 - 7p = 15 to find thenumber of players.27. GEOMETRY Write an equation to representthe length of −−− PQ . Then find the value of y.P2812 y 3yQChapter 8 SC StudyText, Course 3 223

NAME DATE PERIOD8-2 Problem-Solving PracticeSolving Two-Step EquationsSCAS 8-3.41. SHOPPING Jenna bought 5 reams ofpaper at the store for a total of $21.The tax on her purchase was $1. Solve5x + 1 = 21 to find the price for eachream of paper.2. CARS It took Lisa 85 minutes to washthree cars. She spent x minutes oneach car and 10 minutes puttingeverything away. Solve 3x + 10 = 85to find how long it took to wash eachcar.3. EXERCISE Rick jogged the same distanceon Tuesday and Friday, and 8 miles onSunday, for a total of 20 miles for theweek. Solve 2x + 8 = 20 to find thedistance Rick jogged on Tuesday andFriday.4. MOVING Heather has a collection of26 mugs. When packing to move, sheput the same number of mugs in eachof the first 4 boxes and 2 mugs in thelast box. Solve 4x + 2 = 26 to find thenumber of mugs in each of the firstfour boxes.5. TELEVISION Burt’s parents allow him towatch a total of 10 hours of televisionper week. This week, Burt is planningto watch several two-hour movies andfour hours of sports. Solve 2x + 4 = 10to find the number of movies Burt isplanning to watch this week.7. MONEY McKenna had $32 when shegot to the carnival. After riding 6 rides,she had $20 left. Solve 32 - 6x = 20 tofind the price for each ride.6. TRAVEL Lawrence drives the samedistance Monday through Fridaycommuting to work. Last week,Lawrence drove 25 miles on theweekend, for a total of 60 miles for theweek. Solve 5x + 25 = 60 to find thedistance Lawrence drives each daycommuting to work.8. GARDENING Jack has 15 rosebushes.He has the same number of yellow, red,and pink bushes, and 3 multicoloredbushes. Solve 3x + 3 = 15 to find thenumber of yellow rosebushes Jackhas.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.224 SC StudyText, Course 3 Chapter 8

NAME DATE PERIOD8-3 Explore Through ReadingWriting Two-Step EquationsGet Ready for the LessonRead the introduction at the top of page 427 in your textbook.Write your answers below.1. Let n represent the number of payments. Write an expression thatrepresents the amount of the camp fee paid after n payments.SCAS 8-3.2, 8-3.42. Write and solve an equation to find the number of payments you willhave to make in order to pay off the balance of the camp.3. What type of equation did you write for Exercise 2? Explain yourreasoning.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Read the LessonJennifer bought 3 CDs, each having the same price. Her total for thepurchase was $51.84, which includes $3.84 in sales tax. Find the priceof each CD.4. Explain how to define the variable in the problem. Then define thevariable.5. The next step is to write an equation for the problem. Assuming that thetotal, 51.84, will be on the right side of the equals sign by itself, determinewhich two operations will be represented on the left side of the equalssign. Which is performed first? Explain.6. Complete the equation. Then solve it. How much does each CD cost?= $51.84Remember What You Learned7. Work with a partner. Have one partner write a word problem that involvesa two-step equation and solve it. Have the other partner check the solution.Then have partners switch tasks.Chapter 8 SC StudyText, Course 3 225

NAME DATE PERIOD8-3 Study GuideWriting Two-Step EquationsSCAS 8-3.2, 8-3.4Some verbal sentences translate to two-step equations.Example 1SentenceTranslate each sentence into an equation.EquationFour more than three times a number is 19. 3n + 4 = 19Five is seven less than twice a number. 5 = 2n - 7Seven more than the quotient of a number and 3 is 10. 7 + n_3 = 10After a sentence has been translated into a two-step equation, you can solve the equation.Example 2 Translate the sentence into an equation. Then find the number.Thirteen more than five times a number is 28.Words Thirteen more than five times a number is 28.VariableLet n = the number.Equation 5n + 13 = 28 Write the equation.5n + 13 - 13 = 28 - 13 Subtract 13 from each side.5n = 15 Simplify.5n_5 = 15_ Divide each side by 5.5n = 3Simplify.Therefore, the number is 3.ExercisesTranslate each sentence into an equation. Then find each number.1. Five more than twice a number is 7.2. Fourteen more than three times a number is 2.3. Seven less than twice a number is 5.4. Two more than four times a number is -10.5. Eight less than three times a number is -14.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6. Three more than the quotient of a number and 2 is 7.226 SC StudyText, Course 3 Chapter 8

NAME DATE PERIOD8-3 Homework PracticeWriting Two-Step EquationsTranslate each sentence into an equation.1. Three more than eight times a number is equal to 19.SCAS 8-3.2, 8-3.42. Twelve less than seven times a number is 16.3. Four more than twice a number is -10.4. Nine less than five times a number is equal to -30.5. ART Ishi bought a canvas and 8 tubes of paint for $24.95. If the canvas cost $6.95, howmuch did each tube of paint cost?6. ENGINEERING The world’s two highest dams are both in Tajikistan. The Rogun dam is 35meters taller than the Nurek dam. Together they are 635 meters tall. Find the height ofthe Nurek dam.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.U.S. PRESIDENTS For Exercises 7 and 8, use theinformation at the right.7. If you double President Reagan’s age at the timeof his first inauguration and subtract his age atthe time he died, the result is 45 years. How oldwas President Reagan when he died?8. If you divide the age of the first President Bushwhen he was inaugurated by 2 and add 14 years,you get the age of President Clinton when hewas first inaugurated. How old was PresidentG. H. W. Bush when he was inaugurated?9. GEOMETRY Find the value of x in the triangleat the right.10. ALGEBRA Three consecutive integers can berepresented by n, n + 1, and n + 2. If the sumof three consecutive integers is 57, what arethe integers?PresidentAge at FirstInaugurationJ. Carter 52R. Reagan 69G. H. W. BushW. Clinton 46G. W. Bush 54x°36°x°Chapter 8 SC StudyText, Course 3 227

NAME DATE PERIOD8-3 Problem-Solving PracticeWriting Two-Step EquationsSolve each problem by writing and solving an equation.SCAS 8-3.2, 8-3.41. CONSTRUCTION Carlos is building ascreen door. The height of the dooris 1 foot more than twice its width.What is the width of the door if itis 7 feet high?2. GEOMETRY A rectangle has a width of6 inches and a perimeter of 26 inches.What is the length of the rectangle?3. EXERCISE Ella swims four times a weekat her club’s pool. She swims the samenumber of laps on Monday, Wednesday,and Friday, and 15 laps on Saturday.She swims a total of 51 laps eachweek. How many laps does she swimon Monday?4. SHOPPING While at the music store,Drew bought 5 CDs, all at the sameprice. The tax on his purchase was $6,and the total was $61. What was theprice of each CD?5. STUDYING Over the weekend, Kokospent 2 hours on an assignment, andshe-spent equal amounts of timestudying for 4 exams for a total of16-hours. How much time did shespend studying for each exam?7. HOME IMPROVEMENT Laura is makinga patio in her backyard using pavingstones. She buys 44 paving stones anda flowerpot worth $7 for a total of $73.How much did each paving stone cost?6. FOOD At the market, Meyer buys abunch of bananas for $0.35 per poundand a frozen pizza for $4.99. The totalfor his purchase was $6.04, withouttax. How many pounds of bananas didMeyer buy?8. TAXI A taxi service charges you $1.50plus $0.60 per minute for a trip to theairport. The distance to the airportis 10 miles, and the total charge is$13.50. How many minutes did theride to the airport take?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.228 SC StudyText, Course 3 Chapter 8

NAME DATE PERIOD8-4 Explore Through ReadingSolving Equations with Variables on Each SideGet Ready for the LessonRead the introduction at the top of page 434 in your textbook.Write your answers below.1. Copy the table. Continue filling in rows to findhow many days until Tanner and Jordan sellthe same number of packages.2. Write an expression for Jordan’s gift wrap salesafter d days.3. Write an expression for Tanner’s gift wrap salesafter d days.4. On which day will Tanner’s sales pass Jordan’s sales?Time(days)Jordan’sSalesTanner’sSales0 8 + 4(0) = 8 5(0) = 01 8 + 4(1) = 12 5(1) = 52 8 + 4(2) = 16 5(2) = 103 8 + 4(3) = 20 5(3) = 15⋮ ⋮ ⋮5. Write an equation that could be used to find how many days it will takeuntil Tanner and Jordan sell the same number of packages.SCAS 8-3.4, 8-3.2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Read the Lesson6. What is the first step in solving an equation with variables on each side?7. What does it mean to isolate the variable when solving an equation?Determine whether the variable is isolated in each equation. Then determinewhether the equation is solved for the variable.8. c = 8 9. 3x + 1 = 7 10. 5d = 15Remember What You Learned11. Create a general set of guidelines to solve any type of equation.Chapter 8 SC StudyText, Course 3 229

NAME DATE PERIOD8-4 Study GuideSolving Equations with Variables on Each SideSome equations, such as 3x - 9 = 6x, have variables on each side of the equals sign. Use theAddition or Subtraction Property of Equality to write an equivalent equation with the variables on oneside of the equals sign. Then solve the equation.Example 1Solve 3x - 9 = 6x. Check your solution.3x - 9 = 6x3x - 3x - 9 = 6x - 3x-9 = 3x Simplify.Write the equation.Subtract 3x from each side.-3 = x Mentally divide each side by 3.To check your solution, replace x with -3 in the original equation.Check 3x - 9 = 6x Write the equation.3(-3) - 9 6(-3) Replace x with -3.SCAS 8-3.4, 8-3.2-18 = -18 ✓ This sentence is true.The solution is -3.Example 2 Solve 4a - 7 = 5 - 2a.4a - 7 = 5 - 2aWrite the equation.4a + 2a - 7 = 5 - 2a + 2a Add 2a to each side.6a - 7 = 5Simplify.6a - 7 + 7 = 5 + 7Add 7 to each side.6a = 12Simplify.a = 2 Mentally divide each side by 6.The solution is 2.Check this solution.ExercisesSolve each equation. Check your solution.1. 6s - 10 = s 2. 8r = 4r - 16 3. 25 - 3u = 2u4. 14t - 8 = 6t 5. k + 20 = 9k - 4 6. 11m + 13 = m + 237. -4b - 5 = 3b + 9 8. 6y - 1 = 27 - y 9. 1.6h - 72 = 4h - 30Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.10. 8.5 - 3z = -8z 11. 10x + 8 = 5x - 3 12. 16 - 7d = -3d + 2230 SC StudyText, Course 3 Chapter 8

NAME DATE PERIOD8-4 Homework PracticeSolving Equations with Variables on Each SideSolve each equation. Check your solution.1. 9m + 14 = 2m 2. 13x = 32 + 5x 3. 8d - 25 = 3dSCAS 8-3.4, 8-3.24. t - 27 = 4t 5. 7p - 5 = 6p + 8 6. 11z - 5 = 9z + 77. 12 - 5h = h + 6 8. 4 - 7f = f -12 9. -6y + 17 = 3y - 1010. 3x - 32 = -7x + 28 11. 3.2a - 16 = 4a 12. 16.8 - v = 6vFind each number.13. Fourteen less than five times a number is three times the number. Define a variable,write an equation, and solve to find the number.14. Twelve more than seven times a number equals the number less six. Define a variable,write an equation, and solve to find the number.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Write an equation to find the value of x so that each pair of polygons has thesame perimeter. Then solve.15.x + 6x + 3x + 9x + 4x + 116.5x5x5x5x5x5xx + 14 x + 1717. GOLF For an annual membership fee of $500, Mr. Bailey can join a country club thatwould allow him to play a round of golf for $35. Without the membership, the countryclub charges $55 for each round of golf. Write and solve an equation to determine howmany rounds of golf Mr. Bailey would have to play for the cost to be the same with andwithout a membership.18. MUSIC Marc has 45 CDs in his collection, and Andrea has 61. If Marc buys 4 new CDseach month and Andrea buys 2 new CDs each month, after how many months will Marcand Andrea have the same number of CDs?8x + 9Chapter 8 SC StudyText, Course 3 231

NAME DATE PERIOD8-4 Problem-Solving PracticeSolving Equations with Variables on Each SideSolve each problem by writing and solving an equation.SCAS 8-3.4, 8-3.21. PLUMBING A1 Plumbing Servicecharges $35 per hour plus a $25 travelcharge for a service call. Good GuysPlumbing Repair charges $40 per hourfor a service call with no travel charge.How long must a service call be forthe two companies to charge the sameamount?2. EXERCISE Mike’s Fitness Center charges$30 per month for a membership.All-Day Fitness Club charges $22 permonth plus an $80 initiation fee for amembership. After how many monthswill the total amount paid to the twofitness clubs be the same?3. SHIPPING The Lone Star ShippingCompany charges $14 plus $2 a poundto ship an overnight package. DiscountShipping Company charges $20 plus$1.50 a pound to ship an overnightpackage. For what weight is the chargethe same for the two companies?5. MONEY The Wayside Hotel charges itsguests $1 plus $0.80 per minute forlong distance calls. Across the street,the Blue Sky Hotel charges its guests$2 plus $0.75 per minute for longdistance calls. Find the length of a callfor which the two hotels charge thesame amount.4. MONEY Julia and Lise are playinggames at the arcade. Julia started with$15, and the machine she is playingcosts $0.75 per game. Lise started with$13, and her machine costs $0.50 pergame. After how many games will thetwo girls have the same amount ofmoney remaining?6. COLLEGE Jeff is a part-time studentat Horizon Community College. Hecurrently has 22 credits, and he plansto take 6 credits per semester until heis finished. Jeff’s friend Kila is also astudent at the college. She has4 credits and plans to take 12 creditsper semester. After how manysemesters will Jeff and Kila havethe same number of credits?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.232 SC StudyText, Course 3 Chapter 8

NAME DATE PERIOD8-5 Study GuideSCAS 8-1.1Problem-Solving Investigation: Guess and CheckYou may need to use the guess and check strategy to solve some problems.UnderstandPlanSolveCheck• Determine what information is given in the problem and what you need to fi nd.• Select a strategy including a possible estimate.• Solve the problem by carrying out your plan.• Examine your answer to see if it seems reasonable.ExampleThe school booster club spent $776 on ski passes for the school ski trip. Adult tickets cost$25 each and student tickets cost $18 each. They bought four times as many student ticketsas adult tickets. Find the number of adult and student tickets purchased.UnderstandPlanAdult tickets cost $25 each and student tickets cost $18 each. They boughtfour times more student tickets than adult tickets. The total amount paidfor the tickets was $776.Make a guess and check to see if it is correct. Remember, the number youguess for the student tickets must be four times more than the number youguess for adult tickets.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.SolveYou need to find the combination that gives a total of $776. Make a listand use a to represent the number of adult tickets and s to represent thenumber of student tickets.Guess $25a + $18s = $776 CheckIf a = 10, then s = 4(10) = 40 $25(10) + $18(40) = $970 too highIf a = 5, then s = 4(5) = 20 $25(5) + $18(20) = $485 too lowIf a = 7, then s = 4(7) = 28 $25(7) + $18(28) = $679 still too lowIf a = 8, then s = 4(8) = 32 $25(8) + $18(32) = $776 correctThe booster club bought 8 adult tickets and 32 student tickets.CheckExercisesThirty-two student tickets is 4 times more than the 8 adult tickets. Sincethe cost of 8 adult tickets, $200, plus the cost of 32 student tickets, $576,equals $776, the guess is correct.Use the guess and check strategy to solve each problem.1. JEWELRY Jana is making necklaces and bracelets. She puts 8 crystals on each necklaceand 3 crystals on each bracelet. She needs to make 20 more necklaces than bracelets.She has 270 crystals. If she uses all the crystals, how many necklaces and bracelets canshe make?2. GIFT BAGS The ninth-grade class is filling gift bags for participants in a school fundraiser.They put 2 raffle tickets in each child’s bag and 4 raffle tickets in each adult’sbag. They made twice as many adult bags as child bags. If they had 500 raffle tickets,how many child bags and adult bags did they make?Chapter 8 SC StudyText, Course 3 233

NAME DATE PERIOD8-5 Skills PracticeProblem-Solving Investigation: Guess and CheckUse the guess and check strategy to solve each problem.1. NUMBER THEORY A number cubed is 1,728. What is the number?SCAS 8-1.12. MONEY Jackson has exactly $43 in $1, $5, and $10 bills. If he has 8 bills,how many of each bill does he have?3. NUMBERS Jona is thinking of two numbers. One number is 18 more thantwice the other number. The sum of the numbers is 48. What twonumbers is Jona thinking of?4. PACKAGES The packages in a mail driver’s truck weigh a total of 950pounds. The large packages weigh 20 pounds each and the smallpackages weigh 10 pounds each. If he has 10 more large packages thansmall packages, how many large and small packages are on the truck?5. NUMBER THEORY One number is twice the other. The sum of the numbersis 246. What are the two numbers?6. MOVIE RENTALS A movie rental store rented 3 times as many DVDs asvideos. DVDs rent for $5 a day and videos rent for $3 a day. If the totalrental income for a weekend was $2,160, how many DVDs and videos didthe store rent?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.234 SC StudyText, Course 3 Chapter 8

NAME DATE PERIOD8-5 Homework PracticeProblem-Solving Investigation: Guess and CheckMixed Problem SolvingFor Exercises 1 and 2, solve using theguess and check strategy.1. NUMBER THEORY A number is squaredand the result is 676. Find the number.SCAS 8-1.15. STATES Of the 50 United States, 14have coastlines on the Atlantic Ocean,5 have coastlines on the Gulf ofMexico, and one state has coastlineson both. How many states do not havecoastlines on either the Atlantic Oceanor the Gulf of Mexico?2. CRAFTS Sabrina has 12 spools of ribbon.Each spool has either 3 yards of ribbon,5 yards of ribbon, or 8 yards of ribbon.If Sabrina has a total of 68 yards ofribbon, how many spools of each lengthof ribbon does she have?6. TIME Melissa spent 7 1_2minutes of thelast hour downloading songs from theInternet. What percent of the last hourdid she spend downloading songs?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Use any strategy to solve Exercises3–7. Some strategies are shown below.Problem-Solving Strategies• Draw a diagram.• Make a table.• Guess and check.3. NUMBERS Among all pairs of wholenumbers with product 66, find the pairwith the smallest sum.4. SHOPPING You are buying a jacket thatcosts $69.95. If the sales tax rate is7.75%, would it be more reasonable toexpect the sales tax to be about $4.90or $5.60?7. VOLUNTEERING Greg helps his motherdeliver care baskets to hospital patientseach Saturday. Last Saturday at noonthey had three times as many basketsleft to deliver as they had alreadydelivered. If they were delivering atotal of 64 baskets that day, how manyhad they delivered by noon?Chapter 8 SC StudyText, Course 3 235

NAME DATE PERIOD8-5 Problem-Solving PracticeProblem-Solving Investigation: Guess and CheckUse the guess and check strategy to solve each problem.SKATES For Exercises 1 and 2, use the information below. It shows the incomea sporting goods store received in one week for skate sharpening.Cost to SharpenHockey SkatesSkate Sharpening Income for Week 6Cost to SharpenFigure SkatesTotal Pairs ofSkates SharpenedSCAS 8-1.1Total Income fromSkate Sharpening$6 a pair $4 a pair 214 $1,0961. How many pairs of hockey skates andfigure skates were sharpened duringthe week?2. How much more did the sporting goodsstore earn sharpening hockey skatesthan figure skates?3. FIELD TRIP At the science museum,the laser light show costs $2 and theaquarium costs $1.50. On a class fieldtrip, each of the 30 students wentto either the laser light show or theaquarium. If the teacher spent exactly$51 on tickets for both attractions,how many students went to eachattraction?5. READING MARATHON Mrs. Johnson’sclass broke the school reading recordby reading a total of 9,795 pages in onemonth. Each student read a book thatwas either 245 pages or 360 pages. If32 students participated in the readingmarathon, how many students readeach book?4. NUMBERS Mr. Wahl is thinking of twonumbers. The sum of the numbersis 27. The product of the numbers is180. What two numbers is Mr. Wahlthinking of?6. REWARDS The soccer coaches boughtgifts for all their soccer players. Giftsfor the girls cost $4 each and giftsfor the boys cost $3 each. There were32 more boy soccer players than girlsoccer players. If the coaches spent atotal of $411 on gifts for their players,how many boys and girls playedsoccer?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.236 SC StudyText, Course 3 Chapter 8

NAME DATE PERIOD8-6 Explore Through ReadingSCAS 8-3.2InequalitiesGet Ready for the LessonRead the introduction at the top of page 441 in your textbook.Write your answers below.1. List three envelope sizes that Iko can use.2. How much will it cost to mail an invitation that weighs 2.5 ounces?Read the Lesson3. Complete the table by providing the symbol used to represent each phrase.Phrase Symbol Phrase Symbolis greater thanis at mostis at leastexceedsis fewer thanis less than or equal tois more thanis no less thanCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.4. Explain the difference between an open and a closed circle on the graphof an inequality.5. What does the arrow to the right or to the left indicate on the graph of aninequality?6. Describe how to graph x > 7.7. Describe how to graph x ≤ -6.Remember What You Learned8. Use a newspaper to find real-world situations in which relationshipsbetween quantities are described by phrases like no more than, at least,greater than, and at most.Chapter 8 SC StudyText, Course 3 237

NAME DATE PERIOD8-6 Study GuideInequalitiesSCAS 8-3.2A mathematical sentence that contains < or > is called an inequality. When used to compare avariable and a number, inequalities can describe a range of values. Some inequalities use thesymbols ≤ or ≥. The symbol ≤ is read is less than or equal to. The symbol ≥ is read is greaterthan or equal to.ExamplesWrite an inequality for each sentence.SHOPPING Shipping is free on orders of more than $100.Let c = the cost of the order.c > 100RESTAURANTS The restaurant seats a maximum of 150 guests.Let g = the number of guests.g ≤ 150Inequalities can be graphed on a number line. An open or closed circle is used to show where thesolutions start, and an arrow pointing either left or right indicates the rest of the solutions. An opencircle is used with inequalities having > or -2Place a open circle at -2. Then draw a line and an arrow to the right.4 3 2 1 0 1 2 3 4ExercisesWrite an inequality for each sentence.1. FOOD Our delivery time is guaranteed to be less than 30 minutes.2. DRIVING Your speed must be at least 45 miles per hour on the highway.Graph each inequality on a number line.3. r > 7 4. x ≤ -1Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.238 SC StudyText, Course 3 Chapter 8

NAME DATE PERIOD8-6 Homework PracticeInequalitiesWrite an inequality for each sentence.1. JOBS Applicants with less than 5 years of experience must take a test.SCAS 8-3.22. FOOTBALL The home team needs more than 6 points to win.3. VOTING The minimum voting age is 18.4. GAMES You must answer at least 10 questions correctly to stay in the game.5. DINING A tip of no less than 10% is considered acceptable.6. MONEY The cost including tax is no more than $75.For the given value, state whether the inequality is true or false.7. 9 + b < 16, b = 8 8. 14 - f > 8, f = 5 9. -5t < 24, t = 510. 51 ≤ 3m, m = 17 11. z_5Graph each inequality on a number line._-28≤ 7, z = 40 12. > 7, d = -4d13. y > 5 14. h < 5 15. c ≤ 1Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.16. t ≥ 2 17. x ≥ 4 18. r < 9For Exercises 19 and 20, use the table that shows the literacy rate inseveral countries.19. In which country or countries is the literacy rate lessthan 90%?20. In which country or countries is the literacy rate atleast 88%?CountryLitracyRateAlbania 87%Jamaica 88%Panama 93%Senegal 40%Chapter 8 SC StudyText, Course 3 239

NAME DATE PERIOD8-6 Problem-Solving PracticeInequalitiesSCAS 8-3.21. SPORTS Colin’s time in the 400-meterrun was 62 seconds. Alvin was at least4 seconds ahead of Colin. Write aninequality for Alvin’s time in the400-meter run.2. RESTAURANTS Before Valerie and hertwo friends left Mel’s Diner, there weremore than 25 people seated. Write aninequality for the number of peopleseated at the diner after Valerie andher two friends left.3. FARM LIFE Reggie has 4 dogs on hisfarm. One of his dogs, Lark, is about tohave puppies. Write an inequality forthe number of dogs Reggie will have ifLark has fewer than 4 puppies.4. MONEY Alicia had $25 when shearrived at the fair. She spent t dollarson ride tickets and she spent $6.50on games. Write an inequality for theamount of money Alicia had when sheleft the fair.5. HEALTH Marcus was in the waitingroom for 26 minutes before beingcalled. He waited at least another5 minutes before the doctor enteredthe examination room. Write aninequality for the amount of timeMarcus waited before seeing the doctor.7. HOMEWORK Nova spent one hour onThursday, one hour on Saturday, andmore than 2 hours on Sunday workingon her writing assignment. Write aninequality for the amount of time sheworked on the assignment.6. POPULATION The population ofEllisville was already less than 250before Bob and Ann Tyler and theirthree children moved away. Writean inequality for the population ofEllisville after the Tyler family left.8. YARD WORK Harold was able to mowmore than 3_ of his lawn on Saturday4night. Write an inequality for thefraction of the lawn that Harold willmow on Sunday.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.240 SC StudyText, Course 3 Chapter 8

NameChapter 8 TestMastering the SC StandardsDate1 Ashley mows lawns to earn money. Shebuys a new mower for $200 and charges$30 per lawn. If she mows n lawns, whichof the following equations could you use tofind p, Ashley’s profit?A p = 30n - 200B p = 30n + 200C p = n(200 - 30)Dp = 200 - 30n8-3.24 Simone’s bank charges a $10 checkingaccount fee per month plus a $0.12 fee forevery check she writes. The equation belowgives c, the total cost of the checkingaccount for a month in which n checks arewritten.c = 10 + 0.12nSimone wants to know how many checksshe wrote during a month in which her totalchecking account fees were $12.52. Whichstep below is the best first step for Simoneto solve for n?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2 The state tree of South Carolina is thepalmetto tree. Palmetto trees can reachheights up to 82 feet with leaves that canspan up to 9.8 feet in length. Which of thefollowing inequalities describes the heightof the palmetto tree?A h < 9.8B h ≤ 9.8C h > 82D h ≤ 828-3.23 Leon correctly simplifies the expression7(4x - 5). What does he get for an answer?A 28x - 35B -7xC 28x - 5D 4x - 128-3.3A Add 10 to both sides.B Subtract 10 from both sides.C Multiply both sides by 0.12.D Divide both sides by 0.12.8-3.45 The table below shows attendance at thelibrary for preschool story time for the firstfour weeks of the year. Which equationdescribes the data?Week (w)A c = 15w + 40B c = 40w + 15CDc = 55wc = 25wNumber ofChildren (c)1 552 703 854 1008-3.2Chapter 8 SC StudyText, Course 3 241

NameDateChapter 8 Test (continued)Mastering the SC Standards6 Taro correctly solves the equation belowfor y. He knows he needs to isolate thevariable on one side of the equation.What answer does he get?A x = 5B x = 3C x =-3D x =-53x - 7 = 7x + 58-3.49 Which choice is equivalent to theexpression 7 + 4x -5 - 9x?A 11x - 14B -15xC 2 - 5xD -5x + 1210 Lian solves for a in the equation below.Which choice below shows the sameequation after Lian adds 6 to each side?8-3.37 Kuri needs to send a package. It cannotweigh more than 28 pounds. Whichinequality represents this situation?A h < 28B h ≤ 28C h > 28D h ≥ 288-3.28 Marino wants to solve the equation belowfor t.6t - 11 = 25Which operations can Marino use on bothsides of the equation to find t?A Add 11, then multiply by 6.B Divide by 6, then add 11.C Subtract 11, then divide by 6.D Add 11, then divide by 6.8-3.4A a - 26 = 8B 8a = 32C 8a = 20D 8a = 268a - 6 = 268-3.411 What is the best first step to solve for n inthe equation below?A Add 5 to 4.4n + 9 - 5= -4B Divide -4 by 4.C Subtract 5 from 9.D Multiply -5 by -4.8-3.4Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.242 SC StudyText, Course 3 Chapter 8

9NAME DATE PERIODAnticipation GuideAlgebra: Linear FunctionsSTEP 1 Before you begin Chapter 9• Read each statement.• Decide whether you Agree (A) or Disagree (D) with the statement.• Write A or D in the first column OR if you are not sure whether you agree or disagree,write NS (Not Sure).STEP 1A, D, or NSStatement1. In the equation f(x) = 5x - 2, x is the dependent variable.2. The set of output values in a function is called the range of thefunction.3. Any three input values can be used to find ordered pairs tograph a linear function.4. The x-intercept of a function is the value of x where the graphof the function passes through the point (0, 0).5. A positive slope indicates a line slanting upward from left to right.6. A vertical line has a slope of 0.STEP 2A or DCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.7. A relationship that can be expressed with an equation in theform y = kx, k ≠ 0, is called a direct variation.8. The graph of a linear equation can be drawn knowing only theslope and the y-intercept.9. In the equation y - 2 = 6x, the y-intercept is -2.10. The equation of a line with a slope of 1_ and a y-intercept of34 is y = 1_3 x + 4.11. A scatter plot with a negative relationship will have no obviouspattern in the ordered pairs graphed.12. A line of fit of a scatter plot will pass through all data pointson the graph.STEP 2 After you complete Chapter 9• Reread each statement and complete the last column by entering an A or a D.• Did any of your opinions about the statements change from the first column?• For those statements that you mark with a D, use a piece of paper to write anexample of why you disagree.Chapter 9 SC StudyText, Course 3 243

9NAME DATE PERIODFamily ActivityState Test PracticeFold the page along the dashed line. Work each problem on another piece ofpaper. Then unfold the page to check your work.1. What is the equation of the linegraphed on the coordinate axisshown below?y2. What is the slope of a line that containsa point at (1, -2) and another point at(2, 1). Use the coordinate axis below tohelp you.yOxOxA y = 2xC y = x + 1B y = 2x + 1D y = -2x + 1Fold here.Solution1. Hint: Slope is the rise over the run of theline and the intercept is the point at whichthe x-coordinate is zero.For this graph, the rise over the run is2_, so the slope is 2. The line crosses the1x-axis at the point (0, 1), so the interceptis 1.Using the form of the line:y = mx + bwhere m is the slope and b is theintercept, our line has the equationy = 2x + 1.A 3B -3C 1_3D -1_3Solution2. Hint: Graph the two points and draw theline that passes through them. Use therise and run of the line to find the slope.Graph the two points and draw the linethrough them as shown below.yOThe rise from the lower point to thehigher point is 3 units. The rise ispositive because you are moving up. Therun, or distance across, is one unit to theright, or 1. The run is positive becauseyou are moving to the right. The riseover the run is 3_ , so the slope is 3.113xCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.The answer is C. The answer is A.244 SC StudyText, Course 3 Chapter 9

NAME DATE PERIOD9-2Explore Through ReadingFunctionsSCAS 8-3.1, 8-3.2Get Ready for the LessonRead the introduction at the top of page 469 in your textbook.Write your answers below.1. Complete the table at the right.2. If 6 DVDs are purchased, what is the total cost?3. Explain how to find the total cost of 9 DVDs.DVDsCost($)1 152 30345Read the Lesson4. If f(x) = x + 5, explain how to find f(2). Then find f(2).5. Identify the input value and the output value in Exercise 4.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6. Define domain. What number in Exercise 4 is part of the domain?7. Explain why the output value is called the dependent variable. Whatrepresents the dependent variable in the function f(x) = x + 5?Remember What You Learned8. When looking at the word domain, you see the word in located at theend of the word. This is a way to remember that the domain is the set ofinput values. Find a way to remember that the range is the set of outputvalues.Chapter 9 SC StudyText, Course 3 245

9-2NAME DATE PERIODStudy GuideFunctionsSCAS 8-3.1, 8-3.2A function connects an input number, x, to an output number, f(x), by a rule. To fi nd the value of afunction for a certain number, substitute the number into the function value in place of x, and simplify.Example 1 Find f(5) if f(x) = 2 + 3x.f(x) = 2 + 3xf(5) = 2 + 3(5) or 17So, f(5) = 17.Write the function.Substitute 5 for x into the function rule and simplify.You can organize the input, rule, and output of a function using a function table.Example 2 Complete the function table for f(x) = 2x + 4.Substitute each value of x, or input, into thefunction rule. Then simplify to find the output.f(x) = 2x + 4f(-1) = 2(-1) + 4 or 2f(0) = 2(0) + 4 or 4f(1) = 2(1) + 4 or 6f(2) = 2(2) + 4 or 8InputxRule2x + 4Outputf(x)-1 2(-1) + 4 20 2(0) + 4 41 2(1) + 4 62 2(2) + 4 8ExercisesFind each function value.1. f(1) if f(x) = x + 3 2. f(6) if f(x) = 2x 3. f(4) if f(x) = 5x - 44. f(9) if f(x) = -3x + 10 5. f(-2) if f(x) = 4x - 1 6. f(-5) if f(x) = -2x + 8Complete each function table.7. f(x) = x - 10 8. f(x) = 2x + 6 9. f(x) = 2 - 3xx x - 10 f(x) x 2x + 6 f(x) x 2 - 3x f(x)-1012-3-124-2034Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.246 SC StudyText, Course 3 Chapter 9

NAME DATE PERIOD9-2Homework PracticeFunctionsSCAS 8-3.1, 8-3.2Find each function value.1. f(6) if f(x) = 4x 2. f(8) if f(x) = x + 11 3. f(3) if f(x) = 2x + 44. f(5) if f(x) = 3x - 2 5. f(-6) if f(x) = 4x + 7 6. f(-14) if f(x) = 2x - 37. f ( 2_9) if f(x) = 3x + 1_38. f ( 3_4) if f(x) = 2x - 1_49. f ( 4_5) if f(x) = 4x - 1_5Complete each function table. Then state the domain and range of the function.10. f(x) = 5x - 4 11. f(x) = 2 - 3x 12. f(x) = 6 + 2xx 5x - 4 f(x)-4-136x 2 - 3x f(x)-3025x 6 + 2x f(x)-3-11413. f(x) = x - 7 14. f(x) = 9x 15. f(x) = 3x + 5Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.x x - 7 f(x)-3-2510x 9x f(x)-6-41316. JACKETS The school baseball team wants to have each player’s nameimprinted on the player’s jacket. The cost is $75 plus $8.50 for each name.Write a function to represent the cost c for n names. What is the cost tohave names imprinted on 25 jackets?17. LEMONADE Gene sold 10 glasses of lemonade while setting up hislemonade stand. After opening, he sold an average of 20 glasses eachhour. Write a function to represent the approximate number of glasses gsold after h hours. About when did he sell the 100th glass of lemonade?x 3x + 5 f(x)-5-126Chapter 9 SC StudyText, Course 3 247

NAME DATE PERIOD9-2 Problem-Solving PracticeFunctionsSCAS 8-3.1, 8-3.21. JOBS Strom works as a valet at theWestside Mall. He makes $48 per dayplus $1 for each car that he parks. Thetotal amount that Strom earns in oneday can be found using the functionf(x) = x + 48, where x represents thenumber of cars that Strom parked.Make a function table to show the totalamount that Strom makes in one day ifhe parks 25 cars, 30 cars, 35 cars, and40 cars.2. PLUMBING Rico’s Plumbing Servicecharges $40 for a service call plus$30 per hour for labor. The totalcharge can be found using the functionf(x) = 30x + 40, where x representsthe number of hours of labor. Make afunction table to show the total amountthat Rico’s Plumbing Service chargesif a job takes 1 hour, 2 hours, 3 hours,and 4 hours.3. GEOMETRY The perimeter of anequilateral triangle equals 3 times thelength of one side. Write a functionusing two variables for this situation.5. LIBRARY FINES The amount that SunriseLibrary charges for an overdue book is$0.25 per day plus a $1 service charge.Write a function using two variablesfor this situation.4. GEOMETRY Explain how to use thefunction that you wrote in Exercise 3to find the perimeter of an equilateraltriangle with sides 18 inches long.Then find the perimeter.6. LIBRARY FINES Explain how to findthe amount of the fine the libraryin Exercise 5 will charge for a bookthat is overdue by 12 days. Then findthe amount.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.248 SC StudyText, Course 3 Chapter 9

NAME DATE PERIOD9-3 Explore Through ReadingSCASRepresenting Linear Functions8-3.1, 8-4.2,8-1.7Get Ready for the LessonRead the introduction at the top of page 475 in your textbook. Writeyour answers below.1. Complete the following function table.InputxRule36.6 xOutputy(Input, Output)(x, y)1 36.6(1) 36.6 (1, 36.6)2 36.6(2)342. Graph the ordered pairs (x, y) on a coordinate plane.What do you notice?yOxRead the LessonCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.3. In your own words, explain how to graph a function.4. Graph y = 2x + 8.5. Graph y = x - 2.Remember What You LearnedyOyxx6. Think of a gas pump with prices for regular and super gasoline. When thesame amount of gas is being pumped into a tank, how does the price pergallon affect the total cost of the gas?Chapter 9 SC StudyText, Course 3 249

NAME DATE PERIOD9-3 Study GuideRepresenting Linear FunctionsSCAS8-3.1, 8-4.2,8-1.7A function in which the graph of the solutions forms a line is called a linear function. A linear functioncan be represented by an equation, a table, a set of ordered pairs, or a graph.Example Graph y = x - 2.Step 1 Choose some values for x.Use these values to make afunction table.x x - 2 y (x, y)0 0 - 1 -2 (0, -2)1 1 - 2 -1 (1, -1)2 2 - 2 0 (2, 0)3 3 - 2 1 (3, 1)Step 2 Graph each ordered pair on acoordinate plane. Draw a linethat passes through the points.The line is the graph of thelinear function.yOy x 2(3, 1)(2, 0)(1, 1)(0, 2)xExercisesComplete the function table. Then graph the function.1. y = x + 3x x + 3 y (x, y)-2012Graph each function.2. y = 3x + 2 3. y = 2 - x 4. y = 3x - 1yyyOxOxOyOxxCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.250 SC StudyText, Course 3 Chapter 9

NAME DATE PERIOD9-3Homework PracticeSCAS8-3.1, 8-4.2,8-1.7Representing Linear FunctionsGraph each function.1. y = 2x 2. y = -4x 3. y = x - 4yyyOxOxOx4. y = x + 3 5. y = 3x + 1 6. y = 1_4 x + 2yyyOxOxOxCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.7. CARPENTRY Mrs. Valdez can assemble a chairin 1 day and a table in 4 days. Graph thefunction 1x + 4y = 20 to determine howmany of each type of furniture Mrs. Valdezcan assemble in 20 days.8. FITNESS A fitness center has set a goal tohave 500 members. The fitness center alreadyhas 150 members and adds an average of 25members per month. The function f(x) = 25x+ 150 represents the membership after xmonths. Graph the function to determine thenumber of months it will take for the fitnesscenter to reach its membership goal.yyxxChapter 9 SC StudyText, Course 3 251

NAME DATE PERIOD9-3 Problem-Solving PracticeSCASRepresenting Linear Functions8-3.1, 8-4.2,8-1.71. FUEL CONSUMPTION The functiond = 18g describes the distance d thatRick can drive his truck on g gallons ofgasoline. Graph this function. Why is itsufficient to graph this function in theupper right quadrant only. How far canRick drive on 2.5 gallons of gasoline?10080d2. HOTELS The function c = 0.5m + 1describes the cost c in dollars of aphone call that lasts m minutes madefrom a room at the Shady Tree Hotel.Graph the function. Use the graph todetermine how much a 7-minute callwill cost.$5.00$4.00dDistance (mi)6040Cost ($)$3.00$2.0020$1.00g0 2 4 6 8 10Gasoline (gal)m0 2 4 6 8 10Length of Call (min)3. A computer store charges $45 formaterials and $50 an hour for serviceto install two new programs and ane-mail connection. The cost C(h) is afunction of the number of hours h ittakes to do the job. Graph the function.C(h) = 45 + 50h. How much will a3-hour installation cost?Cost ($)300250200150100500yx1 1.5 2 2.5 3 3.5Hour5. GIFTS Explain how you can use yourgraph in Exercise 4 to determineduring which week the amountremaining will fall below $190. Thenfind the week.4. GIFTS Jonah received $300 in cashgifts for his fourteenth birthday. Thefunction y = 300 – 25x describes theamount y remaining after x weeks ifJonah spends $25 each week. Graphthe function and determine the amountremaining after 9 weeks.yAmount Remaining ($)4003002001000 4 8 12 16Week6. Ron got a cell phone rate of C(a) =0.22 + 0.10a. Graph the costs perminute. How much will a five-minutecall cost?Rate (¢)80 y70605040300x1 2 3 4 5MinutesxCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.252 SC StudyText, Course 3 Chapter 9

NAME DATE PERIOD9-4 Explore Through ReadingSCAS 8-3.7, 8-4.2SlopeGet Ready for the LessonRead the introduction at the top of page 481 in your textbook.Write your answers below.1. The rate of change of the ladder compares the height it is raised to the distance of itsbase from the building. Write this rate as a fraction in simplest form.2. Find the rate of change of a ladder that has been raised 100 feet and has a base of50 feet from the building.Read the Lesson3. A line passes through the points A(-1, -5), B(0, -1), C(1, 3), and D(2, 7).Does it matter which two points you use to find the slope using the slopeformula? Explain.4. Suppose you choose to find the slope of the line in Exercise 3 using pointsC(1, 3) and D(2, 7). If your numerator after substitution into the slopeformula is 3 - 7, what should be your denominator? Explain.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5. Explain the difference between 0_3Remember What You Learnedand3_0 .6. Fill in the table with the appropriate term, positive or negative.Translating Rise and RunupleftdownrightSlopeChapter 9 SC StudyText, Course 3 253

NAME DATE PERIOD9-4 Study GuideSCAS 8-3.7, 8-4.2SlopeThe slope m of a line passing through points ( x 1, y 1 ) and ( x 2, y 2) is the ratio of the difference in they-coordinates to the corresponding difference in the x-coordinates. As an equation, the slope is givenbym = y __ 2 - y 1x 2- x , where x 1 ≠ x 2 .1Example 1 Find the slope of the line that passesthrough A(-1, -1) and B(2, 3).m = y __ 2 - y 1x 2- x 1__m = 3 - (-1)2 - (-1)m = 4_3Defi nition of slope( x 1 , y 1 ) = (-1, -1),( x 2 , y 2 ) = (2, 3)Simplify.( 1, 1)yOAB(2, 3)xCheck When going from left to right, thegraph of the line slants upward. Thisis correct for a positive slope.Example 2 Find the slope of the line that passesthrough C(1, 4) and D(3, -2).m = y __ 2 - y 1x 2- x __1m = -2 - 43 - 1_Defi nition of slope( x 1 , y 1 ) = (1, 4),( x 2 , y 2 ) = (3, -2)m = -6 or -3 Simplify.2Check When going from left to right, thegraph of the line slants downward.This is correct for a negative slope.ExercisesFind the slope of the line that passes through each pair of points.1. A(0, 1), B(3, 4) 2. C(1, -2), D(3, 2) 3. E(4, -4), F(2, 2)4. G(3, 1), H(6, 3) 5. I(4, 3), J(2, 4) 6. K(-4, 4), L(5, 4)yCO(1, 4)D(3, 22)xCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.254 SC StudyText, Course 3 Chapter 9

NAME DATE PERIOD9-4 Homework PracticeSCAS 8-3.7, 8-4.2SlopeFind the slope of each line.1. y2. y3. yxOxOxThe points given in each table lie on a line. Find the slope of the line. Then graphthe line.4. x -1 1 3 5y -2 0 2 45. x -2 3 8 13y -2 -1 0 16. x -1 2 5 8y 3 -1 -5 -9y8yy4OxOx4 8 12 16Ox 4 8Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.7. HOMES Find the slope of the roof 8. MOUNTAINS Find the slope of aof a home that rises 8 feet for everymountain that descends 100 meters forhorizontal change of 24 feet.every horizontal distance of 1,000 meters.24 ft8 ft100 mFind the slope of the line that passes through each pair of points.1,000 m9. A(1, 3), B(4, 7) 10. C(3, 5), D(2, 6) 11. E(4, 0), F(5, 5)12. P(-2, -5), R(2, 3) 13. S(-7, 4), T(5, 2) 14. V(9, -1), W(7, 6)SNOWFALL For Exercises 15–17, use the graph at theright. It shows the depth in feet of snow after eachtwo-hour period during a snowstorm.15. Find the slope of the line.16. Does the graph show a constant rate of change? Explain.Depth (ft)321ySnowfall17. If the graph is extended to the right, could you expect theslope to remain constant? Explain.0x2 4 6 8 1012HoursChapter 9 SC StudyText, Course 3 255

NAME DATE PERIOD9-4 Problem-Solving PracticeSCAS 8-3.7, 8-4.2Slope1. MOVIES By the end of its first week, amovie had grossed $2.3 million. By theend of its sixth week, it had grossed$6.8 million. Graph the data with theweek on the horizontal axis and therevenue on the vertical axis, and drawa line through the points. Then findand interpret the slope of the line.Revenue (millions of dollars)1086420 2 4 6 8 10Week2. BASKETBALL After Game 1, Feliciahad scored 14 points. After Game 5,she had scored a total of 82 points forthe season. After Game 10, she hadscored 129 points. Graph the data withthe game number on the horizontalaxis and the number of points on thevertical axis. Connect the points usingtwo different line segments.Number of Points16012080400 2 4 6 8 10Game3. BASKETBALL Find the slope of eachline segment in your graph fromExercise 2 and interpret it. Whichpart of the graph shows the greaterrate of change? Explain.5. Use the figure in Exercise 4. What isthe slope of the line through points Aand C? How do you know?4. GEOMETRY The figure shows triangleABC plotted on a coordinate system.Explain how to find the slope of theline through points A and B. Then findthe slope.A( 3, 2)yOB(2, 4)C(2, 2)6. Use the figure in Exercise 4. What isthe slope of the line through points Band C? How do you know?xCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.256 SC StudyText, Course 3 Chapter 9

NAME DATE PERIOD9-6 Explore Through ReadingSlope-Intercept FormGet Ready for the LessonRead the introduction at the top of page 495 in yourtextbook. Write your answers below.1. Write an equation that represents the cost of gasoline at $3 per gallonand a drink that costs $2.2. Graph the equation from Exercise 1.SCAS8-3.7, 8-3.1,8-3.6-3-2-1y87654321y = 3x + 2x1 2 3 4 5Read the Lesson3. In the formula y = mx + b, what do the letters m and b represent?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Identify the slope and the y-intercept of the graph of each equation.4. y = -3x + 45. y = 2_3 x - 76. How can you find the slope and the y-intercept of the graph of x + y = 8?7. If you know the y-intercept of a line is 4 and that the slope is -3_, how do2you graph the line?Remember What You Learned8. Work with a partner. Using a coordinate grid, take turns graphing linesand identifying the slope and y-intercept of each graph.Chapter 9 SC StudyText, Course 3 257

NAME DATE PERIOD9-6 Study GuideSCASSlope-Intercept Form8-3.7, 8-3.1,8-3.6Linear equations are often written in the form y = mx + b. This is called the slope-intercept form.When an equation is written in this form, m is the slope and b is the y-intercept.Example 1 State the slope and y-intercept of the graph of y = x - 3.y = x - 3 Write the original equation.y = 1x + (-3) Write the equation in the form y = mx + b.↑ ↑y = mx + b m = 1, b = -3The slope of the graph is 1, and the y-intercept is -3.You can use the slope-intercept form of an equation to graph the equation.Example 2Graph y = 2x + 1 using the slope and y-intercept.Step 1 Find the slope and y-intercept.y = 2x + 1 slope = 2, y-intercept = 1.Step 2 Graph the y-intercept 1.Step 3 Write the slope 2 as 2_1 . Useit to locate a second point onthe line.m = 2_1← change in y : up 2 units← change in x : right 1 unitStep 4 Draw a line through the two points.ExercisesState the slope and y-intercept of the graph of each equation.1. y = x + 1 2. y = 2x - 4 3. y = 1_2 x - 1Graph each equation using the slope and y-intercept.4. y = 2x + 2 5. y = x - 1 6. y = 1_2 x + 2yOxyOxup 2right 1yOy 2x 1xyOxCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.258 SC StudyText, Course 3 Chapter 9

NAME DATE PERIOD9-6 Homework PracticeSCASSlope-Intercept FormState the slope and the y-intercept for the graph of each equation.1. y = 4x + 1 2. y = -3x + 5 3. -x + y = 48-3.7, 8-3.1,8-3.64. y = -5_x - 3 5. y + 3x = -7 6. y =1_6 5 x + 2Graph each equation using the slope and the y-intercept.7. y = -2x + 2 8. y + x = -3 9. 1 = y - 2_3 xyyyOxOxOxCAMPING For Exercises 10–12, use the following information.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.The entrance fee to the national park is $15. A campsitefee is $15 per night. The total cost y for a camping trip forx nights can be represented by the equation y = 15x + 15.10. Graph the equation.11. Use the graph to find the total cost for 4 nights.12. What do the slope and the y-intercept represent?GEOMETRY For Exercises 13–15, use the diagram shown.x y x y 9013. Write the equation in slope-intercept form.14. Graph the equation.15. Use the graph to find the value of y if x = 30.Chapter 9 SC StudyText, Course 3 259

NAME DATE PERIOD9-6 Problem-Solving PracticeSlope-Intercept FormSCASCAR RENTAL For Exercises 1 and 2, use the following information.Ace Car Rentals charges $20 per day plus a $10 service charge to rentone of its compact cars. The total cost can be represented by the equationy = 20x + 10, where x is the number of days and y is the total cost.8-3.7, 8-3.1,8-3.61. Graph the equation. What do the slopeand y-intercept represent?y1602. Explain how to use your graph to findthe total cost of renting a compact car for7 days. Then find this cost.Cost ($)12080400 2 4 6 8 10Number of DaysxTRAVEL For Exercises 3 and 4, use the following information.Thomas is driving from Oak Ridge to Lakeview, a distance of 300 miles.He drives at a constant 60 miles per hour. The equation for the distanceyet to go is y = 300 - 60x, where x is the number of hours since he left.3. What is the slope and y-intercept?Explain how to use the slope andy-intercept to graph the equation. Thengraph the equation.Distance (mi)300200100y0 1 2 3 4 5Time (h)5. WEATHER The equation y = 0.2x + 3.5can be used to find the amount ofaccumulated snow y in inches x hoursafter 5 P.M. on a certain day. Identifythe slope and y-intercept of the graphof the equation and explain what eachrepresents.x4. What is the x-intercept? What does itrepresent?6. SALARY Janette’s weekly salary can berepresented by the equationy = 500 + 0.4x, where x is the dollartotal of her sales for the week. Identifythe slope and y-intercept of the graphof the equation and explain what eachrepresents.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.260 SC StudyText, Course 3 Chapter 9

9-8NAME DATE PERIODStudy GuideProblem-Solving Investigation: Use a GraphSCAS 8-1.8Example 1 The graph shows the results of a survey of teachers’ ages and gradelevels taught at school. Do the oldest teachers teach the highest grade level?Study the graph. The teachers who are oldest areplotted towards the top of the graph. The teachers whoteach the highest grade levels are plotted towards theright of the graph. The graph shows that the pointstowards the top of the graph are spread out from left toright randomly. The graph shows that the oldestteachers teach all grade levels, not just the highestgrade levels.Age of Teacher656055504540353025200 K1 2 3 4 5 6 7 8 9 10 11 12Grade TaughtCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Example 2 The graph shows the results of asurvey of students’ favorite sports. How manystudents were surveyed?Study the graph. Each bar on the graph represents thenumber of students who voted for that sport as theirfavorite. In order to find the number of studentssurveyed, add the amount from each sport.soccer + track + basketball = total students surveyed Write an equation.34 + 27 + 39 = total students surveyed Substitute.100 = total students surveyed Add.There were 100 students surveyed.ExercisesUse the graph at the right. Each point on the graph represents oneperson in a group that is training for a long-distance bicycle ride. Thepoint shows the number of miles that person cycles each day and thenumber of weeks that person has been in training.1. What is the highest number of miles bicycledeach day by any person in the group? How manyweeks was this person in training?2. Does the number of miles bicycled each dayincrease as the number of weeks in trainingincreases?Distance Bicycled (mi)Students Surveyed50454035302520151054440363228240342739SoccerTrackBasketballFavorite Sport01 2 3 4 5 6 7 8 9 10 11 12Number of Weeks in TrainingChapter 9 SC StudyText, Course 3 261

NAME DATE PERIOD9-8 Skills PracticeProblem-Solving Investigation: Use a GraphFor Exercises 1–3, use the graph at the right. The graph shows the monthly salesfor Wilson’s Flower Shop.1. During which month were sales highest?2. During which month were sales lowest?3. Between which two months did salesincrease the most?For Exercises 4–8, use the graph at the right. The graph shows the results ofa survey of students’ favorite types of music.4. Which type of music received the mostvotes?5. How many more votes did alternativereceive than rock?6. How many total students were surveyed?Sales ($1,000)Students Surveyed10 ,00090008000700060005000400030002000100080070060050040030020010000Jan Feb Mar Apr May JunMonth263RockSCAS 8-1.8318378AlternativePopFavorite Music241Country7. How many more students voted for popthan country?8. If the survey were expanded to 6,000students, about how many would beexpected to vote for alternative as theirfavorite type of music?For Exercises 9 –12, use the graph at the right. Each point on the graph shows theamount in tips that Rachael received and the day that the tips were earned.9. What was the lowest amount that Rachaelwas tipped?10. What was the highest total amount thatRachael was tipped in one day?11. On which day were Rachael’s tips highestoverall?12. Is the correlation between tips earned andday of the week positive, negative, or none?Tips Earned ($)1009080706050403020100S M T W T F SDay of the WeekCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.262 SC StudyText, Course 3 Chapter 9

NAME DATE PERIODCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.9-8 Homework PracticeProblem-Solving Investigation: Use a GraphMixed Problem SolvingFor Exercises 1 and 2, solve by using agraph.1. RESTAURANTS Diners were asked whichaspect of a dining experience was themost important, the quality of food, thefriendliness of the server, or the cost ofthe meal. The graph shows the resultsof the survey. How many diners weresurveyed?80706050403020100Most Important Aspectof Dining ExperienceQualityof FoodFriendlinessof ServerAspectCostof Meal2. COMMUTING Ms. Bonilla recorded theamount of time it took her to drive towork each morning. Make a graph of thedata in the table. Does the earliestdeparture time have the least travel time?DayDeparture TravelTime (A.M.) Time (min)1st Week Monday 7:21 171st Week Tuesday 7:38 261st Week Wednesday 7:32 221st Week Thursday 7:20 151st Week Friday 7:35 222nd Week Monday 7:26 202nd Week Tuesday 7:25 182nd Week Wednesday 7:38 242nd Week Thursday 7:34 212nd Week Friday 7:23 17Use any strategy to solve Exercises 3–5.Some strategies are shown below.Problem-Solving Strategies• Look for a pattern.• Use a graph.• Use logical reasoning.3. FLORIST Ms. Parker charges $29.95for a bouquet of one dozen roses. Lastyear, she paid her supplier $4.50 perdozen roses. This year, she paid $3.25more per dozen. How much less profitdid she make this year on 20 dozenbouquets?4. TOUR BUS One line in the graph showsthe cost of operating a tour bus. Theother line shows the amount of moneyreceived from the passengers. Howmany passengers must ride the tourbus to make a profit?Money (dollars)7006005004003002001000Cost ofOperationsAmount Received10 20 30 40 50Number of PassengersSCAS 8-1.85. TOWN MEETING The Waynesvilleauditorium seats 375 people. In asurvey of 50 residents, 6 stated thatthey plan to attend the next townhall meeting. If the town has 4,200residents, how many would you expectto attend? Is the auditorium largeenough?Chapter 9 SC StudyText, Course 3 263

9-8NAME DATE PERIODProblem-Solving PracticeProblem-Solving Investigation: Use a GraphFor Exercises 1–6, use a graph to solve.1. SURVEY A group of students were askedto name their favorite subject in school.The circle graph shows the results ofthe survey. If 45 students choose mathas their favorite subject, how manystudents were surveyed?Music25%Art12%Math20%English15%18% 10%Social StudiesScience3. EXERCISING Mark runs the mile race atevery track meet. The graph shows histimes, in minutes, for each meet. DidMark’s time improve each time that heran the mile race?Time (mins)9:008:508:408:308:208:108:000123 4 5Meets5. ART EXHIBIT The graph shows thenumber of weekly visitors at an artexhibit. How many more people visitedthe art exhibit during the week withthe most visitors than the week withthe least visitors?Visitors6506005505004504000yx1 2 3 4 5 6Week2. SALES The graph shows the monthlysales of George’s Comic Book Shop.Between which two months did salesdecrease the most?Sales ($1,000)876543210yJanFebMarAprMayJuneMonth4. JOBS Jerry and four friends mow lawnsduring summer vacation to earn money.The graph shows how much eachearned during each week of vacation.Is there any relationship between theamount that the friends earn each weekand the number of the week?Money Earned ($)1009080706050403020100 1 2 3 4 5 6 7 8 9 10Week6. SURVEY A group of students were askedto name their favorite color out of fourcolors. The circle graph shows theresults of the survey. If 150 studentschoose blue as their favorite color, howmany students chose green?Yellow10% Red24%Green36% Blue30%SCAS 8-1.8xCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.264 SC StudyText, Course 3 Chapter 9

NAME DATE PERIOD9-9 Explore Through ReadingScatter PlotsGet Ready for the LessonComplete the Mini Lab at the top of page 510 in your textbook.Write your answers below.1. Graph each of the ordered pairs listed on the board.SCAS8-6.1, 8-6.2,8-1.7, 8-3.1,8-3.2, 8-3.72. Examine the graph. Do you think there is a relationship between heightand arm span? Explain.Read the Lesson3. How is a scatter plot different from the graph of a linear function?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.4. What pattern would you expect to see in a scatter plot that shows a positiverelationship?5. What pattern would you expect to see in a scatter plot that shows anegative relationship?6. Would you expect a scatter plot to show a positive, negative, or norelationship between the population of a state and its number ofrepresentatives in the U.S. Congress? Explain.Remember What You Learned7. Using a newspaper or magazine, find an article with data given. Plot thedata on a coordinate plane and identify whether the data has a positive,negative, or no relationship.Chapter 9 SC StudyText, Course 3 265

NAME DATE PERIOD9-9 Study GuideSCASScatter Plots8-6.1, 8-6.2,8-1.7, 8-3.1,8-3.2, 8-3.7When you graph two sets of data as ordered pairs, you make a scatter plot. The pattern of the datapoints determines the relationship between the two sets of data.• Data points that go generally upward show a positive relationship.• Data points that go generally downward show a negative relationship.• Data points with no clear pattern show no relationship between the data sets.Examples Explain whether the scatter plot of thedata shows a positive, negative, or no relationship.miles driven and gallons of gas usedAs the number of miles driven increases, the amount of gasused increases. Therefore, the scatter plot will show apositive relationship.Gallons of Gas Usedy86420 50 100 150 200Miles Drivenxnumber of minutes a candle burns and acandle’s heightAs the number of minutes increases, the height of the candlewill decrease. Therefore, the scatter plot will show a negativerelationship.ExercisesExplain whether the scatter plot of the data for the following shows apositive, negative, or no relationship.1. a student’s age and the student’s grade level in school2. number of words written and amount of ink remaining in a pen3. square feet of floor space and the cost of carpet for the entire floor4. a person’s height and the number of siblings the person has5. length of time for a shower and the amount of hot water remainingHeight of Candle (in.)642yx0 10 20 30 40 50Minutes BurnedCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6. number of sides of a polygon and the area of the polygon266 SC StudyText, Course 3 Chapter 9

9-9NAME DATE PERIODHomework PracticeScatter PlotsExplain whether the scatter plot of the data for each of the followingshows a positive, negative, or no relationship.1.Games Won1086420y100200300400500Average Game Attendancex2.Car Value(% cost new)1009080706050403020100yx2 4 6 8 10Car Age (yr)3.Pumpkin Weight(pounds)50403020100ySCAS8-6.1, 8-6.2,8-1.7, 8-3.1,8-3.2, 8-3.7x30 60 90 120150Growth Time (days)For Exercises 4–6, use the following table.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.River Width (m) 15 18 20 28 30 32 38 40 42 45Water Speed (km/h) 12.6 10.7 11.2 9.7 8.1 8.7 6.9 5.4 3.9 4.14. Draw a scatter plot for the data. Then draw a lineof fit.5. Write an equation for the line of fit.6. Use your equation to estimate the speed of the waterwhen the river is 50 meters wide.Explain whether a scatter plot of the data for each of the following wouldshow a positive, negative, or no relationship.7. daily attendance at an outdoor carnival and the number of hours of rain8. number of diagonals of a polygon and the number of sides of a polygonChapter 9 SC StudyText, Course 3 267

NAME DATE PERIOD9-9 Problem-Solving PracticeSCASScatter PlotsWAGES For Exercises 1 and 2, usethe table at the right.YearAverageHourly Wage2000 $11.282001 $11.782002 $12.242003 $12.752004 $12.832005 $13.058-6.1, 8-6.2,8-1.7, 8-3.1,8-3.2, 8-3.71. Explain how to draw a scatter plot forthe data. Then draw one.14y2. Does the scatter plot show a positive,negative, or no relationship? Explain.Wage ($)131211100200020012002200320042005xYearRESALE VALUE For Exercises 3–6, use the scatter plotat the right. It shows the resale value of 6 SUVsplotted against the age of the vehicle3. Does the scatter plot show a positive,negative, or no relationship? Explainwhat this means in terms of the resalevalue of a SUV.5. Find the slope and y-intercept ofthe line of fit and explain what eachrepresents.Value (thousands)3020104. The equation y = -2,000x + 25,000 isan equation of a line of fit for the data.Explain what a line of fit is.6. Explain how to use the equation inExercise 4 to estimate the resale valueof an 8-year-old SUV. Find the value.y0 2 4 6Age (years)xCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.268 SC StudyText, Course 3 Chapter 9

NameChapter 9 TestMastering the SC StandardsDate1 Mr. Washington shows his class a pattern ofequilateral triangles.The table shows the data that the studentswere asked to find.3 A bicycle courier in New York City recordsthe distance she travels and the time foreach delivery she makes in a day. Whichscatter plot most likely represents therecorded data?ANumber ofTrianglesOuterPerimeter(Units)1 2 4 5 n3 4 6 7 ?Which function rule matches the sequenceshown in the table where n is the number oftriangles and p is the perimeter?BAp = 2nC p = n + 2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.B p = 3n - 1D p = n + 18-3.12 Tanya made the data table below. She plansto graph the line on a grid. What is theslope of the line?A1_31_ B2xy0 01 32 63 9C 2D 38-3.7CD8-6.2Chapter 9 SC StudyText, Course 3 269

NameDateChapter 9 Test (continued)Mastering the SC Standards4 What is the slope of the line?-4-3-2(-1, -2) -2-3-4y 4 (1,4)321O 1 2 3 4xA 2 C 0.5B 5 D 38-3.76 Shannon and Chris sell magazines toraise money for their school. For eachsubscription Chris sells, Shannon sellstwo. Which function table matches thissituation?A Chris Shannon6 43 14 2B Chris Shannon6 123 64 85 The scatter plot below shows therelationship between the number of hoursper week that a basketball team practicesand the number of points the team scores.C Chris Shannon6 83 54 6Points ScoredOyPractice Time(hours)Which statement best describes thisrelationship?A As practice time increased, pointsscored increased.B As practice time increased, pointsscored decreased.C As practice time decreased, pointsscored increased.D As practice time increased, pointsscored increased first, and thendecreased.xD Chris Shannon6 123 94 107 What is the value of the functionf(x) = 3x - 1 when x = 2?A 3B 5C 6D 88-3.18-3.1Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.8-6.1270 SC StudyText, Course 3 Chapter 9

NAME DATE PERIOD10 Anticipation GuideAlgebra: Nonlinear Functions and PolynomialsSTEP 1 Before you begin Chapter 10• Read each statement.• Decide whether you Agree (A) or Disagree (D) with the statement.• Write A or D in the first column OR if you are not sure whether you agreeor disagree, write NS (Not Sure).STEP 1A, D, or NSStatement1. If an equation can be written in the form y = mx + b, then itis a linear function.2. The equations y = 3x - 1, y - x = 4, and y = 2_x all representlinear functions because the coefficient of x in each equation is 1.3. A quadratic function is a function in which the greatestexponent of the variable is 2.4. The graph of a cubic function is a parabola.5. To multiply powers with the same base, add the exponents.6. 8 4 · 8 3 is equal to 8 12 .STEP 2A or DCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.7. To find the quotient of two powers with the same base, subtractthe exponents.8. To find the power of a power, multiply the exponents.9. To find the power of a product, find the power of eachfactor and add.10. A number that can be raised to the third power to createanother number is the cube root of that number.STEP 2 After you complete Chapter 10• Reread each statement and complete the last column by entering an A or a D.• Did any of your opinions about the statements change from the first column?• For those statements that you mark with a D, use a piece of paper to write anexample of why you disagree.Chapter 10 SC StudyText, Course 3 271

10NAME DATE PERIODFamily ActivityState Test PracticeFold the page along the dashed line. Work each problem on another piece ofpaper. Then unfold the page to check your work._1. Simplify 36 b 59b .A 4 b 5B 4 b 4C 4 b 3D 4 b 22. Simplify √ 3 27 f 15 g 9 .A 3 f 5 g 3B 3 f 12 g 6C 9 f 5 g 3D 24 f 5 g 3Fold here.SolutionHint: To divide powers with the samebase, subtract their exponents._ 36 b 59b = 4 b 5 - 1 The common base is b.= 4 b 4 Simplify.SolutionHint: The cube root of a monomialis one of the three equal factors of themonomial.3√ 27 ƒ 15 g 9 = √ 3 27 · √ 3 ƒ 15 · √ 3 g 9 Product Propertyof Cube Roots= 3 · ƒ 5 · g 3 or 3 ƒ 5 g 3 (3) 3 = 21;( f 5 ) 3 = ƒ 15 ; and( g 3 ) 3 = g 9Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.The answer is B. The answer is A.272 SC StudyText, Course 3 Chapter 10

NAME DATE PERIOD10-1Explore Through ReadingLinear and Nonlinear FunctionsSCAS 8-3.5, 8-1.7Get Ready for the LessonRead the introduction at the top of page 528 in your textbook.Write your answers below.1. Did the football travel the same height each half-second?Justify your answer.2. Did the football travel the same length each half-second? Justify youranswer.3. Graph the ordered pairs (time, height) and (time, length) on separate grids.Connect the points with a straight line or smooth curve. Then compare the graphs.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Read the Lesson4. How does the rate of change of a nonlinear function differ from the rate ofchange of a linear function?5. Determine whether the table represents a linear or nonlinear function.Explain.x 3 7 11 15y 46 35 24 136. How can you distinguish the equations of linear functions from theequations of nonlinear functions?Remember What You Learned7. Using a newspaper or magazine, find one example of a linear graph and oneexample of a nonlinear graph.Chapter 10 SC StudyText, Course 3 273

NAME DATE PERIOD10-1Study GuideLinear and Nonlinear FunctionsSCAS 8-3.5, 8-1.7Linear functions, which have graphs that are straight lines, represent constant rates of change. Therate of change for nonlinear functions is not constant. Therefore, its graphs are not straight lines.The equation for a linear function can always be written in the form y = mx + b, where m represents theconstant rate of change. You can determine whether a function is linear by examining its equation. In alinear function, the power of x is always 1 or 0, and x does not appear in the denominator of a fraction.Example 1 Determine whether the graph representsa linear or nonlinear function. Explain.The graph is a curve, not a straight line. So, it represents anonlinear function.Example 2 Determine whether y = 2.5x representsa linear or nonlinear function. Explain.yOy 1 x 3xSince the equation can be written as y = 2.5x + 0, the function is linear.A nonlinear function does not increase or decrease at the same rate. You can use a table to determineif the rate of change is constant.Example 3 Determine whether the table represents a linear or nonlinearfunction. Explain.+ 4 + 4 + 4x -2 2 6 10y 8 3 -1 -4Exercises- 5 - 4 - 3As x increases by 4, y decreases by a differentamount each time. The rate of change is notconstant, so this function is nonlinear.Determine whether each graph, equation, or table represents a linearor nonlinear function. Explain.1. yOy 2 x 2 2. y4. y = 5 - 2x 5.xOx 1 2 3 4y 3 6 9 12x3. y = 2 - x 36.x 0 2 4 6y 5 3 0 -4Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.274 SC StudyText, Course 3 Chapter 10

NAME DATE PERIOD10-1Homework PracticeLinear and Nonlinear FunctionsSCAS 8-3.5, 8-1.7Determine whether each graph, equation, or table represents a linearor nonlinear function. Explain.1.y2.y3.yOxOxOx4.y5.y6.yOxOxOxCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.7. y = 9 - x 2 8. y = -2.3x 9. y = x_910. y = 3_x13.x 2 4 6 8y 12 9 6 315. MINIMUM WAGE The state of Washingtonhas the highest hourly minimum wage inthe United States. The graphic showsWashington’s minimum wage from1999 to 2006. Would you describe theyearly increase as linear or nonlinear?Explain your reasoning.11. 2x + 3y = 6 12. 2xy = 1214. x 1.5 3 4.5 6y 2 4 8 16Hourly Wage$8.00$7.00$6.00$5.00$5.70Washington's Minimum Wage$7.63$7.16 $7.35$6.90 $7.01$6.72$6.500199 9 200 0 200 1 200 2 2003 2004 2005 2006Source: Washington State Department of Labor and IndustriesYearChapter 10 SC StudyText, Course 3 275

NAME DATE PERIOD10-1 Problem-Solving PracticeLinear and Nonlinear FunctionsSCAS 8-3.5, 8-1.7GEOMETRY For Exercises 1 and 2, use thefollowing information.sRecall that the perimeter of a square is equal to4 times the length of one of its sides, and the areaof a square is equal to the square of one of its sides.s1. Write a function for the perimeter ofthe square. Is the perimeter of a squarea linear or nonlinear function of thelength of one of its sides? Explain.2. Write a function for the area of thesquare. Is the area of a square a linearor nonlinear function of the length ofone of its sides? Explain.3. BUSINESS The Devon Tool Companyuses the equation p = 150t to calculatethe gross profit p the company makes,in dollars, when it sells t tools. Isthe gross profit a linear or nonlinearfunction of the number of tools sold?Explain.5. LONG DISTANCE The table shows thecharge for a long distance call as afunction of the number of minutesthe call lasts. Is the charge a linear ornonlinear function of the number ofminutes? Explain.Minutes 1 2 3 4Cost (cents) 5 10 15 204. GRAVITY A camera is accidentallydropped from a balloon at a height of300 feet. The height of the cameraafter falling for t seconds is given byh = 300 - 16 t 2 . Is the height of thecamera a linear or nonlinear functionof the time it takes to fall? Explain.6. DRIVING The table shows the cost ofa speeding ticket as a function of thespeed of the car. Is the cost a linear ornonlinear function of the car’s speed?Explain.Speed (mph) 70 80 90 100Cost (dollars) 25 50 150 300Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.276 SC StudyText, Course 3 Chapter 10

NAME DATE PERIOD10-3 Study GuideProblem-Solving Investigation: Make a ModelYou may need to use the make-a-model strategy to solve some problemSCAS 8-1.8You can always use the four-step plan to solve a problem.Understand • Determine what information is given in the problem and what you need to fi nd.Plan • Select a strategy including a possible estimate.Solve • Solve the problem by carrying out your plan.Check • Examine your answer to see if it seems reasonable.ExampleCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Kisha is trying to make a box out of a piece of cardboard by cutting asquare out of each corner. She will then fold up the sides and tapethem together. The cardboard measures 4 feet 6 inches by 6 feet 6inches. She wants the box to measure 3 feet wide by 5 feet long. Whatsize squares should Kisha cut out of the corners to make the box?UnderstandPlanSolveCheckExercisesShe wants to know what size squares to cut out of each cornerto make a box which measures 3 feet by 5 feet by 9 inches.Start by making a model of the cardboard. Label the sides of thecardboard in feet. Draw lines to show the squares that will becut out of the corners.? in.? in.? in.? in.6 ft 6 in.? in.? in.? in.? in.4 ft 6 in.Subtract 5 feet from 6 feet 6 inchesand divide by 2.1 ft 6 in. = 18 in. 18 in. ÷ 2 = 9 in.The square must have sides thatare 9 inches long.Check that the width of the box meets the specifications.Subtracting 18 inches or 1 foot 6 inches from 4 feet 6 inchesyields 3 feet, which is the width required.Make a model to solve each problem.1. CONSTRUCTION A chicken coop will be 20 feet long and 16 feet wide. One side that is20 feet long will be formed by the barn. The other three sides will be made of wirefencing with posts at every corner and every 4 feet between each corner. How manyfeet of fencing and how many posts are needed to build the chicken coop?2. GEOMETRY What is the fewest number of one-inch cubes needed to make a rectangularprism that measures 4 inches by 5 inches by 6 inches? (Hint: The prism can be hollowinside.)Chapter 10 SC StudyText, Course 3 277

NAME DATE PERIOD10-3 Skills PracticeProblem-Solving Investigation: Make a ModelMake a model to solve each problem.SCAS 8-1.81. SHIPPING A spice distributor is making boxes in which to pack cylindrical spicecontainers. The diameter of each container is 2 inches. The height of each containeris 4 inches. If they place 4 rows with 3 containers in each row in a box, what is thevolume of the box?2. SEWING Jordan has a bread basket in the shape of a rectangular prism that measures12 inches high, 18 inches long, and 16 inches wide. She wants to cover the inside ofthe basket with a 50-inch by 20-inch piece of fabric. Does Jordan have enough fabricto cover the inside of the basket? Explain your answer.3. BEADS Elsa is making a wooden box for sorting and storing her bead collection.The outer dimensions of the box are 10 inches by 10 inches. She wants to make 100compartments that are approximately 1-inch squares. How many horizontal andvertical dividers will Elsa need to make the compartments?4. ARRANGING TABLES Donna is arranging four tables to make seating for her party guests.Standing alone, each table will seat 4 people on each side and 2 people at each end. Shecan either place the tables end-to-end to make one long table or she can separate thetables into four individual tables. How many more guests can she seat if she separatesthe tables than if she places them end-to-end?5. MAKING FRAMES Julian is making pictures frames by gluing square tiles onto thewooden sides. The wooden sides measure 8 inches wide by 10 inches long by 1 inchwide. If he glues a 1-inch square tile at every corner and covers the remainder of thewood sides with 1_ -inch square tiles, how many of each size tile does Julian need to2make 4 frames?Use any strategy to solve each problem.6. QUIZ SCORES Mandy answered 10 questions out of 12 correctly on her math quiz. Howmany questions must she answer correctly to get the same score on a quiz with 30questions?7. NUMBER THEORY There are two single digit numbers. One number is 4 less than theother number. The sum of the digits is 12. Find the two numbers.8. GARDENING Justin helped his dad in the yard 3 times as long as Paula. Paula helpedher dad 2 hours less than Carly. Carly helped her dad in the yard 4 hours. How manyhours did Justin help his dad?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.278 SC StudyText, Course 3 Chapter 10

NAME DATE PERIOD10-3Homework PracticeProblem-Solving Investigation: Make a ModelSCAS 8-1.8Mixed Problem SolvingFor Exercises 1 and 2, solve using themake-a-model strategy.1. QUILTS Mrs. Renoir has completedthe interior portion of a quilt topmeasuring 4 feet by 6 feet. She isoutlining this with squares measuring4 inches on each side. How many suchsquares will she need?4. GAMES Jamal has a deck of 40 cards.After giving each player in the gamean equal number of cards, he has fourcards left over, which is not enough togive each player another card. Howmany players could be in the game?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2. GEOMETRY Kumiko has four plasticshapes, a circle, a square, a triangle,and a pentagon. In how many ways canshe line up the four shapes if the circlecannot be next to the square?Use any strategy to solve Exercises 3–6.Some strategies are shown below.Problem-Solving Strategies• Draw a diagram.• Guess and check.• Make a model.3. FOOTBALL The attendance at the firsttwo football games of the season areshown in the table. Did the attendanceincrease by about 1% or about 10%?Football AttendanceGame 1 5,049Game 2 5,5825. CLOTHING Salome has 5 T-shirts,3 pairs of jeans, and 2 pairs ofsneakers. In how many ways can shechoose one T-shirt, one pair of jeans,and one pair of sneakers to wear today?6. NUMBER THEORY After adding 8 to anumber and then dividing by 3, theresult is 19. What is the number?Chapter 10 SC StudyText, Course 3 279

NAME DATE PERIOD10-3 Problem-Solving PracticeSCAS 8-1.8Problem-Solving Investigation: Make a ModelMake a model to solve each problem.SHIPPING COCOA For Exercises 1 and 2, usethe information at the right. This tablegives information about cocoa tins thata distributor needs to box up and ship tovarious stores around the country.Sure-Safe Cocoa Tinsdimensions diameter: 4”, height: 8”quantity to beshipped153 tinsdimensions of largeshipping boxes18” × 18” × 24” high1. How many large shipping boxes can befilled with cocoa tins? How many cocoatins will be left over?2. What are the dimensions of thesmallest box that could be used to shipthe remaining cocoa tins?3. GAMES A hollow tower is built of1-inch cubes with dimensions of4 inches wide by 4 inches long by15 inches high. How many 1-inchcubes would it take to fill the tower?5. TILING A wooden box is to becovered with 1-inch square tiles. Thedimensions of the box are 10 inchesby 6 inches by 4 inches. There is anopening in the top of the box thatmeasures 8 inches by 4 inches. Howmany 1-inch tiles are needed to coverthe sides and the top of the box?4. STAMPS Angie wants to display herstamp collection on a poster. Eachstamp is a 1-inch square. She wants toarrange the stamps in a 24 by 48 arraywith one-half inch between each stampand leave a 2-inch border around theouter edges of the array. What shouldthe length and width of the posterboard be?6. PICTURE DISPLAY Julia is arrangingpictures of her mother, her father,her brother, and herself on a shelf. Ifshe wants to keep the pictures of herparents next to each other, how manydifferent ways can she arrange the fourpictures?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.280 SC StudyText, Course 3 Chapter 10

NameChapter 10 TestMastering the SC StandardsDate1 Which graph shows a linear relationship?Ay3 Look at the graph shown below. The points(1, 2) and (-1, -2) lie on the graph.Which equation is represented on the graph?Ox-4-3-2321Oy 41 2 3 4xBy-2-3-4Ay = 2xOxB y = 2 x 2C y = -2 x 2CyD y = 2 x 38-3.5Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.DOOy2 Which expression is equivalent to5 a 2 × 7a b2?A 12 a 2 b 2B 12 a 3 b 2C 35 a 2 b 2D 35 a 3 b 2 8-3.3xx8-3.54 Which expression has the same valueas 1_n 4 ?ABCDn_41_4n1_n × 1_n × 1_n × 1_nn × n × n8-1.45 Mieko needs to find an equivalentexpression for 4a × b. Which expressionbelow is the best choice?A 4aB 4bC 4abD 5ab8-3.3Chapter 10 SC StudyText, Course 3 281

NameDateChapter 10 Test (continued)Mastering the SC Standards6 John needs to find √ 200 . Between whichtwo whole numbers is the correct answer?A 12 and 13B 13 and 14C 14 and 15D 15 and 168-2.68 Which graph represents y =- 1_ 3 x 2 ?A-4-3-2x321O 1 2 3 4y4-2-3-4B4 y x7 Which table represents a nonlinearequation?321A x 1 2 3 4y 2 4 6 8-4-3-2O-2-3-41 2 3 4B x 1 2 3 4y 4 5 6 7C x 1 2 3 4y 5 8 11 14D x 1 2 3 4y 2 8 18 328-3.5CD-4-3-2-4-3-2x321O 1 2 3 4y4-2-3-4x321O 1 2 3 4y4-2-3-48-3.5Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.282 SC StudyText, Course 3 Chapter 10

11NAME DATE PERIODAnticipation GuideStatisticsSTEP 1 Before you begin Chapter 11• Read each statement.• Decide whether you Agree (A) or Disagree (D) with the statement.• Write A or D in the first column OR if you are not sure whether you agree or disagree,write NS (Not Sure).Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.STEP 1A, D, or NSStatement1. The bars of a histogram are all equal in width because theintervals are equal.2. An interval is not included in a histogram when the frequencyof that interval is zero.3. If a section of a circle graph is one fourth of the circle, thatsection represents 90%.4. The mean of a set of data is always more representative ofthe data set than the median or mode.5. The median of a set of data may be a number not in the dataset.6. The interquartile range of a set of data is the differencebetween the greatest and least numbers in the set.7. An outlier is a data value that is much higher or lower thanthe rest of the data set.8. The upper and lower quartiles of a data set are used todetermine where to draw the “box” of a box-and-whisker plot.9. Because outliers are extreme values they are not included ina box-and-whisker plot.10. A bar graph would be the best choice to show how muchchange has occurred over a period of time.11. To show how many times each number occurs in a data set, aline plot would be an appropriate display.STEP 2 After you complete Chapter 11• Reread each statement and complete the last column by entering an A or a D.• Did any of your opinions about the statements change from the first column?• For those statements that you mark with a D, use a piece of paper to write anexample of why you disagree.STEP 2A or DChapter 11 SC StudyText, Course 3 283

11NAME DATE PERIODFamily ActivityState Test PracticeFold the page along the dashed line. Work each problem on another piece ofpaper. Then unfold the page to check your work.1. A survey was taken of studentsat Huckleberry Middle Schools todetermine their favorite ice creamflavors. The following graph shows theresults of that survey.Favorite Ice Cream FlavorsVanillaChocolateOtherStrawberryAbout what percentage of studentsprefer vanilla ice cream?A 33% C 50%B 20% D 25%Fold here.Solution1. Hint: Relate the fraction of the circle thatrepresents the students who prefer vanillato the corresponding percentage.SolutionWe can estimate from the circle graphthat about 1_ of the students prefer4vanilla ice cream. A proportion can beused to calculate the correspondingpercent.1_4 = ?_1004 is multiplied by 25 to get 100, so inorder to make the proportion, 1 must bemultiplied by 25.25_100 = 25%2. The following data table showsinformation collected during Amy Jo’sscience experiment.DayHighTemperatureMonday 80°Tuesday 75°Wednesday 77°Thursday 88°Friday 93°Saturday 99°Sunday 81°What kind of graph would be best toshow Amy Jo’s data?A a bar graph C a circle graphB a line graph D a histogram2. Each type of graph listed can be bestused for certain types of situations.A bar graph is most useful to show thenumber of items in specific categories.A line graph is used to show a slowchange over a period of time.A circle graph compares the parts of thedata to the whole.A histogram is used to show thefrequency of data divided into equalintervals.In this case, we have a small variationin temperature over a period of time, soa line graph is the best choice.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.The answer is D. The answer is B.284 SC StudyText, Course 3 Chapter 11

NAME DATE PERIOD11-1Study GuideProblem-Solving Investigation: Make a TableSCAS 8-1.8You may need to use the make a table strategy to solve some problems.UnderstandPlanSolveCheckDetermine what information is given in the problem and what you need to fi nd out.Select a strategy including a possible estimate.Solve the problem by carrying out your plan.Examine your answer to see if it seems reasonable.ExampleFor his science fair project, August decided to classify the 20 rocks and minerals in hiscollection by their hardness using the Mohs scale. After performing various tests forhardness, he recorded the hardness value of each rock or mineral in his collection in a list.Organize the data in a table using hardness intervals 1–2, 3–4, 5–6, 7–8, 9–10. What is themost common interval of rock hardness?2 1 5 3 3 10 2 9 4 7 6 3 4 2 3 3 1 5 6 3UnderstandPlanYou have a list of the hardness values for each rock or mineral. You need toknow how many rocks have a hardness between 1 and 2, 3 and 4, 5 and 6,7 and 8, and 9 and 10. Then you need to determine the most commoninterval of hardness.Make a frequency table with intervals to organize the information.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Hardness Interval Tally Frequency1 –2 53 –4 85–6 47 –8 19–10 2Solve The most common interval of rock hardness is 3 –4.Check August tested 20 rocks for hardness. Since there are 20 values listed, thetable seems reasonable.ExercisesMake a table to solve each problem.1. BANKING The list shows the amount of cash requested by each person that used acertain Automated Teller Machine (ATM) in one day. What is the most common amountof money requested by ATM users?$20 $40 $20 $100 $300 $80 $40 $40 $80 $100 $120 $20$40 $80 $100 $60 $60 $20 $80 $100 $40 $20 $80 $402. COFFEE The list shows the coffee sizes in ounces purchased in one hour at a local coffeehouse. What is the most commonly purchased size of coffee?8 16 16 20 8 12 16 8 12 2020 16 12 8 8 16 16 20 16 20Chapter 11 SC StudyText, Course 3 285

NAME DATE PERIOD11-1 Skills PracticeProblem-Solving Investigation: Make a TableMake a table to solve each problem.SCAS 8-1.81. SCIENCE Ecology students investigated the number of chirps a cricket makes in 15seconds. Their results are shown below. What is the most common number of chirpsmade by crickets in a 15-second interval?30 31 30 32 32 31 30 30 30 31 30 32 31 30 30 31 3231 30 31 30 30 32 30 30 31 31 32 30 30 32 32 30 302. SPORTS TRAINING Thirty athletes were surveyed to determine how many hours per weekthey spend training for a marathon. Organize the data in a table using intervals 1–5,6–10, 11–15, 16 or more. What is the most common interval of hours practiced in a week?Interval Tally Frequency4 12 15 6 14 13 9 18 14 813 4 11 13 11 2 17 7 14 158 11 15 1 12 16 9 18 10 193. BOOKS Mr. Whitney’s class listed the number of bookseach student read during the first grading period. Theresults are shown at the right. Find the number of booksread that is listed most frequently.4. GAS PRICES A local news station researched the price of gas at 20 gas stationsthroughout the state and recorded the following results. Organize the data in a tableusing intervals $1.99 or less, $2–$2.15, more than $2.15. What is the most commoninterval of gas prices?$2.05 $2.19 $2.18 $2.15 $2.19 $2.20 $2.29 $2.05 $1.99 $2.18$2.19 $2.08 $2.00 $2.16 $2.19 $1.99 $2.21 $2.20 $2.00 $2.16Interval Tally Frequency0 3 62 8 47 5 32 9 67 55 6 33 3 47 8 29 7 41 05. ATTENDANCE The number of days students in Ms. Roe’s class were absent are as follows.1 0 3 4 1 0 2 0 3 4 1 3 4 1 2 0 1 2 0 34 1 3 4 1 2 0 1 2 4 3 1 2 2 2 1 3 1 1 2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.What is the most frequent number of days absent?286 SC StudyText, Course 3 Chapter 11

NAME DATE PERIOD11-1Homework PracticeProblem-Solving Investigation: Make a TableSCAS 8-1.8Mixed Problem SolvingUse the make a table strategy to solveExercises 1 and 2.1. LIZARDS Biologists recorded the lengthsof lizards they found in the desert.About what percent of the lizardlengths are from 3.0 to 6.9 inches?Use any strategy to solve Exercises 3–5.Some strategies are shown below.Problem-Solving Strategies• Use logical reasoning.• Act it out.• Make a table.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lengths of Lizards FoundLength(in.)Tally Frequency1.0–1.9 32.0–2.9 43.0–3.9 54.0–4.9 45.0–5.9 46.0–6.9 27.0–7.9 22. BOOKS The list below shows bookprices for various books at a used booksale. Organize the data in a table usingintervals $1.00–$1.99, $2.00 –$2.99,$3.00–$3.99, and so on. What is themost common interval of book prices?$3.78 $1.05 $6.52 $1.65 $4.99 $2.83$1.52 $4.85 $4.64 $5.10 $3.09 $1.90$6.29 $3.72 $6.50 $3.39 $2.55 $1.89$3.22 $4.26 $5.29 $4.99 $1.10 $2.503. ART FAIR At the art fair, 95 artistsexhibited their work. Of those 95artists, 25 showed sculptures and 48showed paintings. If 12 showed bothsculptures and paintings, how manyartists showed only sculptures orpaintings?4. NUMBER CUBE Jacy tossed a numbercube several times and recordedthe number shown after each toss.His results are listed below. Findthe number that was tossed mostfrequently.3 6 1 3 5 3 4 2 61 5 4 4 5 6 6 1 44 2 5 6 1 1 2 3 65. GEOGRAPHY Finland has a land area of117,943 square miles. If the total areaof Finland is 130,128 square miles,what percent of Finland's total area iswater, to the nearest tenth of a percent?Chapter 11 SC StudyText, Course 3 287

NAME DATE PERIOD11-1 Problem-Solving PracticeProblem-Solving Investigation: Make a TableMake a table to solve each problem.SCAS 8-1.8SURVEY For Exercises 1 and 2, use the information in the box. It shows the results of asurvey that asked consumers how many hours of television they watched, on average, eachweek.12 0 11 8 5 20 32 2 5 10 12 24 7 5 3 15 18 30 32 12 22 3 9 16 1 8 20 4 7 10 12 11 30 6 141. Organize the data in a table usingintervals 0-10, 11-20, 21-30, and morethan 30. What is the most commoninterval of hours of television watched?2. About what percent of the consumerssurveyed watch 10 hours or less oftelevision in a week?3. SPORTS The number of runs scored pergame by a baseball team are shownbelow. What is most frequent number ofruns scored?3, 3, 5, 7, 8, 7, 0, 1, 7, 6, 1, 1, 3, 4, 3, 5, 6,6, 3, 3, 5, 1, 2, 0, 3, 2, 8, 7, 3, 0, 3, 4, 3, 5,3, 2, 15. DISTANCES The distances that studentslive from school are shown below.Organize the data in a table usingintervals less than 1 mile, 1–3.9 miles,4–6.9 miles, 7 miles or more. What isthe most common interval of distancefrom school?1_2 , 2 1_2, 4, 3, 2, 1, 11_21, 2, 1, 3, 4 1_2 , 1_2 , 1_4 , 6 1_2 , 2 1_, 2, 3, 51_, 7, 6, 5, 21_2 4 ,2 , 3 1_ , 4, 21_24. SLEEP SURVEY Thirty ninth graderswere asked how many hours of sleepthey got the night before. The results ofthe survey are shown below. What isthe most common amount of sleepstudents got?6, 8, 7, 8, 9, 6, 10, 8, 7, 8, 9, 9, 8, 6, 10, 8,9, 7, 9, 8, 9, 6, 11, 7, 8, 9, 9, 7, 9, 10, 9, 76. TEST SCORES The scores on a recentmath test are shown below. Organizethe data in a table using intervals lessthan 70, 70–79, 80–89, 90–100. What isthe most common score interval?47, 71, 75, 70, 59, 78, 88, 82, 89, 92, 99,78, 88, 82, 92, 70, 85, 80, 90, 1004 , 1Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.288 SC StudyText, Course 3 Chapter 11

11-2NAME DATE PERIODExplore Through ReadingHistogramsGet Ready for the LessonRead the introduction at the top of page 576 in your textbook.Write your answers below.1. What do you notice about the price intervals in the table?SCAS 8-1.8, 8-1.72. How many tickets were at least $20.00 but less than $50.00?Read the Lesson3. Explain the difference between a bar graph and a histogram.4. What does a histogram display?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5. Can the data in the table at the right be usedto draw a histogram? Explain.6. What is wrong with the histogram at the right?Remember What You LearnedEye Color in anEighth-Grade ClassColor Tally FrequencyBlue 12Brown 9Green 37. Work with a partner. Have one partner create a frequency table. Have theother partner draw a histogram from the table.Number of Students10864200–5960–69Test Scores70–79Score80–8990–100Chapter 11 SC StudyText, Course 3 289

NAME DATE PERIOD11-2 Study GuideHistogramsSCAS 8-1.8, 8-1.7Data from a frequency table can be displayed as a histogram. A histogram is a type of bar graphused to display numerical data that have been organized into equal intervals. To make a histogramfrom a frequency table, use the following steps.Step 1 Draw and label a horizontal and a vertical axis. Include a title.Step 2 Show the intervals from the frequency table on the horizontal axis.Step 3 For each interval on the horizontal axis, draw a bar whose height is given by the frequencies.ExampleFOOTBALL The frequency tableat the right shows the scores ofall NFL teams in the first gameof a recent season. Draw ahistogram to represent the data.NFL Team ScoresScore Tally Frequency0–9 710–19 820–29 1330–39 340–49 1The histogram was created using the steps listed above.The horizontal axis is labeled “Score,” the vertical axisis labeled “Number of Teams,” and the histogram istitled “NFL Team Scores.” The intervals are shown onthe horizontal axis, and the frequencies are shown onthe vertical axis. A bar is drawn in each interval toshow the frequencies.ExercisesTAXES The frequency table shows thetax on gasoline for the 50 states. Drawa histogram to represent the set of data.Gas Tax for Each StateTax(cents/gal)Tally Frequency8.1 –12 212.1–16 516.1–20 2220.1–24 1224.1–28 628.1–32 3Number of Teams141210864200–9NFL Team Scores10–19 20–29 30–39 40–49ScoreCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.290 SC StudyText, Course 3 Chapter 11

NAME DATE PERIOD11-2 Homework PracticeHistograms1. GOVERNMENT The list gives the yearof birth for each state governor in theUnited States in 2007. Choose intervalsand make a frequency table. Thenconstruct a histogram to represent thedata.SCAS 8-1.8, 8-1.71944 1956 1952 1970 1957 19501964 1946 1942 1955 1941 19601957 1953 1955 1948 1963 19511946 1942 1963 1944 1940 19581947 1956 1956 1957 1944 19471956 1949 1954 1947 1942 19471946 1966 1960 1959 1954 19501935 1948 1947 1950 1943Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.FOOTBALL For Exercises 2–5, use the histograms shown.Number of Teams1816141210864200–910– 19Scores of Winning Teams, 1960—2006Gator BowlSugar Bowl1820– 2930– 3940–4950–592. Which bowl game had the higher winning team score?3. In which bowl game was the winning team score in the interval 30-39 pointsmore often?4. Determine which bowl game has had a winning team score of at least 30 pointsmore often.5. What was the lowest winning team score in each bowl game? Explain.Number of Teams16141210864200–910– 1920– 2930– 3940–4950– 59Chapter 11 SC StudyText, Course 3 291

NAME DATE PERIOD11-2 Problem-Solving PracticeSCAS 8-1.8, 8-1.7HistogramsEXAMS For Exercises 1–3, use thehistogram below that shows dataabout scores on a history test.MOVIES For Exercises 4–6, use thehistogram below that shows dataabout movie revenues in a recent year.Number of Students1412108642051–60Exam Scores61–7071–80Score81–9091–100Number of Movies1412108642061–100Revenues of the 25 Top Grossing Movies101–140141–180181–220221–260261–300301–340Revenue (millions)341–380381–420421–4601. How many students scored at least 81on the test? Explain how you foundyour answer.2. How many students scored less than81 on the exam? Explain how you foundyour answer.3. Can you determine the highest gradefrom the histogram? Explain.5. How many movies grossed between$61 million and $180 million? Explainhow you found your answer.4. How many movies grossed at least$141 million? Explain how you foundyour answer.6. Can you determine how many moviesgrossed between $121 and $140 millionfrom the histogram? Explain.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.292 SC StudyText, Course 3 Chapter 11

NAME DATE PERIOD11-4 Explore Through ReadingMeasures of Central Tendency and RangeGet Ready for the LessonRead the introduction at the top of page 591 in your textbook.Write your answers below.1. What number(s) appear the most in the bronze category?SCAS 8-6.82. What is the average number of medals won by the United States in thebronze category?3. Place the numbers in the bronze category in order from least to greatest.What is the middle number?Read the Lesson4. Name the most common measures of central tendency.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5. Explain in your own words how to find the mean of a data set.6. When finding the median, what first must be done to the set of data?Remember What You Learned7. Think about the hours of television you have watched each day in the pastweek. List the times, and find their mean, median, mode, and range. Whichmeasure of central tendency best represents the data? Compareyour findings with your classmates.Chapter 11 SC StudyText, Course 3 293

NAME DATE PERIOD11-4 Study GuideMeasures of Central Tendency and RangeSCAS 8-6.8The most common measures of central tendency are mean, median, and mode. The range is alsoused to describe a set of data. To fi nd the mean of a data set, fi nd the sum of the data values thendivide by the number of items in the set. To fi nd the median of a data set, put the values in order fromleast to greatest, then fi nd the middle number. If there are two middle numbers, add them togetherand divide by 2. The mode of a data set is the number or numbers that occur most often. If no numberoccurs more than once, the data set has no mode. The range of a data set is the difference betweenthe greatest number and the least number in a set of data.Example Find the mean, median, mode, and range of the set of data. Roundto the nearest tenth if necessary. The ages, in years, of relativesstaying at your home are listed below.5, 14, 8, 2, 89, 14, 10, 2MeanMedianMode5 ______+ 14 + 8 + 2 + 89 + 14 + 10 + 28The mean age is 18.= 18Arrange the numbers in order from least to greatest.2 2 5 8 10 14 14 89The middle numbers are 8 and 10. Since__ 8 + 10 = 9,2the median age is 9.Range 89–2 or 87The numbers 2 and 14 each occur twice. The dataset has two modes, 2 and 14.Different circumstances determine which measure of central tendency or range is mostappropriate to describe a set of data. The mean is most useful when the data has no extremevalues. The median is most useful when the data has a few extreme values with no biggaps in the middle of the data. The mode is most useful when the data has many identicalnumbers.ExercisesFind the mean, median, mode, and range of each set of data. Roundto the nearest tenth if necessary.1. 2, 4, 5, 1, 3 2. 7, 5, 7, 7, 6, 43. 18, 14, 15, 11, 14, 12, 17 4. 19, 24, 22, 16, 15, 27, 22, 275. 2.3, 1.1, 1.5, 3.2, 1.7, 2.0, 2.4, 1.8 6. 36, 32, 34, 34, 35, 38, 36, 34Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.7. 30, 29, 30, 31, 30 8. 4.2, 5.2, 2.3, 4.0, 4.6, 6.0, 2.3, 5.3294 SC StudyText, Course 3 Chapter 11

NAME DATE PERIOD11-4 Homework PracticeMeasures of Central Tendency and RangeFind the mean, median, mode, and range of each set of data. Round tothe nearest tenth if necessary.1. The prices, in dollars, of day packs 2. Points on quizzes37, 43, 41, 36, 43 13, 6, 9, 8, 14, 5, 10, 7SCAS 8-6.83. 4. 0 5 10 150 0.5 1.0For Exercises 5 and 6, select the appropriate measure of central tendency orrange to describe the data in each table. Justify your reasoning. Sample answersare given.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5. Known Mountains on MarsMountain Height (km)Alba Patera 3Arsia Mons 9Ascraeus Mons 11Olympus Mons 27Pavonis Mons 76. Average Lengths of Wild CatsCat Length Cat LengthCheetah 50.5 in. Lion 102 in.Eurasian 24.3 in. Puma 60 in.WildcatJaguar 57.5 in. Serval 33.5 in.Leopard 57 in. Tiger 128 in.Source: Facts on File: Animal Fact File7. MARS Refer to the table of mountains on Mars in Exercise 5. Describe how the mean,median, mode, and range are each affected if the data for Olympus Mons is notincluded.Chapter 11 SC StudyText, Course 3 295

NAME DATE PERIOD11-4 Problem-Solving PracticeSCAS 8-6.8Measures of Central Tendency and RangeANIMALS For Exercises 1–4, use theinformation in the table below thatshows the lifespan of selected mammals.Round to the nearest tenth if necessary.Average Lifespan for MammalsMammal Average LifespanBaboon20 yrCamel12 yrChimpanzee20 yrCow15 yrGoat 8 yrGorilla20 yrMoose12 yrPig10 yrFOOTBALL For Exercises 5 and 6,use the information in the tablebelow. Round to the nearest tenthif necessary.2006 NFL Season, Games WonTeam Games WonAtlanta 7Carolina 8Denver 9Kansas City 9New Orleans 10Oakland 2St. Louis 8San Diego 14San Francisco 7Seattle 91. Explain how to find the mean of thelifespans listed in the table. Then findthe mean.3. Explain how to find the mode of the setof data. Then find the mode.5. What are the mean, median, mode, andrange of the number of games won bythe teams in the table?2. Explain how to find the median of theset of data. Then find the median.4. Which measure of central tendencyis most representative of the data?Explain.6. Which measure of central tendencyis most representative of the data?Explain.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.296 SC StudyText, Course 3 Chapter 11

NAME DATE PERIOD11-7 Explore Through ReadingStem-and-Leaf PlotsGet Ready for the LessonRead the introduction at the top of page 612 to Lesson 11-7 in yourtextbook. Write your answers below.a. Is there an equal number of electors in each group? Explain.SCAS 8-1.8, 8-1.7b. Name an advantage of displaying the data in groups.Read the Lesson 1–4.Write a definition and give an example of each new vocabulary word or phrase.Vocabulary Definition Example1. stem-andleafplotCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2. stems3. leaves4. back-to- backstem-andleafplotRemember What You Learned5. How will you rememberwhich numbers of a stemand-leafplot representthe greater place value?Use the data to drawa back-to-back stemand-leafplot like actualleaves on stems. Readthe data from the treetrunk and move outward.Ages of PersonsApartmentBuilding AApartmentBuilding B33 16 1939 21 20 126 23 1110 21 36 3734 24 3732 22 11 217 2910 1 32 3812 36 39Chapter 11 SC StudyText, Course 3 297

NAME DATE PERIOD11-7 Study GuideStem-and-Leaf PlotsSCAS 8-1.8, 8-1.7Stem-and-Leaf PlotWords One way to organize and display data is to use a stem-and-leaf plot.In a stem-and-leaf plot, numerical data are listed in ascending ordescending order.Stem LeafModelThe greatest placevalue of the data isused for the stems.2340 1 1 2 3 5 5 61 2 2 3 7 90 3 4 8 83 7 = 37The next greatestplace value formsthe leaves.Example ZOOS Display the data shownat the right in a stem-and-leaf plot.Step 1 The least and the greatestnumbers are 55 and 95. Thegreatest place value digit ineach number is in the tens.Draw a vertical line and writethe stems from 5 to 9 to theleft of the line.Step 2 Write the leaves to the right ofthe line, with the correspondingstem. For example, for 85, write5 to the right of 8.Step 3 Rearrange the leaves so theyare ordered from least togreatest. Then include a key oran explanation.ExercisesStem56789Stem56789Display each set of data in a stem-and-leaf plot.1. {27, 35, 39, 27,Leaf2. {94, 83, 88, 77,24, 33, 18, 19} 95, 99, 88, 87}ROLLER COASTERS For Exercises 3 and 4, use thestem-and-leaf plot shown.3. What is the speed of the fastest roller coaster?The slowest?4. What is the median speed?LeafLeaf8 5455 0 05 0 25 8450 0 50 2 58 5 = 85 acresThe Fastest Roller CoastersStem8910LeafSize of U. S. ZoosZooSize(acres)Audubon58(New Orleans)Cincinnati 85Dallas 95Denver 80Houston 55Los Angeles 80Oregon 64St. Louis 90San Francisco 75Woodland92Park (Seattle)3 52 508 3 = 83 mphCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.298 SC StudyText, Course 3 Chapter 11

NAME DATE PERIOD11-7Homework PracticeStem-and-Leaf PlotsSCAS 8-1.8, 8-1.7Display each set of data in a stem-and-leaf plot.1. {68, 63, 70, 59, 2. {27, 32, 42, 31, 36,78, 64, 68, 73, 37, 47, 23, 39,61, 66, 70} 31, 41, 38, 30,34, 29, 42, 37}3. Major League BaseballLeading Pitchers, 2007PlayerWinsJ. Beckett 20F. Carmona 19J. Lackey 19B. Webb 18A. Harang 16T. Hudson 16K. Escobar 18T. Wakefield 17J. Peavy 19J. Francis 174. Average Prices Received byU.S. FarmersPriceCommodity (dollars per100 pounds)Beef Cattle 86Hogs 49Lambs 101Milk 16Veal Calves 119Source: U. S. Department of AgricultureCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.RECREATION For Exercises 5–7, use the informationin the back-to-back stem-and-leaf plotshown at the right.5. The category with the lowest total expenditurein 2002 was motion pictures. What was itstotal?6. What is the median total recreational spendingfor 2002? For 2006?7. Compare the total spending on recreation in2002 with that in 2006.Total U.S. Spending on Personal Recreation (by Category)2002 20067 5 58 7 2 07 24 0Chapter 11 SC StudyText, Course 3 2991012345678990 2 824 5 74607 2 = $27 billion 3 5 = $35 billion4

NAME DATE PERIOD11-7Problem-Solving PracticeStem-and-Leaf PlotsSCAS 8-1.8, 8-1.71. CUSTOMER SERVICE A restaurant ownerrecorded the average time in minutescustomers waited to be seated eachnight. His data are shown in the tablebelow. To organize the data into a stemand-leafplot, how many stems wouldyou need?Week 1 15 8 10 5 20 35 45Week 2 9 3 7 8 25 38 432. PHONE Allison’s mother makes astem-and-leaf plot to track the time inminutes that Allison spends talkingon the phone each night. In whichinterval are most of the Allison’s calls?4. TEST SCORES The scores from the mostrecent test in Mr. James’ biology classare shown in the stem-and-leaf plotbelow. Find the highest and lowestscores, and then write a statement thatdescribes the data.Stem56789Leaf4 53 7 80 1 5 5 8 90 2 3 7 90 3 5 8 85 4 = 54%Stem1234Leaf0 53 4 5 8 90 5 81 3 51 5 = 15 minutes3. ELECTRIC BILLS Jenny’s family is sellingtheir house. Jenny’s mother wantsto put together a table of monthlyelectricity costs. Below is a list oftheir electric bills for the past twelvemonths. Organize the data in a stemand-leafplot. In which interval aremost of the electric bills?$95, $99, $85, $79, $82, $88,$98, $95, $94, $87, $89, $90Stem789Leaf92 5 7 8 90 4 5 5 8 9SPORTS For Exercises 5–7, use thefollowing information.Tamara and LaDawn have recorded theirtimes in seconds in the 100-meter dashfrom the past six track meets in the tablebelow.LaDawn 16.5 16.6 17.0 16.8 17.2 17.1Tamara 16.7 16.4 16.1 17.0 16.5 16.85. Organize the times in a back-to-backstem-and-leaf plot.6. What are the median times for LaDawnand for Tamara?7. If you were the coach, who would youchoose to represent the team at thenext competition? Explain.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.300 SC StudyText, Course 3 Chapter 11

NAME DATE PERIOD11-8 Explore Through ReadingSelect an Appropriate DisplayGet Ready for the LessonRead the introduction at the top of page 617 in your textbook.Write your answers below.1. Which display(s) show how many cities had a temperature of exactly 79° F?SCAS 8-1.7, 8-1.62. Which display(s) show the interval of temperatures for half of the cities?Read the Lesson3. Name three different ways to display data.4. What two questions should you ask yourself when determining which typeof display to use?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Remember What You LearnedChoose the letter that best matches the type of display to its use.5. Circle Graph a. shows the frequency of data that has been organizedinto equal intervals6. Line Graph b. lists all individual numerical data in a condensed form7. Bar Graph c. shows the number of items in specific categories in thedata using bars8. Histogram d. compares part to a whole9. Line Plot e. shows change over a period of time10. Stem-and-Leaf Plot f. shows how many times each number occurs inthe dataChapter 11 SC StudyText, Course 3 301

NAME DATE PERIOD11-8 Study GuideSCAS 8-1.7, 8-1.6Select an Appropriate DisplayThere are many different ways to display data. Some of these displays andtheir uses are listed below.Type of DisplayBar GraphBox-and-Whisker PlotCircle GraphHistogramLine GraphLine PlotStem-and-Leaf PlotVenn DiagramBest Used toshow the number of items in specific categories.show measures of variation for a set of data.compare parts of the data to the whole.show frequency of data divided into equal intervals.show change over a period of time.show how many times each number occurs in the data.list all individual numerical data in condensed form.show how elements among sets of data are related.As you decide what type of display to use, ask the following questions.• What type of information is this?• What do I want my graph or display to show?Remember, all data sets can be displayed in more than one way. And there is often morethan one appropriate way to display a given set of data.ExamplesChoose an appropriate type of display for each situation.the change in the winning times for the Kentucky Derby for the last 15 yearsThis data does not deal with categories or intervals. It deals with the change of a valueover time. A line graph is a good way to show changes over time.energy usage in the U.S., categorized by the type of userIn this case, there are specific categories. If you want to show the specific amount ofenergy used in each category, use a bar graph. If you want to show how each category isrelated to the whole, use a circle graph.ExercisesSelect an appropriate type of display for each situation. Justify your reasoning.1. the cost of homeowners insurance over the past 10 years2. the amount of federally owned land in each state, arranged in intervalsCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.302 SC StudyText, Course 3 Chapter 11

NAME DATE PERIOD11-8 Homework PracticeSelect an Appropriate DisplaySelect an appropriate type of display for each situation. Justify yourreasoning.1. prices of athletic shoes in the store arranged by intervals2. the numbers of teens who spend Saturdays doing homework, playing,and/or doing choresSCAS 8-1.7, 8-1.63. the number of each of four kinds of trees found in the forest4. the spread of the run times for the first 1_4a marathonof the runners completingSelect an appropriate type of display for each situation. Justify yourreasoning. Then construct the display.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5.Heights of Mountains on the MoonHeight Percent of the Mts.Less than 1 km 11.8%1-2 km 17.7%2-3 km 17.7%3-4 km 35.3%More than 4 km 17.7%6. WORK Jim worked 1 hour on Monday. OnTuesday, he worked 2 more hours than he workedon Monday. On Wednesday, he worked 2 morehours than he worked on Tuesday. The patterncontinued through Friday.Chapter 11 SC StudyText, Course 3 303

11ANAME DATE PERIODStudy GuideOrganize Data In MatricesOrganize and Analyze DataMatrixa rectangular array of variables or constants in horizontal rows and verticalcolumns, usually enclosed in brackets.SCAS 8-6.2A matrix can be described by its dimensions. A matrix with m rows and n columns is anm × n matrix.Example 1 Owls’ eggs incubate for 30 days and their fledgling period is also30 days. Swifts’ eggs incubate for 20 days and their fledgling period is 44 days.Pigeon eggs incubate for 15 days, and their fledgling period is 17 days. Eggs of theking penguin incubate for 53 days, and the fledgling time for a king penguin is360 days. Write a 2 × 4 matrix to organize this information.⎡ Owl Swift Pigeon King Penguin ⎤IncubationFledgling ⎢ 30 20 1553 ⎣ 30 44 17360 ⎦Example 2What are the dimensions of matrix A if A = ⎡ 13⎢⎣ 2108-31545 ⎤ 80 ⎦ ?Since matrix A has 2 rows and 4 columns, the dimensions of A are 2 × 4.ExercisesCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.State the dimensions of each matrix.1.⎡ 1523⎢ 14⎣ 63567032702442-4 ⎤5-3 30 ⎦2. [16 12 0] 3.⎡⎢⎣71 4439 2745 1692 5378 654. A travel agent provides for potential travelers the normal high temperatures for themonths of January, April, July, and October for various cities. In Boston these figuresare 36°, 56°, 82°, and 63°. In Dallas they are 54°, 76°, 97°, and 79°. In Los Angeles theyare 68°, 72°, 84°, and 79°. In Seattle they are 46°, 58°, 74°, and 60°, and in St. Louisthey are 38°, 67°, 89°, and 69°. Organize this information in a 4 × 5 matrix.⎤⎦Chapter 11 SC StudyText, Course 3 305

11ANAME DATE PERIODSkills PracticeOrganize Data in Matrices1. The selling prices for various luxury condominiums are listed in the table below.Condo Devopment 1 Bedroom 2 Bedrooms 3 BedroomsFoxpointe Estates $349,000 $449,000 $499,000Condos at Salmon $329,900 $389,900 $439,900BrookKean Mills $499,000 $649,000 $799,000a. Write a matrix to organize the selling prices of the condos.SCAS 8-6.2b. What are the dimensions of the matrix?c. Which condo is the most expensive? least expensive?2. TICKET PRICES The table at the rightgives ticket prices for a concert. Writea 2 × 3 matrix that represents the costof a ticket.3. INVENTORY A store manager records the number of light bulbs in stock for 3different brands over a five-day period. The manager decides to make a matrixof this information. Each row represents a different brand, and each column representsa different day. The entry in column N represents the inventories at the beginning ofday N.⎡ 25⎢ 30⎣ 2824272522252120221919 ⎤21 19 ⎦Cost Purchasedin AdvanceCost Purchasedat the DoorChild Student Adult$6 $12 $18$8 $15 $22Assuming that the inventories were never replenished, which brand holds the record formost light bulbs sold on a given day?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.306 SC StudyText, Course 3 Chapter 11

11ANAME DATE PERIODHomework PracticeOrganize Data in MatricesSCAS 8-6.21. WEATHER The temperatures observed on different days in different cities are shownin the table below.CityMonday Tuesday Wednesday Thursday Fridaya. Write a matrixto organize theLas Vegas 94°F 99°F 101°F 98°F 89°FtemperaturePhoenix 92°F 86°F 99°F 104°F 101°Fb. What are the dimensions of the matrix?c. Which day and location had the highest temperature? lowest temperature?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2. STOCK PRICES The chart below showsthe performance of one share of PQRCorp. and ABC Corp. over the lastweek.Price Per Share5249464340PQR Corp.ABC Corp.Mon Tue Wed ThuDay of the WeekOrganize the data in the chart into amatrix.Fri3. FOOD SALES The daily sales at variousfast food restaurants in various citiesare shown in the table below.City McPizza BurgerHutQuikSubsDulles $25,000 $17,400 $21,000Fitchburg $3,600 $4,400 $5,900Newton $19,200 $20,100 $17,400a. Write a matrix to organize the salesdata.b. What are the dimensions of thematrix?c. In which city does Burger Hut sellmore food than its competitors?Chapter 11 SC StudyText, Course 3 307

NAME DATE PERIOD11AProblem-Solving PracticeOrganize Data in MatricesSCAS 8-6.21. LAUNDRY Carl is looking for aLaundromat. SuperWash has 20 smallwashers, 10 larger washers, and 20dryers. QuickClean has 40 smallwashers, 5 large washers, and 50dryers. ThoughSuds has 15 smallwashers, 40 larger washers, and 100dryers. Write a matrix to organize thisinformation.2. HAWAII The table shows thepopulation and area of some of theislands in Hawaii. What would bethe dimensions of a matrix thatrepresented this information?Island Population AreaHawaii 120,317 4,038Maui 91,361 729Oahu 836,231 594Kauai 50,947 549Lanai 2,426 1403. SHOE SALES A shoe store managerkeeps track of the amount of moneymade by each of three salespeoplefor each day of a workweek. Mondaythrough Friday, Carla made $40, $70,$35, $50 and $20. John made $30, $60,$20, $45, and $30. Mary made $35,$90, $30, $40, and $30.a. Organize this data in a 3 by 5matrix.b. Which salesperson made the mostmoney that week?4. BASEBALL In Tuesday’s baseball game,Reggie scored 1 run and had 4 hitsand 1 stolen base. Jeremy scored 2runs, had 5 hits, and stole no bases.In Wednesday’s baseball game, Reggiedidn’t score any runs, but did have 3hits and 1 stolen base. Jeremy had 1run, 4 hits, and 1 stolen base.a. Create a matrix showing Reggie andJeremy’s performance in Tuesday’sbaseball game.b. Create a matrix showing Reggieand Jeremy’s performance inWednesday’s baseball game.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.308 SC StudyText, Course 3 Chapter 11

NameChapter 11 TestMastering the SC StandardsDateCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.1 The list below shows the high temperaturesMaria recorded for 8 days in her hometownof Columbia.70ºF 80ºF 62ºF 93ºF68ºF 87ºF 73ºF 87ºFWhich histogram correctly displays theinformation?ABCD 8-1.82 Mark’s science test scores for the firstquarter are 50, 50, 79, 82, 83, and 84.Which measure would show the highestresult?A meanB medianC modeD range8-6.83 A farmer measures the heights of his tenhorses and ponies. The results of the dataare summarized in the box-and-whiskerplot below.50 55 60inchesWhat is the difference in height betweenthe tallest horse and the shortest pony?A 2 inchesB 6 inchesC 8 inchesD 12 inchesReview of 7-6.24 Which of the following types of datadisplays is most appropriate for showinghow data changes over time?A bar graphB circle graphC line graphD line plot8-1.7Chapter 11 SC StudyText, Course 3 309

NameDateChapter 11 Test (continued)Mastering the SC StandardsUse the following information to answerquestions 5 and 6.The Carolina mantid, a type of praying mantis,became South Carolina’s state insect in 1988. Ithelps to control the number of harmful insects inthe area. Sarah studies the Carolina mantid for ascience project. She records the number ofmantids she sees in a 6-day period in the chartbelow.Number ofDaymantids1 32 53 04 45 16 57 Chen conducts a survey of his classmates.He asks each student to chose his or herfavorite cafeteria lunch. He lists the resultsin the table below.FavoriteLunch ItemNumber ofStudentsturkey sandwich 5pizza 9soup 3pasta 4salad 4other 5If Chen creates a circle graph to show thepercentage of students who chose each typeof lunch, what will be the degree measureof the sector labeled “pizza”?5 What is the mode of Sarah’s data?A 3B 3.5C 4D 58-6.86 Sarah needs to find the mean number ofmantids that she saw over the 6 days. Whatis the correct answer?A 3B 3.5C 4D 58-6.8A 154ºB 108ºC 30ºD 9ºReview of 7-6.28 Jerome counted the number of people thatcame into his family’s kayak rental store onLake Marion each day for 5 days. What isthe range of the data?A 8B 9C 11D 1515 7 11 8 48-6.8Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.310 SC StudyText, Course 3 Chapter 11

12NAME DATE PERIODAnticipation GuideProbabilitySTEP 1 Before you begin Chapter 12• Read each statement.• Decide whether you Agree (A) or Disagree (D) with the statement.• Write A or D in the first column OR if you are not sure whether you agree or disagree,write NS (Not Sure).Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.STEP 1A, D, or NSStatement1. In a tree diagram, all possible outcomes of a certain eventare listed.2. To count the number of possible outcomes when there areseveral events, it is better to use a tree diagram than theFundamental Counting Principle.3. Choosing a card from a deck and holding it, then choosing asecond card from the deck is an example of two independentevents.4. Experimental probability is found by dividing the number offavorable outcomes by the number of possible outcomes.5. The experimental and theoretical probabilities of an eventare not expected to be the same.6. One example of picking an unbiased sample for a surveywould be for a magazine to ask if readers would like toparticipate in the survey.7. Surveying every tenth person could be an example of asystematic random sample.STEP 2 After you complete Chapter 12• Reread each statement and complete the last column by entering an A or a D.• Did any of your opinions about the statements change from the first column?• For those statements that you mark with a D, use a piece of paper to writean example of why you disagree.STEP 2A or DChapter 12 SC StudyText, Course 3 311

12NAME DATE PERIODFamily ActivityState Test PracticeFold the page along the dashed line. Work each problem on anotherpiece of paper. Then unfold the page to check your work.1. Callyn is using the spinner shown belowin a probability experiment.01233 02 1Which of the following is not true of thespinner shown above?A There are four outcomes.B The probability of spinning a 0 is 1_4 .C There are eight outcomes.D None of these are false.2. A breeder is making a waiting list ofgood homes for puppies that are to beborn in June. All of the customers onthe list wish to purchase a femalepuppy.If the dog has five puppies, what is theprobability that they will all be female?AB1_325_32C 1_5D 0Fold here.Solution1. Hint: The number of outcomes is equal tototal number of DIFFERENT possibilitiesin a probability experiment.A There are four possible outcomes: 0,1, 2, or 3, so this statement is true.B The probability of spinning a 0 is2 out of 8 because there are two 0spaces and 8 total spaces. 2 out of8 can be reduced to 1 out of 4, so thisstatement is true.C Since there are two of each outcome,there are only 4 possible outcomes,so this statement is not true.D Since we determined that option Cis not true, this statement does notapply.Solution2. Hint: The probability of each puppybeing female is 1 in 2, or 1_2 .When you are calculating theprobability of compound events, ormultiple things happening, you multiplythe probabilities of all of the individualevents. In this case, the probability thateach puppy will be female is one out oftwo, so the probability that they will allbe female is:1_2 × 1_2 × 1_2 × 1_2 × 1_2 = 1_32 .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.The answer is C. The answer is A.312 SC StudyText, Course 3 Chapter 12

12-2NAME DATE PERIODExplore Through ReadingProbability of Compound EventsGet Ready for the LessonRead the introduction at the top of page 637 in your textbook.Write your answers below.1. What is the probability of buying a beach towel? receiving a red tote bag?2. What is the product of the probabilities in Exercise 1?3. Draw a tree diagram to determine the probability that someone buys abeach towel and receives a red tote bag.SCAS 8-6.4, 8-6.5Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Read the Lesson4. What is a compound event?5. Are the events of spinning a spinner and rolling a number cubeindependent events? Why or why not?6. Explain how to find the probability of two independent events.Remember What You Learned7. Look up the everyday definitions of the words dependent and independentin a dictionary. How does each definition relate to what you have learnedin this lesson?Chapter 12 SC StudyText, Course 3 313

NAME DATE PERIOD12-2 Study GuideProbability of Compound EventsSCAS 8-6.4, 8-6.5The probability of two independent events can be found by multiplying the probability of the fi rst eventby the probability of the second event.Example 1 Two number cubes, one red and one blue, are rolled. What is theprobability that the outcome of the red number cube is even and the outcome ofthe blue number cube is a 5?P(red number cube is even) = 1_ 2P(blue number cube is a 5) = 1_ 6P(red number cube is even and blue number cube is a 5) = 1_ 2 · 1_ 6 or 1_ 12This probability that he two events will occur 1_ 12If two events, A and B, are dependent, then the probability of both events occurring is the product ofthe probability of A and the probability of B after A occurs.Example 2 There are 6 black socks and 4 white socks in a drawer. If one sockis taken out without looking and then a second is taken out, what is theprobability that they both will be black?P(first sock is black) = 6_10P(second sock is black) = 5_9P(two black socks) = 3_5 · 5_9or3_5or1_3The probability of choosing two black socks is 1_3 .Exercises6 is the number of black socks; 10 is the total number of socks.5 is the number of black socks after one black sock is removed;9 is the total number of socks after one black sock is removed.A card is drawn from a deck of 10 cards numbered 1 through 10 and anumber cube is rolled. Find each probability.1. P(10 and 3) 2. P(two even numbers)3. P(two prime numbers) 4. P(9 and an odd number)5. P(two numbers less than 4) 6. P(two numbers greater than 5)There are 4 red, 6 green, and 5 yellow pencils in a jar. Once a pencil isselected, it is not replaced. Find each probability.7. P(red and then yellow) 8. P(two green)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.9. P(green and then yellow) 10. P(red and then green)314 SC StudyText, Course 3 Chapter 12

NAME DATE PERIOD12-2Homework PracticeProbability of Compound EventsSCAS 8-6.4, 8-6.5The two spinners at the right are spun. Find each probability.1. P(4 and C) 2. P(1 and A)3. P(even and C) 4. P(odd and A)768 15423ABCAAB5. P(greater than 3 and B) 6. P(less than 5 and B)GAMES There are 10 yellow, 6 green, 9 orange, and 5 red cards in a stack ofcards turned facedown. Once a card is selected, it is not replaced. Find eachprobability.7. P(two yellow cards) 8. P(two green cards)9. P(a yellow card and then a green card) 10. P(a red card and then an orange card)11. P(two cards that are not orange)12. P(two cards that are neither red nor green)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.13. OFFICE SUPPLIES A store sells a box of highlighters that contains 4 yellow, 3 blue, 2 pink,and 1 green highlighter. What is the probability of randomly picking 1 blue and1 pink highlighter from the box?14. BASKETBALL Angelina makes 70% of her free throws. What is the probability that shewill make her next two free throws?CAR RENTALS For Exercises 15 and 16, use thefollowing information and the information inthe table.At a car rental office, 63% of the customers aremen and 37% are women.15. What is the probability that the next customerwill be a woman who requests a convertible?16. What is the probability that the next customerwill be a man who requests either a compact car or luxury car?Car RequestsCompact 25%Full-size 37%Convertible 10%SUV 16%Luxury 12%Chapter 12 SC StudyText, Course 3 315

NAME DATE PERIOD12-2 Problem-Solving PracticeProbability of Compound EventsSCAS 8-6.4, 8-6.51. CHECKERS In a game of checkers, thereare 12 red game pieces and 12 blackgame pieces. Julio is setting up theboard to begin playing. What is theprobability that the first two checkershe pulls from the box at random will betwo red checkers?2. CHECKERS What is the probability thatthe first two pieces are a red followedby a black? Explain how you foundyour answer.CHESS For Exercises 3–5, use the following information.Ingrid keeps her white and black chess pieces in separate bags. For each color,there are 8 pawns, 2 rooks, 2 bishops, 2 knights, 1 queen, and 1 king.3. Are the events of drawing a knightfrom the bag of white pieces anddrawing a pawn from the bag of blackpieces dependent or independentevents? Explain. Find the probability ofthis compound event.5. Find the probability of drawing apawn, a knight, and another pawnfrom the bag of white pieces.4. Are the events of drawing a bishopfrom the bag of white pieces and thendrawing the queen from the samebag dependent or independent events?Explain. Find the probability of thiscompound event.6. SOCCER During a soccer season, Mariomade approximately 2 goal points forevery 5 of his shots on goal. What is theprobability that Mario would make 2goal points on two shots in a rowduring the season?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.316 SC StudyText, Course 3 Chapter 5

NAME DATE PERIOD12-3 Explore Through ReadingSCASExperimental and Theoretical ProbabilityGet Ready for the LessonComplete the Mini Lab at the top of page 643 in your textbook.Write your answers below.______number of times color was drawn1. Find the ratio for each color.total number of draws8-6.3, 8-6.6,8-1.22. Is it possible to have a certain color marble in the bag and never drawthat color?3. Open the bag and count the marbles. Find the rationumber _____of each color marblefor each color of marble.total number of marbles4. Are the ratios in Exercises 1 and 3 the same? Explain.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Read the Lesson5. The table at the right shows the resultsof a survey.How many people bought balloons? __________How many people were surveyed? __________What is the experimental probability thata person surveyed preferred balloons?6. A bag contains 15 red marbles, 25 purple marbles, and 10 yellow marbles.Describe an experiment that you could conduct with the marbles to findan experimental probability.Remember What You LearnedItem Number of Peopleballoons 75cards 15decorations 25cake 507. One way to remember the difference between experimental probabilityand theoretical probability is to note that experimental probability isbased on an experiment and theoretical probability is based on whatshould happen in theory. Look in a newspaper and find an example ofeach type of probability.Chapter 12 SC StudyText, Course 3 317

NAME DATE PERIOD12-3 Study GuideExperimental and Theoretical ProbabilitySCAS8-6.3, 8-6.6,8-1.2Probabilities based on the outcomes obtained by conducting an experiment are called experimentalprobabilities. Probabilities based on known characteristics or facts are called theoreticalprobabilities. Theoretical probability tells you what should happen in an experiment.Examples Kuan is conducting an experiment tofind the probability of getting 0, 1, 2,or 3 heads when tossing three coinson the floor. The results of hisexperiment are given at the right.Based on the results in the bar graph, what is the probability of getting 3heads on the next toss?There were 22 tosses and 2 of those had 3 heads. The experimental probability is 2_22or1_11 .Based on the experimental probability, how many times should Kuan expectto get 3 heads in the next 55 tosses?Kuan should expect to get 3 heads about 1_ · 55 or 5 times.11What is the theoretical probability of getting 3 heads on a toss?The theoretical probability is 1_2 · 1_2 · 1_ or1_2 8 .The experimental probability and the theoretical probability seem to be consistent.ExercisesUse the table that shows the results ofspinning a game spinner 50 times.1. Based on the results in the table, whatis the probability of spinning green?2. Based on the results, how many green spins would you expect to occur in 300 spins?3. What is the theoretical probability of spinninggreen?4. Based on the theoretical probability, how many greenspins would you expect to occur in 300 spins?5. Compare the theoretical probability to the experimentalprobability.Number of TossesColor Number of Timesgreen 18red 24blue 81086420RedGreenResults of Tossing 3 Coins0GreenBlue1 2Heads3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.318 SC StudyText, Course 3 Chapter 12

NAME DATE PERIOD12-3Homework PracticeSCAS8-6.3, 8-6.6,8-1.2Experimental and Theoretical ProbabilityTELEPHONES For Exercises 1 and 2, use the following information.Of the last 45 telephone calls received at a bank, 6 involved questions aboutAutomatic Teller Machines (ATM) locations.1. What is the probability that the next call will involve a question about thelocation of an ATM?2. If 500 calls are received in one day, how many would you expect to be questions aboutATM locations?3. ARCHERY Julius hit the center of the target with 8 of his last 36 arrows.What is the experimental probability that he will hit the center with hisnext arrow?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.DRINKS For Exercises 4 and 5, use theinformation about drinks ordered by 200customers at a restaurant.4. What is the probability that a customerordered milk?5. On a day when the restaurant has 800customers, how many would you expect toorder milk?6. NEWSPAPERS In the last 40 days, Mr. Neptune’s newspaper has beendelivered late 6 times. What is the experimental probability that it willbe delivered late tomorrow?TECHNOLOGY For Exercises 7 and 8, use theresults of a survey of 80 teens at a schoolshown at the right.7. What is the probability that a teen at theschool owns a digital camera?8. Out of 750 students at the school, how manywould you expect to own a digital camera?Drinks OrderedDrink NumberWater 64Milk 22Coffee 35Soft Drink 68Other 11TechnologyDeviceNumber WhoOwnCell Phone 45Digital Camera 32DVD Player 65Laptop Computer 18Chapter 12 SC StudyText, Course 3 319

NAME DATE PERIODMini-Project(Use with Lesson 12-3)SCAS8-6.3, 8-6.6,8-1.2Experimental and Theoretical Probability1. Find the probability of rolling each number on a number cube. This is called thetheoretical probability.1 2 3 4 5 62. Roll a number cube six times. Record the results of each roll in the table.Roll 1 2 3 4 5 6Result3. Find the experimental probability for the data above.1 2 3 4 5 64. Compare the experimental probability with the theoretical probability. How do they differ?What could you do to make the results closer?5. Roll a number cube 30 times. Record the results of each roll in a frequency table.Roll 1 2 3 4 5 6Number of Times6. Find the experimental probability for the data above. Sample answers:1 2 3 4 5 67. Compare the experimental probability of 30 rolls with the theoretical probability.How do they differ?8. Write a summary statement. Describe any connections you notice. Mention theexperimental probability, the theoretical probability, and the effect of thenumber of trials on the experimental probability.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.320 SC StudyText, Course 3 Chapter 12

12-4NAME DATE PERIODStudy GuideProblem-Solving Investigation: Act It OutSCAS 8-1.8, 8-6.3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Example Michael has a red square tile, a blue square tile, a green square tile,and a yellow square tile. How many different ways can he arrange the tiles so thatthey form a larger square?UnderstandPlanThere are four tiles that can be arranged into a larger 2 by 2 square. Howmany different ways can the tiles be arranged into the larger square?Use letters to stand for each color tile. Arrange the tiles starting with eachcombination of tiles that has the red tile in the upper left corner. Thenrepeat this step for each of the other three colors.Solve RB RB RG RG RY RY There are 6 large squares with theGY YG BY YB BG GB red tile in the upper left.CheckExercisesBR BR BG BG BY BY There are 6 large squares with theGY YG RY YR RG GR blue tile in the upper left.GR GR GB GB GY GY There are 6 large squares with theBY YB RY YR RB BR green tile in the upper left.YR YR YB YB YG YG There are 6 large squares with theBG GB RG GR RB BR yellow tile in the upper left.Each larger square with the red square in the upper left corner is shownfor a total of six. Therefore there should be 6 sets for each color. 4 × 6 = 24.There are 24 ways that Michael can arrange the tiles into larger squares.For Exercises 1 –3, solve each problem using the act it out strategy.1. GEOMETRY How many different pairs of regular polygons can be made from16 toothpicks with none left over if only one toothpick is used for each side?2. MONEY Byron wants to buy a comic book that costs $0.65. If he uses exact change, howmany different combinations of nickels, dimes, and quarters can he use?3. NUMBER LINE In a math class game, players are using a number line on the floor. Gracestarts at zero and moves forward 7 numbers on her first turn and moves backward4 numbers on her second turn. If this pattern continues, how many turns will it takefor her to move forward to 16?Chapter 12 SC StudyText, Course 3 321

12-4NAME DATE PERIODSkills PracticeProblem-Solving Investigation: Act It OutFor Exercises 1–7, use the act it out strategy to solve.1. A piece on a game board moves forward 8 spaces on its first turn and moves backward3 spaces on its second turn. If the pattern continues, how many turns will it take forthe piece to move at least 30 spaces?2. How many ways can you arrange 3 paintings in a row on a wall?SCAS 8-1.8, 8-6.33. How many different combinations of nickels, dimes, and pennies can be used to make$0.10?4. A piece on a game board moves forward 6 spaces on its first turn and moves backward5 spaces on its second turn. If the pattern continues, how many turns will it take forthe piece to move at least 10 spaces?5. Joey is taller than Greg, who is taller than Rick, who is taller than Mike. How manydifferent ways can they stand in line so that the tallest person is always last?6. How many different combinations of quarters, nickels, dimes, and pennies can be usedto make $0.25?7. Roll a number cube 10 times and record the results. Repeat 3 times. Using your results,is there any way to predict which number the number cube will land?Set 1Set 2Set 3Roll 1 Roll 2 Roll 3 Roll 4 Roll 5 Roll 6 Roll 7 Roll 8 Roll 9 Roll 10Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.322 SC StudyText, Course 3 Chapter 12

NAME DATE PERIOD12-4 Homework PracticeProblem-Solving Investigation: Act It OutSCAS 8-1.8, 8-6.3Mixed Problem SolvingFor Exercises 1 and 2, use the act itout strategy.1. BILLS Joaquin bought a DVD for $21.He gave the cashier two $20 bills. Howmany different combinations of $1, $5,and $10 bills can the cashier give himfor change?4. CHORES Kimberley has the choice ofwashing the car, mowing the lawn, orraking leaves on Saturday and bakinga cake, washing the dishes, or doing thelaundry on Sunday. In how many wayscan she choose one chore for each day?2. TENNIS Felix, Lolita, Tetsuo, Ling, andMaxine are on the school tennis team.When ranked from first to fifth, howmany ways can they be ranked ifMaxine is always first and Felix isalways ranked above Tetsuo?Use any strategy to solve Exercises 3–6.Some strategies are shown below.5. FUNDRAISER The drama club is selling100 T-shirts for $15 each for afundraiser. The T-shirts cost a total of$623. If they sell all the T-shirts, howmuch money will be raised for thedrama club?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Problem-Solving Strategies• Work backward.• Look for a pattern.• Use logical reasoning.• Act it out.3. PUMPKINS Mr. Greene harvestedpumpkins for selling at four markets.He sold one-fifth of his crop at thefirst market, 40 at the second, 25% ofthe remaining at the third, and twicewhat he sold at the second at the forthmarket. If Mr. Greene has one pumpkinremaining, how many pumpkins did hesell?6. DELICATESSEN A delicatessen offers thepossibility of 180 kinds of sandwichesmade with wheat, rye, white, orsourdough breads. If the delicatessenadds multi-grain bread to the menu,find the number of possible kinds ofsandwiches the delicatessen now offers.Chapter 12 SC StudyText, Course 3 323

NAME DATE PERIOD12-4 Problem-Solving PracticeProblem-Solving Investigation: Act It OutFor Exercises 1–6, use the act it out strategy to solve.SCAS 8-1.8, 8-6.31. PHOTOGRAPHY Julie has six photosthat she has taken framed and hangingin a row on the wall. If she wants torearrange them so that the middletwo photos stay in place, how manydifferent ways can she arrange thephotos?2. TEAMS There are 5 players on abasketball team. If Melvin always playsin the point guard position, and Kevinalways plays in the power forwardposition, how many different ways canthe coach arrange Rick, Mark, and Joeyin the center, small forward, and offguardpositions?3. MONEY Elaine wants to buy an applethat costs $0.55. How many differentcombinations of quarters, nickels, anddimes can be used to make $0.55?4. AGES Melissa is older than Susan, whois older than Meg, who is older thanJulie, who is older than Vicky, who isolder than Zoe. How many differentways can they stand in line so that theyoungest person is always first, and theoldest person is always last?5. GEOMETRY How many different setsof four different polygons can be madefrom 20 toothpicks by using all 20 withnone left over? One set is shown below.6. MONEY Brian wants to buy a muffinthat costs $0.80. How many differentcombinations of nickels and dimes canbe used to make $0.80?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.324 SC StudyText, Course 3 Chapter 5

12ANAME DATE PERIODStudy GuideProbability with Geometric ModelsSCAS 8-6.7Probability can be expressed as the ratio of areas.The probability of landing in a specifi c region of a target is the ratio of the area of the specifi c region tothe area of the target.area of specifi c regionP(specifi c region) =____area of the targetExample 1 Find the probability that a randomlythrown dart will land in the shadedregion of the dartboard. Assume it isequally likely for a dart to landanywhere in the rectangle.15 in.35 in.100 in.50 in.P(shaded region) =area ____of shaded regionarea of the targetCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Area of shaded region Area of dartboardl × w = 15 × 100 l × w = 50 × 100= 1,500 sq in. = 5,000 sq in.P(shaded region) =_ 1,500 or3_5,000 10So, the probability that a randomly thrown dart will land in the shaded regionis 3_ , 0.30, or 30%.10Example 2 Predict how many times a dart will land in the shaded area aboveif 30 darts are randomly thrown.Write a proportion that compares the number of darts landing in the shadedregion to the number of darts thrown. Let n = the number of darts landing inthe shaded region.n_30 = 3_ ←darts landing in the shaded region10 ←darts thrownn × 10 = 30 × 3 Write the cross products.10n = 90Multiply._ 10n10 = _ 90Divide each side by 10.10n = 9So, if 30 darts are randomly thrown, 9 darts will land in the shadedregion.ExercisesUse the dartboard from Example 1.1. What is the probability that a randomly thrown dart will land inthe region that is not shaded?2. Predict the number of darts that will land in the region that is notshaded if 40 darts are randomly thrown.Chapter 12 SC StudyText, Course 3 325

12ANAME DATE PERIODSkills PracticeProbability with Geometric ModelsFind the probability that a randomly thrown dart will land in theshaded region of each dartboard.1. 2. 3.SCAS 8-6.7Suppose you randomly throw 10 darts at each dartboard below. Howmany darts would you expect to land in each shaded area?4. 10 ft5. 10 yd6. 6 m2 ft8 yd3 m3 ft5 yd10 yd2 m10 mUse the dartboard at the right.7. What is the probability of a randomly thrown dart landingon a consonant?8. If 40 darts are randomly thrown, how many would you predict to land ona consonant?9. What is the probability that a randomly thrown dart would land on avowel?VEQ WZ IOXCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.10. If 200 darts are randomly thrown, how many would you predict to landon a vowel?326 SC StudyText, Course 3 Chapter 12

12ANAME DATE PERIODHomework PracticeProbability with Geometric ModelsUse the information below to answer questions 1 and 2.SCAS 8-6.7A dartboard has three regions, A, B, and C. Region B has an area of 8 in 2 and regions Aand C each have an area of 10 in 2 .1. What is the probability of a randomlythrown dart hitting region B?2. If you threw a dart 105 times, howmany times would you expect it to hitregion B?Each figure below represents a dartboard. It is equally likely that a dart willland anywhere on the dartboard. Find the probability of a randomly-throwndart landing in the shaded region. How many of 100 darts thrown would hiteach shaded region?3. 4.5.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.On a dartboard, region A has an area of 5 in 2 and region B has an area of 95 in 2 .5. What is the probability of a randomlythrowndart hitting region A?Exercises7. About 2_ of the ground under an apple3tree is covered with grass, and the restwith dirt. It is equally likely that anapple will fall anywhere on the ground.What is the probability that it will fallon dirt?6. If you threw a dart 400 times, howmany times would you expect it to hitregion A?8. 5_ of a spinner is colored blue and the8rest is red. It is equally likely thatthe pointer will land anywhere on thespinner. What is the probability of thespinner landing on red?Chapter 12 SC StudyText, Course 3 327

NAME DATE PERIOD12AProblem-Solving PracticeProbability with Geometric ModelsSCAS 8-6.7GAMES For Exercises 1–5, use the following information and the game boardsbelow.Game Board 1 is for a beanbag toss game in which you are blindfolded and toss a beanbagat the board. The game board shows a bird’s head with eyes, beak, and a hole for a mouth.Game Board 2 is for a dart game in which you randomly throw a dart at the board.Game Board 1 Game Board 212 in.18 in.30 in.30 in.1. Refer to Game Board 1. The shadedregion represents the mouth hole.Dawn will randomly throw a beanbagat the board. What is the probabilitythat the beanbag will go into themouth hole? What is the probabilitythat the beanbag will not go into themouth hole?3. Use your answer from Exercise 1.Predict how many beanbags will not gointo the mouth hole if Dawn throws40 beanbags.5. Use your answer from Exercise 4.Predict the number of darts that willland in the shaded area if Pamrandomly throws 60 darts.2. Use your answer from Exercise 1.Predict how many beanbags will go intothe mouth hole if Dawn throws 20beanbags. Explain.4. Refer to Game Board 2. Pam willrandomly throw a dart at thedartboard. What is the probability thather dart will land in the shaded region?Explain.6. SKYDIVING A skydiver is dropped froma plane above a field that is 35 yards by16 yards. In the center is a region ofsand that is 7 yards by 7 yards. What isthe probability that the skydiver willland in the sandy region?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.328 SC StudyText, Course 3 Chapter 5

NameChapter 12 TestMastering the SC StandardsDateCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.This chapter includes a review of some Grade 7Data Analysis and Probability standards.1 Mr. Williams bought three raffle ticketsat a marching band fund-raiser. He findsout how many tickets were sold andcalculates that his theoretical probabilityof winning is 1 in 150. How many ticketswere sold?A 50B 150C 300D 4508-6.32 A spinner and a fair-number cube are usedin a game. The spinner has four equalsections: red, blue, yellow, or green. Thefaces of the cube are numbered 1 through6. What is the probability that a player willspin the color red and roll a 5 or 6?A1_24B 1_12C1_7D 7_12Review of 7-6.53 A penny is tossed on a 4 × 4 grid100 times. The grid is made up of 6 redsquares and 10 green squares. The resultsare shown in the table below.OutcomeNumber ofOutcomesPenny lands on a red square 32Penny lands on a green square 48Penny lands on both 20Total 100Using the results in the table, what is theexperimental probability of the pennylanding on both colors?A 0.20 C 0.48B 0.32 D 0.808-6.34 The scatter plot below shows several datapoints and a best-fit line for lemonade salesas a function of the outside temperature.What is a reasonable prediction of thenumber of sales when the temperaturereaches 90ºF? A about 60 cupsB about 75 cups C about 85 cupsD about 90 cupsReview of 7-6.1Chapter 12 SC StudyText, Course 3 329

NameDateChapter 12 Test (continued)Mastering the SC Standards5 Luke is designing a game with a numbercube numbered 1–6 and a spinner with3 equal parts, numbered 1–3. How manydifferent combinations of 1 roll of thenumber cube and 1 spin of the spinner mustLuke consider for his game?A 4B 8C 12D 188-6.38 The table below shows adult ticket prices atan amusement park.Adult Ticket PricesYear Price1965 $3.501975 $7.001985 $14.951995 $26.952005 $45.00Based on the data, what is a reasonableprediction for the adult ticket price in2015?6 Flora takes a jewelry class at a craft shop.She can make a bracelet, necklace, orearrings. For each piece of jewelry she canuse one color of beads. Her color choicesare blue, green, purple, and red. How manydifferent combinations can she make?A 4B 6C 9D 12Review of 7-6.87 Lee tosses three coins. What is thetheoretical probability that all three coinswill land tails up?A 1_ 2B 1_3C 1_4D 1_8Review of 7-6.5A $46.00B $48.00C $72.00D $120.00Review of 7-6.19 The spinner below is divided into 8 equalsections.How many sections of the spinner shouldbe colored red in order to make theprobability of the arrow landing on red0.125 in a single spin?A 1B 3C 5D 78-6.3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.330 SC StudyText, Course 3 Chapter 12

NameDateTips for Taking the PASSIn eighth grade, you will take a test called the Palmetto Assessment of State Standards,or PASS.The following pages will help you get ready to take the PASS.• Most of the questions you will answer on the PASS are multiple-choice questions.A multiple-choice question can be the easiest kind of problem to answer becauseyou know that one of the answer choices is the right answer. You will answer themultiple-choice questions in your test booklet.• Two other kinds of questions on the PASS are short-response and extended-responsequestions. There are no choices given to select from for these types of questions.You must figure out the answer on your own and then record your answer in thespace provided in your test book. Often you are asked to show your work or givea reason for your answer.• It is important to check over your work. These pages teach you how to check overyour work so that you do your best when you take the PASS.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Mastering the PASS, Grade 8 A1

NameDateTips for Taking the PASS (continued)How do I answer multiple-choice questions?Read the question and choose the best answer.The ratio of dogs to cats in pet storeis 3 to 4. If there are 24 cats in thepet store, how many dogs are there?A 12B 15C 18D 20• Read the question carefully and determinewhat information is needed to solve thequestion.• If there are any words in the question thatyou are unsure of, use context clues tohelp you solve the question.• Do any work in your test booklet besideor below the question.• Work slowly and carefully. Check yourwork.• Solve the problem and look for youranswer in the choices.• Use a pencil to record your answer inyour test booklet.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A2 Mastering the PASS, Grade 8

NameDateTips for Taking the PASS (continued)How do I fill in the bubble?Did you find your answer among the choices given?If not, go back and work the problem again.• If your answer is one of the choices, usea pencil to fill in the answer bubble with theletter of your choice.• Make sure you fill in the bubble completely.The chart below shows you how to do this best.• Make your marks dark.CorrectIncorrectIncorrectIncorrectCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A 2xB 2x + 1C 4xD 4x - 1A 2xB 2x + 1C 4xD 4x - 1A 2xB 2x + 1C 4x•D 4x - 1• If you make a mistake be sure to erase your first mark completely beforemarking the correct choice.The next two pages will show you how to answer short-response andextended-response questions.A 2xB 2x + 1C 4xD 4x - 1Mastering the PASS, Grade 8 A3

NameDateTips for Taking the PASS (continued)How do I answer short-response andextended-response questions?Some of the questions on your test will be short-response or extended-response items.These questions will ask you to solve a problem and write your own answer in thespace provided. You may also need to show your work by writing down each step inthe problem, drawing a picture, completing a chart, or explaining in words how youfound the answer.The only difference between a short- and an extended-response question is that anextended-response question has more than one part to it.Follow these steps to help you answer these types of questions:• Read the problem carefully.• Make sure you understand what the question is asking.• Decide which facts you need to solve the problem.• Decide which operation you would use.• Work the problem in the space provided in yourtest booklet.• Check that the answer makes sense.• When a problem asks you to show your work,you may do so by writing down each step inthe problem, drawing a picture, completing achart, or describing in words how you solvedthe problem.• Record your answer in the space provided.Question 1 on the next page is a short-response question.Question 2 on the next page is an extended-response question.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A4 Mastering the PASS, Grade 8

NameDateTips for Taking the PASS (continued)Read each question and write in your answers completely onthe lines provided.1 √ 280 is between which two consecutive integers?2 A box company makes three sizes of boxes in the shape ofrectangular prisms. The medium sized box has a volume of500 cubic inches.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.If the length, width, and height of the large box are twicethose of the medium size box, what is the volume of thelarge box?If the length, width and height of the small box are one halfthose of the medium size box, what is the volume of thesmall box?Mastering the PASS, Grade 8 A5

NameDateTips for Taking the PASS (continued)How can I check my work?Ask yourself these questions:• Did I use the right information from the problem?• Did I answer the question that was asked?• When solving the problem, did I copy the correct numbers from the problem?• Did I do the math correctly?• Does my answer make sense?• Did I fill in the bubbles correctly for multiple-choice?• Did I write my answer on the line provided and show all of my work whenrequired for short-response and extended-response questions?Test-Taking Hints• Go to bed early the night before the test. You will think more clearly aftera good night’s rest.• Eat breakfast in the morning. An empty stomach will distract you while takingyour test.• Relax. Most people get nervous when taking a test. It is natural. Just do yourbest.• Answer questions you are sure about first. If you do not know the answer toa question, skip it and go back to that question later.• Think positively. Some problems may seem hard to you, but you may be ableto figure out what to do if you read each question carefully.• Become familiar with a variety of formulas and when theyshould be used.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A6 Mastering the PASS, Grade 8

NameDateTips for Taking the PASS (continued)Practice QuestionsRead the question and choose the best answer.Be sure to mark your answer.1 Lines QT and UX are parallel. If ∠RVX is 48°, what is themeasure of ∠SRQ?A 48°B 123°C 132°D 148° 2 Sasha plots part of her neighborhood on a coordinate grid sothat each intersection is an ordered pair. Sasha places her home,on the corner of Williams and Front street, at the origin.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.If Sasha plots her school three blocks north and four blockseast of her house, what ordered pair shows the location ofher school?Sasha plots the library six blocks east and two blocks northof her house. What ordered pair would show the location ofthe library?Sasha plots the grocery store five blocks north and one blockwest of the library. What order pair would show the locationof the grocery store?Turn the page to check your answers.Mastering the PASS, Grade 8 A7

NameDateTips for Taking the PASS (continued)Practice QuestionsRead the question and choose the best answer.Be sure to mark your answer.1 Lines QT and UX are parallel. If ∠RVX is 48°, what is themeasure of ∠SRQ?A 48°B 123°Recall what you knowabout complementary andsupplementary angles.C 132°D 148°The correct answer is C.You need to fill in bubbleC in your test booklet. 2 Sasha plots part of her neighborhood on a coordinate grid sothat each intersection is an ordered pair. Sasha places her home,on the corner of Williams and Front street, at the origin.If Sasha plots her school three blocks north and four blockseast of her house, what ordered pair shows the location ofher school?(4, 3)Sasha plots the library six blocks east and two blocks northof her house. What ordered pair would show the location ofthe library?(6, 2)Sasha plots the grocery store five blocks north and one blockwest of the library. What order pair would show the locationof the grocery store?(5, 7)10987654321OUse the white space todraw a grid and plotSasha’s neighborhood.homeschoolstorelibrary1 2 3 4 5 6 7 8 9 10NWSECopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A8 Mastering the PASS, Grade 8

NameDateDiagnostic Test1 The letters of the words SOUTHCAROLINA are placed in a bag. Zachwants to find the probability of pickingtwo O’s from the bag without looking.Which expression shows how Zach canmake this calculation?A1_13 + 1_2_12B13 + 1_12C1_13 × 1_2_12D13 × 1_128-6.43 Which property is used in the equationbelow?13(z + 5) = 13z + 65A Associative Property of AdditionB Commutative Property of AdditionC Distributive PropertyD Inverse Property of Addition8-3.32 Which graph shows a linear relationshipbetween the variables time and distance?A4 These two triangles are similar.6090Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.BCD8-3.56090˚30Which proportion is true for thesetriangles?Ax_f = _ y eBe_f = _ y xCDz_f = x_x_dz = e_f308-5.1Mastering the PASS, Grade 8 A9

NameDateDiagnostic Test (continued)5 Dora wants to measure the length of herpencil. Which unit is best for her to use?A inchesB feetC yardsD miles8-5.66 What is the circumference of a circle with aradius of 4 units?ABC2π4π8πD 12π8-5.47 A large tree in Mrs. Santiago’s yard wasstruck by lightning and fell as shown in thediagram below. Which equation could beused to find the length of the fallen part ofthe tree?A 8 2 + 13 2 = xB √ 8 2 + 13 2 = xC 132- 8 2 = xD √ 213 - 8 2 = x 8-4.18 ABC is shown on the coordinate grid.yOWhich represents a dilation of ABC by ascale factor of 2 using the origin as thecenter of dilation?ABCDOOOyy′′′′x′ ′xy ′y′′′ ′O′xxxCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.8-4.3A10 Mastering the PASS, Grade 8

NameDateDiagnostic Test (continued)9 Rachel knows that there are 16 fluid ouncesin 1 pint. She also knows that there are2 pints in 1 quart. Rachel has 3 quarts oflemonade for sale. How many fluid ouncesof lemonade does she have?A 32B 48C 64D 968-5.710 The scatter plot below shows the highschool and college grade point averages of7 students who attend the University ofSouth Carolina. Which statement bestdescribes the data?4y11 Jamal wants to solve 15 × 12. Whichchoice below shows an equivalentexpression?A 15 × 10 + 15 × 2B 15 × 10 + 12 × 2C 10 × 10 + 5 × 2D 10 × 5 + 10 × 212 Rectangle ABCD was dilated to formrectangle WXYZ.84y8-2.1Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.College GPA32101 2 3 4High School GPAA A student’s high school GPA is usuallysimilar to his or her college GPA.B A student’s high school GPA is usuallyequal to his or her college GPA.C A student’s high school GPA does notusually affect his or her college GPA.D A student’s high school GPA is usuallymuch higher than his or her collegeGPA.x-8 -6 -4 O 4-4-6-8Which fraction represents the scale factorused to change rectangle ABCD intorectangle WXYZ?AB1_32_3C3_23_ D18x8-4.48-6.1Mastering the PASS, Grade 8 A11

NameDateDiagnostic Test (continued)13 Which equation matches the followingstatement?Six less than four times a number is twomore than three times that number.16 If the dimensions of a rectangular prismare scaled by a factor of 1_ , by what factor4does the volume of the solid decrease?A 4n - 6 = 3n + 2B 4 (n - 6) = 3 (n + 2)C 6 - 4n + 2 = 3D 6 - 4n = 2n + 314 Kevin wrote the equation y = 3x - 4. Ifhe graphs the equation, what will be theslope of the line he creates?8-3.1AB1_641_32C1_16D 1_48-5.2A -4B -3_4C 1_3D 315 Which point on the number line bestrepresents √ 8 ?1A Point AB Point BC Point CD Point D 2348-3.78-2.317 Which of the following equations shouldMaria use to calculate the volume of thecone below?4 cm8 cmA V = 2 2 × π × 8B V = 1_3 × 2 2 × π × 8C V = 4 2 × π × 8D V = 1_3 × 4 2 × π × 88-5.3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A12 Mastering the PASS, Grade 8

NameDateDiagnostic Test (continued)18 The spinner is divided into six equalsections. 20 Jake hangs a bird feeder on a tree in hisbackyard. He leans an eight-foot ladderagainst the tree as shown. The distancebetween the tree and the bottom of theladder is 6 feet.The spinner was spun 84 times. The totalnumber of times the spinner landed on eachnumber is shown in the table below. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ColorFrequencyRed 15Blue 20Green 7White 8Purple 15Black 19Based on the theoretical probability, howmany times should the spinner land onWHITE in 84 spins?A 4 C 8B 6 D 148-6.319 What is the solution to the equation below?A -15B -9C 9D 15|-12| + |3| = About how high above the ground is thetop of the ladder?A 3 feetB 5 feetC 12 feetD 13 feet21 Which symbol will make the numbersentence true when placed in the blank?A >B

NameDateDiagnostic Test (continued)22 Paul has a number cube that is numbered1–6. He wants to calculate the probabilityof rolling an even number 3 times in a row.Which equation below shows how he cancalculate this probability?A1_2 × 1_2 × 1_2 = 1_1_8B3 × 1_3 × 1_3 = 1_1_27C2 + 1_2 + 1_2 = 3_1_2D3 + 1_3 + 1_3 = 1 8-6.625 The graph of an equation is drawn on thecoordinate grid.Oyx23 Mandy has a bag with 2 red marbles, 4 bluemarbles, and 6 green marbles. If she drawstwo marbles from the bag without looking,what is the probability that she will draw2 red marbles?AB1_361_66C 1_120D 1_1448-6.424 Using the Pythagorean theorem, Kaycalculates that the distance from her homein Summerville to her office in NorthCharleston is √ 300 miles. Between whichtwo integers is √ 300 ?A 15 and 16B 16 and 17C 17 and 18D 18 and 19Which answer choice shows the correct x-and y-intercepts of the graph?A x-intercept: 2y-intercept: 1B x-intercept: -2y-intercept: 1C x-intercept: 1y-intercept: 2D x-intercept: 1y-intercept: -226 Carlos solves the problem below.3m - 11 = 15Which first step is best to solve for m?A Add 11 to both sides.B Subtract 11 from both sides.C Multiply both sides by 3.D Divide both sides by 3.8-3.48-3.6Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.8-2.6A14 Mastering the PASS, Grade 8

NameDateDiagnostic Test (continued)27 Horatio places a rubber duck in the currentof the Pee Dee River. The rubber duckfloats 12 miles downstream in22_hours. At this rate, about how many5miles will the duck travel in 5 hours?A 15 milesB 20 milesC 25 milesD 30 miles30 Which scatter plot shows the relationshipbetween the number of gallons of gasolineremaining in a motorcycle’s tank and thenumber of miles driven since the tank wasfilled?A 8-2.728 What is the solution to the equation below?B -12 ÷ -3 =A -9 C 4B -4 D 9 8-2.2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.29 Randy makes a large wall hanging in artclass. What is the area of the wall hanging to thenearest square inch?A 524 in 2B 678 in 2C 768 in 2C 880 in 2CD 8-5.58-6.2Mastering the PASS, Grade 8 A15

NameDateDiagnostic Test (continued)31 Working together, Sam and Bev collected54 pounds of newspapers for recycling. IfSam collected s pounds, which of thefollowing equations shows b, the number ofpounds of newspaper that Bev collected?33 Which graph shows a line that contains thepoints (2, 3), (4, 5), and (0, 1)?AyA s + 54 = bBs - 54 = b__C 54 - s = b2D 54 - s = bOx8-3.2By32 Janet has 2 bags of marbles. One bag has2 blue marbles and 2 red marbles. Theother bag has 1 blue marble, 2 greenmarbles, and 1 red marble. She drew thearea model below to show the differentcombinations of selecting 1 marble fromeach bag without looking.B G G RB BB BG BG BRB BB BG BG BRR RB RG RG RRR RB RG RG RRBased on the area model she created, whatis the probability that Janet will draw atleast 1 red marble?A1_8B 1_2C 5_8D 3_48-6.7CDOOOyyxxx8-4.2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A16 Mastering the PASS, Grade 8

NameDateDiagnostic Test (continued)34 The estimated populations of 6 towns arelisted below.48,000 23,000 27,00025,000 28,000 24,000Which measure of central tendency has thelargest value?A meanB medianC modeD range36 A kilometer is about 6_ of a mile. If the10speed limit along a stretch of highway inEurope is 90 kilometers per hour, what isthe approximate speed limit in miles perhour?A 45 mphB 55 mphC 60 mphD 65 mph8-5.7Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.8-6.835 A local newspaper plans to print theaverage salary of the mayor and themembers of the city council. The editortakes into consideration that the mayor’ssalary is considerably higher than thesalaries of the city council members. In thiscase, which measure of central tendencybest represents the average city councilsalary?A meanB medianC modeD range8-6.837 The ratio of boys to girls in Mrs. Maloney’sdrama class is 3 to 4.If there are 20 girls in drama class, howmany boys are there?A 12B 15C 16D 248-2.7Mastering the PASS, Grade 8 A17

NameDateDiagnostic Test (continued)38 What is the slope of the linear functionshown below?4321-4-3-2 -1-1-2-3-4yx 1 2 3 440 A spinner is divided into 6 equal sections.Debbie spins the spinner 30 times andrecords the outcome of each spin. Herresults are in the table below.A -4B -1_4C 1_4D 48-3.7Letter FrequencyA 7B 0C 2D 8E 7F 639 A block of wood is shaped like arectangular prism with dimensions l, w,and h. A hole is drilled out of the middleof the prism with radius r.Write an expression to find the volume ofthe remaining wood.rwh8-5.3How do the results of Debbie’s experimentcompare to the theoretical probability ofthe pointer landing on B? Why?What are the theoretical and experimentalprobabilities of spinning D?theoretical:experimental:8-6.3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A18 Mastering the PASS, Grade 8

NameDatePractice by StandardNumber and Operations1 Which point on the number line bestrepresents √44 ?A Point AB Point BC Point CD Point D8-2.34 √ 250 is between which two consecutiveintegers?A 15 and 16B 16 and 17C 17 and 18D 18 and 195 Which symbol will make the numbersentence true when placed in the box?8-2.6Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2 At Sam’s middle school, there are700 boys. The ratio of boys to girls is5 to 4. How many girls are there in theschool?A 240B 480C 560D 8758-2.73 What is the solution to the equation below?A -5B 5C 18D 21|8 - 13| =8-2.59 √80A >B

NameDatePractice by StandardNumber and Operations (continued)7 Which equation is equal to (6 + 2) × 4?A 8 × 4 + 2 × 4B 6 × 6 + 2 × 2C 6 × 2 + 4 × 2D 6 × 4 + 2 × 48-2.110 Which symbol will make the numbersentence true when placed in the box?A >B

NameDatePractice by StandardAlgebra1 Rafael walks 2 miles and burns 300 caloriesevery day. Which graph best represents therelationship shown in the table?Miles Walked Calories Burned2 3004 6006 9008 1,2002 Which expression is equivalent to(3x + 7) + 5y?A 15xyB 8xy + 7C 10x + 5yD 3x + (7 + 5y)8-3.3ACalories Burned1,2001,000800600400200yx3 What is the slope of the line below?y4321xCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.BCDCalories BurnedCalories BurnedCalories Burned01,2001,00080060040020001,2001,00080060040020001,2001,000800600400200yyy2 4 6 8Miles Walkedx2 4 6 8Miles Walked2 4 6 8Miles WalkedxxA -3B -1C 1D 3-4-3-2O-2-3-41 2 3 44 Maria wants to solve the problem below.6x + 3 = 27Which first step would be best to solvefor x?A Add 3 to both sides.B Subtract 3 from both sides.C Multiply both sides by 6.D Divide both sides by 6.8-3.702 4 6 8Miles Walked8-3.48-3.1Mastering the PASS, Grade 8 A21

NameDatePractice by StandardAlgebra (continued)5 Carlos sells video games on a web site. Theweb site costs him $75 per year. He sellseach video game for $25. Which equationcan Carlos use to determine how manyvideo games, g, he must sell to make aprofit of $50 per year?A 100g = 50B 75g + 25 = 50C 25g + 75 = 50D 25g - 75 = 506 Which equation below is nonlinear?A y = 1_ x + 58-3.2B y = 3x + 4C y = 1_2 x - 1D y = - 2_3 x - 3 8-3.57 Which is equivalent to the followingexpression?A 24 x 3B 24 x 4C 18 x 3 + 2xD 20 x 33 x 2 (6x + 2x)8-3.38 What is the slope of the line graphedbelow?A -3B -1_3C1_3D 3Oyx8-3.79 The table shows the pattern of a sequence.Which expression describes the pattern?ABCDn_2__ 2n - 32n_2 - 1_ n + 12ns1 -0.52 0.53 1.54 2.58-3.2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A22 Mastering the PASS, Grade 8

NameDatePractice by StandardGeometry1 Which point on the coordinate grid belowrepresents the ordered pair (4, 0) ?y3 Alec has a back yard in the shape of arectangle with a length 18 yards and awidth 24 yards. What is the distance fromthe front-left corner to the back-right cornerof his yard?OxA 3 yardsB 13 yardsC 23 yardsD 30 yardsABCDABCD8-4.14 If △ABC is dilated by a factor of 3, whatare the coordinates of point B'?yCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2 What scale factor was used to dilatequadrilateral ABCD?'A 0.5B 1.5C 2D 2.5''8-4.28-4.4A (3, 0)B (-3, 0)C (0, 3)D (0, -3)BOACx8-4.3Mastering the PASS, Grade 8 A23

NameDatePractice by StandardGeometry (continued)5 Square ABCD was dilated to form squareEFGH.7 The diagram shows the side view of asupport bracket used to hold a bookshelf.y 54-5 -421-2 -1 0-1-2124x -4 Which fraction represents the scale factorused to change square ABCD into EFGH?AB1_31_2CD3_22_18-4.4What is the approximate length of thesupport rod?A 6 in.B 18 in.C 24 in.D 28 in.8-4.16 Which line contains the ordered pair(-4, -5) ?prqA line pB line qOysC line rD line sx8 If square QRST is dilated by a factor of 3,what are the coordinates of point Q'?A (-6, 9)B (-4, 6)C (-5, 6)D (-1, 9)421-4 -3 -1 0-2-3-4y134x8-4.3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.8-4.2A24 Mastering the PASS, Grade 8

NameDatePractice by StandardMeasurement1 Which equation shows the volume of asphere with a radius of 3?A V = 4_ 3 × π × 3 3B V = 1_3 × π × 33C V = 4 × π × 3 3D V = π × 3 38-5.34 There are 12 inches in 1 foot. There areabout 3.28 feet in 1 meter. About howmany inches are in 1 meter?A 32.8B 39.4C 49.2D 69.68-5.72 What value of x would make △ABCsimilar to △XYZ?322440x5 If the radius and height of a cylinder arescaled by a factor of 2, by what factor doesthe volume of the solid increase? 2835Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A 26B 28C 30D 488-5.13 Which unit is best to measure the distancefor a car trip from Columbus to Charleston?A inchesB feetC yardsD miles8-5.6A 2B 4C 6D 88-5.26 Which equation below shows how to findthe area of a circle with a radius of 3 units?A A = π × 3 2B A = π × 6 2C A = 2 × π × 3D A = 2 × π × 68-5.4Mastering the PASS, Grade 8 A25

NameDatePractice by StandardMeasurement (continued)7 Abdul is putting a fence around his gardento keep rabbits away from the vegetables.The diagram below shows the perimeter ofthe garden.13 ft?14 ft12 ftAbdul measured three sides of the garden,but his measuring tape was not long enoughto measure the fourth side. Which measurecould be the garden’s perimeter?A 19 feetB 39 feetC 48 feetD 58 feet9 The trapezoids below are similar. What isthe length of side x?15 cm25 cm 30 cm35 cmA 15 cmB 18 cmC 20 cmD 24 cm12 cm28 cmx8-5.110 The South Carolina quarter was the 8thstate quarter released. It first appeared in2000. If the radius of the coin is about12 millimeters, what is the area? Round tothe nearest whole number.8-5.58 A paper drinking cup is shaped like a conewith a diameter of 8 centimeters and aheight of 10 centimeters. About how manycubic centimeters of water does the cuphold?A 160 cm 3B 168 cm 3C 251 cm 3D 670 cm 38-5.3A 370 mm 2B 395 mm 2C 438 mm 2D 452 mm 28-5.411 One quart is equal to about 0.95 liters.There are 4 quarts in 1 gallon. About howmany liters are in 1 gallon?A 3.05B 3.80C 4.21D 4.958-5.7Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A26 Mastering the PASS, Grade 8

NameDatePractice by StandardData Analysis and Probability1 The scatterplot shows the relationshipbetween a person’s height and the amountof time that person spends reading books.Which conclusion can be drawn from thescatterplot?2 For a school carnival, Mia creates a gameinvolving the spinners below.A contestant plays the game by firstchoosing one of the four rules listed belowand then spins each spinner. Which ruleshould a contestant choose to have thegreatest chance of winning a prize?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A As a person’s height increases, theamount of time that person spendsreading books increases.B A person’s height and the amount oftime that person spends reading booksare not related.C As a person’s height decreases, theamount of time that person spendsreading books increases.D As a person’s height increases, theamount of time that person spendsreading books decreases.8-6.1A Win a prize if the product is greaterthan 17.B Win a prize if the product is odd.C Win a prize if the sum is less than 3.D Win a prize if the sum or the productis 10.8-6.43 Chloe collects data on the ages and heightsof a random sample of 5th-, 7th-, and 9thgradestudents at her school. She plots thedata points on a scatterplot. Whatrelationship between age and height islikely seen on the scatterplot?A positive correlationB negative correlationC no correlationD both positive and negative correlation8-6.2Mastering the PASS, Grade 8 A27

NameDatePractice by StandardData Analysis and Probability (continued)4 The table shows the ages of two groups ofsenior citizens who reside at a nursing carecenter.Group1Group265 70 70 71 75 85 88 89 9062 70 70 76 81 84 85 86 87Which measure of central tendency has agreater value for Group 1 than Group 2?A meanB medianC modeD range6 Dominic wants to simulate randomguessing on a 10-question True or Falsetest. How can he best conduct thissimulation?A Roll a number cube 10 times. Let evennumbers be True and odd numbers beFalse.B Toss 3 coins 10 times. Let all heads beTrue and all tails be False.C Spin a 4-section spinner 10 times.D Ask his sister to say “True” or “False”10 times.8-6.68-6.85 Camila has two spinners, one labeled A, B,and C, the other with A, B, A, and B. Thearea model below shows the differentoutcomes of spinning each spinner once.A B CA AA AB ACB BA BB BCA AA AB ACB BA BB BCBased on the area model she created, whatis the probability that Camila will spin Bon at least one spinner?A1_23_ B52_ CD33_48-6.77 Lauren rolled a number cube 25 times.Her results are shown in the chart below.NumberFrequency1 62 53 24 25 76 3What is the theoretical probability thatLauren will roll an even number on hernext roll?A 0.2 C 0.5B 0.4 D 0.68-6.3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A28 Mastering the PASS, Grade 8

NameDatePractice TestCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.1 The highest peak of Sassafras Mountain ismore than 3,500 feet above sea level. Thereare 5,280 feet in one mile. Which distancebelow is about 3,500 feet?A2_3 miB 1 1_4 miC 2 miD 2 1_2 mi2 What scale factor was used to dilaterectangle ABCD to make FGHJ?A 1.5B 2C 2.5D 38yFG7654A3B2 JH1D CO 1 2 3 4 5 6 7 8 9 10x3 What is the value of the expression below?A -3B 3C 7D 15⎪4 - 6⎥ + ⎪-5⎥4 Which expression is equivalent to 8xy?A 8x + 8yB xy + 8C 4xy + 4xyD 4x + 4y5 On which spinner is the probability of thepointer landing on A 1_3 ?A Spinner QB Spinner RC Spinner SD Spinner TMastering the PASS, Grade 8 A29

NameDatePractice Test (continued)6 Which point on the number line bestrepresents _ 327 ?A Point AB Point BA Point CD Point D 2 3 4 5 68 The graph shows the mean temperaturein Amy’s town for each month. Thesetemperatures are 30-year averages. Whichconclusion can be drawn from the graph?30 year Mean Monthly TemperaturesTemperature (°F)80706050403020100J F M A M J J A S O N DMonth7 If triangle ABC is dilated by a scale factorof 3, which ordered pair shows the newlocation of vertex B′?87654321OA (9, 15)B (6, 8)C (9, 3)D (7, 5)yBAC1 2 3 4 5 6 7 8 xA The average temperatures tend todecrease from January to June.B The average monthly temperature iswarmest in August.C The average temperature tends toincrease from July to September.D The average temperatures in Decemberand January are aboutthe same.9 Which symbol will make the numbersentence true when placed in the blank?A >B

NameDatePractice Test (continued)10 Which of the following expressionsrepresents the verbal phrase $5 tip added toa lunch bill?A b ÷ 5B b × 5C b - 5D b + 513 Javier is the catcher for his school’sbaseball team. A catcher must be able tothrow the baseball from home plate tosecond base. What is the distance fromhome plate to second base? Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.11 As an electrician, Sarah charges a servicecall fee of $65 and $45 per hour for everyhour she spends on the job. Whichexpression shows how much she willcharge for a 5-hour job?A 65 + 5 + 45B 45 + 5 + 65C 65 × 5 + 45D 45 × 5 + 6512 Which coordinate pair is located on the liney = 1_2 x + 4?A (5, 7 1_2 )B (2, 6)C (6, 7)D ( 1_2 , 5 )A 90 feetB 90 √ 2 feetC 150 feetD 180 feet 14 Which equation is equal to2 × 3 + 7 × 3?A 3 × (2 + 7)B 2 × (7 + 3)C 2 × 7 + 3 × 3D 2 × (3 + 7) × 3 Mastering the PASS, Grade 8 A31

NameDatePractice Test (continued)15 What is the y-intercept of the equationy = -4x + 3?A -4BC3_44_3D 317 Corinne plays a game with cards. If shedraws two cards at random, what is theprobability of selecting two stars?16 What scale factor was used to dilate △JKLto make △RST?A 1.5B 2C 2.5D 310987654321OyJRKSL T1 2 3 4 5 6 7 8 xABCD1_102_154_104_2518 The side lengths of Cube D are one-thirdthe side lengths of Cube C. Which correctlydescribes the volume of Cube D comparedto the volume of Cube C?A The volume of Cube D is 1_27 thevolume of Cube C.B The volume of Cube D is 1_18 thevolume of Cube C.C The volume of Cube D is 1_9 thevolume of Cube C.D The volume of Cube D is 1_3 thevolume of Cube C.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A32 Mastering the PASS, Grade 8

NameDatePractice Test (continued)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.19 Which symbol will make the numbersentence true when placed in the blank?A >B

NameDatePractice Test (continued)24 Marie wants to approximate the valueof √ 230 between two whole numbers.Which square roots should she use to findher answer?ABCD√ 200 and √ 250√ 225 and √ 269√ 196 and √ 289√ 225 and √ 25625 What is the value of the expression below?⎪2⎥ × ⎪-4⎥ + ⎪-2⎥ =A -10B -6C 6D 1027 Bernardo drew the triangle on the gridbelow.87654321Oy1 2 3 4 5 6 7 8 xIf Bernardo draws a new triangle bydilating his triangle by a factor of 2, whichcoordinate pair below would be a vertexon Bernardo’s new triangle?A (6, 0)B (6, 7)C (4, 10)D (2, 0)26 Which equation below is nonlinear?A y = 5 - xB y = x + 4C y = x 2 - 1D y =-x - 328 What value of x would make △ABCsimilar to △XYZ?x 6A 4B 5C 6D 7312.5 7.515Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A34 Mastering the PASS, Grade 8

NameDatePractice Test (continued)29 Which unit is best to measure the length ofa Carolina mantis, the state insect of SouthCarolina?A inchesB feetC yardsD miles30 The cone and the cylinder have the samebase diameter and the same height. Howmany times less is the volume of the conethan the volume of the cylinder?31 For the first grading period, Chelsea earnedthe following scores on her math tests:62, 76, 76, 80, 84, 100For this set of data, which measure is thegreatest?A meanB medianC modeD range32 Which point on the number line bestrepresents √12 ? 1234Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A 2B 3C 4D 5A Point AB Point BC Point CD Point DMastering the PASS, Grade 8 A35

NameDatePractice Test (continued)of the line in the equation33 For which triangle does the relationship 35 What is the slopea 2 + b 2 = c 2 fit?y = 2_3 x + 1_2 ?AA1_2 B2_3C3_2D y = (x + 3) 2BD 2 C 536 Before the last hour of the bake salefundraiser, the Student Council had sold atotal of 82 cakes. Then, they sold 13 in the89last hour. The Student Council sold anaverage of 9.5 cakes per hour for the day.To find how long the bake sale lasted, theD10first step is to find the sum of 82 and 13.Which of the following is the second step?1213A Multiply the sum by 9.5.B Subtract 9.5 from the sum.C Add the sum to 9.5.D Divide the sum by 9.5.34 Which equation below is linear?A y = 17x + 1_ 2B y = 1_xC y = 3 x 2 - 2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A36 Mastering the PASS, Grade 8

NameDatePractice Test (continued)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.37 Which graph shows a nonlinear equation?ABCD8765432187654321O87654321O8765321Oyyyy1 2 3 4 5 6 7 8 x1 2 4 5 6 7 8 x1 2 3 4 5 6 7 8 x1 2 3 4 5 6 7 8 x38 The graph shows the annual sales for Stan’sSavory Snacks since 1985. Based on thedata shown in the graph, which is the bestprediction for sales in the year 2015?Thousands of Dollars500450400350300250200150100500A $350,000B $400,000C $450,000D $500,000Snack Sales1985 1990 1995 2000 2005Year39 Abigail is heating water to make some tea.The temperature of the water increasesfrom 22° C to 35° C in 20 seconds. If thewater continues to heat up at the same rate,how long will it take for the watertemperature to increase from 35° C to100° C?A 60 secondsB 90 secondsC 100 secondsD 120 secondsMastering the PASS, Grade 8 A37

NameDatePractice Test (continued)40 Colleen is an interior decorator. Herdrawing of the layout of the BrownFamily’s new living room furniture isshown on the coordinate grid.42 Charlie has 2 spinners. The first spinner has3 sections labeled A and 2 sections labeledB. The second spinner is labeled A, B, andC. The area model below shows theoutcomes of spinning each spinner once.A B CA AA AB ACA AA AB ACA AA AB ACB BA BB BCB BA BB BCIf the center of the lamp is located at thecoordinates (0, 0), what are the coordinatesof the center of the coffee table?A (0, 5)B (5, 0)C (5, 4)D (0, 4)41 What is the area of the trapezoid below?4A 24 square unitsB 28 square unitsC 36 square unitsD 56 square units68Based on the area model, what is theprobability that at least one spinner willland on B?ABC1_32_53_5D 11_15Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A38 Mastering the PASS, Grade 8

NameDatePractice Test (continued)43 Which expression represents therelationship in the table below, using p torepresent the regular price?Regular Price Discounted Price$10 $5$15 $10$20 $15$25 $20$30 $25A p + 5B p - 5C 5pD p ÷ 546 A T-shirt shop keeps records of how manyshirts they sell. The most popular shirtcolors from one week are shown in thetable.Color of Shirt Number SoldRed 26Blue 32Yellow 18Purple 14Gray 10What is the probability that the next shirtpurchased will be yellow?A 0.05 C 0.18B 0.08 D 0.32Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.44 What property is shown in the equationbelow?(2x + 3) + 4 = 2x + 7A Associative Property of AdditionB Distributive PropertyC Commutative Property of AdditionD Associative Property of Multiplication45 Mario’s father cuts down a palmetto tree inthe yard, leaving a circular tree stump. Hemeasures the radius of the trunk, which is15 inches. What is the circumference of thetop of the stump? Use 3.14 for π. Roundyour answer to the nearest whole number.A 47 in 2 C 707 in 2B 94 in 2 D 830 in 247 When you multiply a number by -4, theresult is 60. What is the number?A -15 C 12B -12 D 1548 Wendy tosses three fair coins. What is theprobability that all three coins will landtails up?AB1_21_4CD1_81_16Mastering the PASS, Grade 8 A39

NameDatePractice Test (continued)52 Cora has $9 less than Di. Together they49 What is the slope of the line y = 4 - x?A1_ (4 + 5) × 132 B (13 + 5) × 42 C (13 + 4) × 52 D2 (13 + 4) × 2 have $21. Which equation could be solvedA -4to find d, the amount Di has?B -1AC(d - 9) + d = 211BDd + (d + 9) = 214C d = 21 - 9D d = (21 + d) - 950 Milk is the state beverage of SouthCarolina. Mato bought a 1_ -gallon container2of milk at the store. If there are about 53 In the triangle below, what is the3.8 liters in 1 gallon, how many liters ofapproximate length of side AB?milk did Mato buy?AA 0.45 LB 0.9 L4C 1.9 LBC 9D 3.8 LA between 5 and 6B between 8 and 951C between 9 and 10Rosa wants to find the area of the trapezoidD between 10 and 11below.1354Which expression should she simplify tofind the area?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A40 Mastering the PASS, Grade 8

NameDatePractice Test (continued)54 The area model below shows the possibleoutcomes of flipping two coins.H TH HH HTT TH TTBased on the area model, what is theprobability that at least one coin will landon tails?56 A square with an area of 45 square inchesis dilated so that it now has an area of12.25 square inches. What scale factorwas used to dilate the square?A 1.5B 2C 2.5D 3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A 0.25B 0.5C 0.75D 155 The scatterplot shows the number of digitalcameras sold each year at a photographystore. Which description best represents therelationship in the data?A no trendB positive trendC negative trendD both positive and negative trends57 √ 375 is between which two consecutiveintegers?A 16 and 17B 17 and 18C 18 and 19D 19 and 2058 A plastics company makes two sizes ofrecycling bins in the shape of rectangularprisms. The smaller bin has a volume of500 cubic inches. The length, width, andheight of the larger bin are twice those ofthe smaller bin. What is the volume of thelarger bin?A 1,000 in 3B 2,000 in 3C 4,000 in 3D 8,000 in 3Mastering the PASS, Grade 8 A41

NameDatePractice Test (continued)59 Julie has a bag of 26 tiles. Each tile islabeled a different letter of the alphabet.She wants to calculate the probability ofrandomly choosing the letters S and C, theinitials of South Carolina, from the bag.Which expression can she use?A1_26 + 1_2_25B26 + 1_1_25C26 × 1_25D 2_26 × 1_2561 Which line graphed below best representsthe table of values?ABx 0 1 2 4y -1 1 3 7Oyyx60 △ABC is similar to △DEF.A13.5 m24 mBCWhat is the length of −− DF ?A 8 metersB 9 metersC 12 metersD 15 metersD4.5 mE?FCDOyOyOxxxCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A42 Mastering the PASS, Grade 8

NameDatePractice Test (continued)62 What is the circumference of an ice skatingrink with a radius of 30 yards? Use 3.14for π and round your answer to the nearesttenth.64 Which scatterplot below best represents thestatement that as x increases, y at firstincreases and then decreases?Ay30 ydOxA 172.1 ydB 188.4 ydBC 205.5 ydD 212.4 ydCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.63 A skier competes in a slalom event. Shemakes 5 runs down the slope. The skier’stimes for the first four runs are shown inthe table.RunTime (sec.)Run 1 38.2Run 2 40.3Run 3 38.2Run 4 41.5Run 5 ?If her mean time is 39.55 for the 5 runs,what is her time in Run 5?A 38.2 secondsB 39.28 secondsC 39.55 secondsD 40.3 secondsCDOyOyO ٍّxxMastering the PASS, Grade 8 A43

NameDatePractice Test (continued)65 A bed and breakfast in Georgetown recordsthe number of visitors each month. Thegraph below shows the number of visitorsover the last 6 months.Bed and Breakfast VisitorsVisitors6050403020100Jan.Feb.Mar.MonthApr.MayJuneWhat measure of central tendency wouldmake the number of visitors appear to bethe highest?66 Adita starts training for the Myrtle BeachMarathon. During her training program sheplans to increase her running distance bythe same amount each week. The tablebelow shows her progress through Week 5.Weekly Miles RunWeek (x) Miles Run (y)1 82 8.53 94 9.55 10678Complete the table. Write an equation toshow the relationship between x, the week,and y, the number of miles run.The Myrtle Beach Marathon is 26 mileslong. Adita’s training goal is to run thesame distance as the marathon in one week.If Adita starts her training program20 weeks before the race, does she haveenough time to meet her goal? Explain.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A44 Mastering the PASS, Grade 8