I Tavi

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I <strong>Tavi</strong> navis sakuTari siCqarea navis siCqare mdgar wyalSi. 36 26 naxazis mixedviT aRadgineT amocana da ipoveT CK-s sigrZe. 27 wiladis mniSvneli 4-iT metia mricxvelze, Tu am wiladis mricxvelsac da mniSvnelsac 3-iT gavzrdiT, maSin wiladi 1 -iT gadiddeba. 9 ipoveT Tavdapirveli wiladi. 28 400 km sigrZis manZili Cqarma matarebelma gaiara 1 saaTiT ufro swrafad, vidre sabargom. ras udris TiToeuli matareblis moZraobis siCqare, Tu sabargo 1 saaTSi gadioda 20 kmiT nakleb manZils, vidre Cqari matarebeli? 29 Tu matareblis siCqares 10km/sT-iT gavzrdiT, maSin igi 720kmis gavlas 1 saaTiT nakleb dros moandomebs. ipoveT matareblis Tavdapirveli siCqare. 30 manZili or navsadgurs Soris mdinariT 48 km-ia. gemi am manZilis gavlas iqeT-aqeT 5 sT-s andomebs. ipoveT gemis siCqare mdgar wyalSi, Tu mdinaris dinebis siCqare 4km/sT-ia. 31 navma mdinaris dinebis sawinaaRmdego mimarTulebiT 221 2 kilometri gaiara, xolo dinebis mimarTulebiT – 281 2 kilometri. sul am mgzavrobas 8 saaTi dasWirda. ipoveT navis saku- Tari siCqare, Tu mdinaris dinebis siCqare 21 2 km/sT-ia. 32 or qalaqs Soris manZili 840km-ia. am qalaqebidan gamosuli matareblebi erTmaneTs Sua gzaSi Sexvdnen. ipoveT TiToeuli matareblis siCqare, Tu cnobilia, rom meore gamovida 40 wuTiT adre da misi siCqare 7km/sT-iT naklebia pirveli matareblis siCqareze. 33 15 tona bostneulis gadasazidad saWiro iyo gansazRvruli tvirTmzidaobis ramdenime sabarguli. aseTi tvirTmzidaobis sabargulebis uqonlobis gamo garaJma 1 toniT naklebi 2 tvirTmzidaobis, magram erTiT meti sabarguli gagzavna. ramden tona bostneuls itevda TiToeuli sabarguli? 34 18 tona Rvino garkveuli tevadobis kasrebSi unda CaesxaT, magram aseTi kasrebis uqonlobis gamo Rvino 0,3t-iT meti tevadobis kasrebSi gaanawiles, risTvisac 5 kasriT naklebi dasWirdaT. ramden kasrSi gaanawiles Rvino? 35 qsovilis fasma imdeni procentiT daiklo, ramdeni laric Rirda fasebis daklebamde. ramdeni procentiT gaiafda qsovili, Tu 1 m-is fasi 16 lari gaxda?
36 likam da Takom yvavilebis dargva nakveTSi 4 saaTSi daam- Tavres. ramdeni saaTi dasWirdeboda TiToeuls cal-calke am yvavilnaris gasaSeneblad, Tu marto likas SeeZlo yvavilebis dargva 6 saaTiT adre daesrulebina, vidre marto Takos? 37 orma glexma simindis yana 6 dReSi gaToxna. ramdeni dRe das- Wirdeboda TiToeuls cal-calke am yanis gasaToxnad, Tu erTs damoukideblad SeeZlo mTeli samuSaos Sesruleba 5 dRiT nakleb droSi, vidre meores? 38 Tu axla saaTis isrebs Soris kuTxe 18 gradusia, ramden saa- TSi iqneba pirvelad maT Soris kuTxe 66°? 39 ipoveT naxatze gamosaxul saaTis isrebs Soris kuTxis gradusuli zoma. 40 sakoordinato sibrtyeze moniSneT yvela is P(x;y) wertili, romlisTvisac gamosaxulebas azri aqvs: a) ; b) + ; g) + ; d) ; e) . 41* a ricxvis ra mniSvnelobebisaTvis ar eqneba (x − a)( +1)= 0 gantolebas amonaxseni? 42 ipoveT n, Tu m 5–n = 4 da m 3+n = 64. 43 ipoveT y = |x – 4| funqciis udidesi da umciresi mniSvnelobebi [1;6] intervalSi. 44 sad mdebareobs y=x 2 +bx+c parabolas wvero, Tu a) b>0; c>0; D>0; b) b0; D0; c0 (daxazeT Sesabamisi sqematuri naxazebi) amocana damoukidebeli kvlevisTvis: 11 12 1 10 2 9 3 8 4 7 6 5 45 a-s ra mniSvnelobE BebisTvis aqvs gantolebas mxolod erTi amonaxseni? a) ax 2 – 12x + 3a – 3 = 0; b) (a – 3)x 2 + 5x + a + 3 = 0. 37
Page 3: nana jafariZe maia wilosani nani
Page 6 and 7: IV Tavi . . . . . . . . . . . . . .
Page 8 and 9: 6 rogor visargebloT wigniT wignze m
Page 10 and 11: I Tavi 8 f funqciaa h ar aris funqc
Page 12 and 13: I Tavi gasaxseneblad! p(A) = m n ,
Page 14 and 15: I Tavi -4 12 4 a) savarjiSoebi: 1 r
Page 16 and 17: I Tavi 14 4) rodis moawyves turiste
Page 18 and 19: I Tavi 16 2 amovicnoT wrfivi funqci
Page 20 and 21: I Tavi 18 SeavseT gamotovebuli adgi
Page 22 and 23: I Tavi 20 proeqti: gazomvebidan fun
Page 24 and 25: I Tavi 22 y 10 -3 -2 -1 0 1 2 3 9 8
Page 26 and 27: I Tavi 24 15% 1,5 < n ≤ 2 20% 1 <
Page 28 and 29: I Tavi 26 nax. 1 kvadratul gantoleb
Page 30 and 31: I Tavi 28 3 dawereT kvadratuli gant
Page 32 and 33: I Tavi davazustoT! roca D = 0, kvad
Page 34 and 35: I Tavi 32 amovxsnaT formuliT (3x 2
Page 36 and 37: I Tavi 34 z) 10x 2 −120 + 6x = 98
Page 40 and 41: I Tavi 38 6 amovxsnaT jgufuri mecad
Page 42 and 43: I Tavi x 1 da x 2 ricxvebi arian x
Page 44 and 45: I Tavi 42 17 amoxseniT gantoleba: a
Page 46 and 47: I Tavi 44 yuradReba: Tu D=0, maSin,
Page 48 and 49: I Tavi gavixsenoT! x = a, maSin a 2
Page 50 and 51: I Tavi 48 I Tavis damatebiTi savarj
Page 52 and 53: I Tavi 50 K y = x 2 A B -3 -2 -1 K
Page 54 and 55: I Tavi 52 39 A punqtidan B punqtisa
Page 56 and 57: I Tavi narevSi gaxsnili nivTierebis
Page 58: 56 I TavSi Seswavlili masalis mokle

I Tavi

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