Solution Manual for College Algebra Concepts Through Functions, 3rd Edition

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Ch.0Foundations:APreludetoFunctions0.1TheDistanceandMidpointFormulas1UsetheDistanceFormulaMULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.Plotthepoint.1) (1,3)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6A)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6B)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6C)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6D)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6Page1

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2) (-4,3)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6A)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6B)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6C)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6D)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6Page2

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3) (2,-4)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6A)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6B)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6C)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6D)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6Page3

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4) (-2,-4)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6A)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6B)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6C)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6D)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6Page4

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5) (0,6)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6A)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6B)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6C)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6D)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6Page5

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6) (-4,0)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6A)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6B)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6C)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6D)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6Tellinwhichquadrantoronwhatcoordinateaxisthepointlies.7) (10,13)A) QuadrantIB) QuadrantIIC) QuadrantIIID) QuadrantIV8) (-6,13)A) QuadrantIIB) QuadrantIC) QuadrantIIID) QuadrantIV9) (-18,-3)A) QuadrantIIIB) QuadrantIC) QuadrantIID) QuadrantIV10) (6,-12)A) QuadrantIVB) QuadrantIC) QuadrantIID) QuadrantIII11) (0,6)A) y-axisB) x-axisC) QuadrantID) QuadrantIIPage6

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12) (-8,0)A) x-axisB) y-axisC) QuadrantID) QuadrantIIFindthedistanced(P1,P2)betweenthepointsP1 andP2.13)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6A)10B)2C) 3D) 114)x-8-6-4-22468y8642-2-4-6-8x-8-6-4-22468y8642-2-4-6-8A)53B) 35C) 14D) 515)x-8-6-4-22468y8642-2-4-6-8x-8-6-4-22468y8642-2-4-6-8A) 210B) 322C) 32D) 8Page7

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16)x-8-6-4-22468y8642-2-4-6-8x-8-6-4-22468y8642-2-4-6-8A) 25B) 123C) 12D) 617) P1=(1,1);P2=(1,-5)A) 6B)6C) 7D) 518) P1=(-4,-5);P2=(-16,0)A) 13B) 169C) 14D) 2619) P1=(0,-2);P2=(-4,-2)A) 4B) 2C) 25D) 1620) P1=(0,0);P2=(9,10)A)181B) 181C) 19D)1921) P1=(1,2);P2=(-3,-5)A)65B)33C) 28D) 322) P1=(4,-2);P2=(2,-6)A) 25B) 123C) 12D) 223) P1=(-5,-1);P2=(7,-4)A) 317B) 13515C) 135D) 1524) P1=(-0.6,-0.8);P2=(-2,2.2)Roundtothreedecimalplaces,ifnecessary.A) 3.311B) 22C) 10.469D) 3.411Decidewhetherornotthepointsaretheverticesofarighttriangle.25) (-2,-9),(7,-9),(7,-6)A) YesB) No26) (3,-4),(5,0),(7,-1)A) YesB) No27) (1,7),(7,9),(6,4)A) NoB) Yes28) (3,10),(9,12),(15,5)A) NoB) YesPage8

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Solvetheproblem.29) Findallvaluesofksothatthegivenpointsare29unitsapart.(-5,5),(k,0)A)-3,-7B)-7C) 3,7D) 730) FindtheareaoftherighttriangleABCwithA=(-2,7),B=(7,-1),C=(3,9).A) 29squareunitsB) 58squareunitsC)582squareunitsD)292squareunits31) Findallthepointshavinganx-coordinateof9whosedistancefromthepoint(3,-2)is10.A) (9,6),(9,-10)B) (9,2),(9,-4)C) (9,-12),(9,8)D) (9,13),(9,-7)32) Amiddleschoolʹsbaseballplayingfieldisasquare,80 feetonaside.Howfarisitdirectlyfromhomeplatetosecondbase(thediagonalofthesquare)?Ifnecessary,roundtothenearestfoot.A) 113feetB) 114feetC) 112 feetD) 120 feet33) Amotorcycleandacarleaveanintersectionatthesametime.Themotorcycleheadsnorthatanaveragespeedof20milesperhour,whilethecarheadseastatanaveragespeedof48milesperhour.Findanexpressionfortheirdistanceapartinmilesattheendofthours.A) 52tmilesB) t68milesC) 52tmilesD) 2t13miles34) FindthelengthofeachsideofthetriangledeterminedbythethreepointsP1,P2,andP3.Statewhetherthetriangleisanisoscelestriangle,arighttriangle,neitherofthese,orboth.P1=(-5,-4),P2=(-3,4),P3=(0,-1)A) d(P1,P2)=217;d(P2,P3)=34;d(P1,P3)=34bothB) d(P1,P2)=217;d(P2,P3)=34;d(P1,P3)=34isoscelestriangleC) d(P1,P2)=217;d(P2,P3)=34;d(P1,P3)=52righttriangleD) d(P1,P2)=217;d(P2,P3)=34;d(P1,P3)=52neither2UsetheMidpointFormulaMULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.FindthemidpointofthelinesegmentjoiningthepointsP1 andP2.1) P1=(1,7);P2=(9,9)A) (5,8)B) (10,16)C) (-8,-2)D) (8,5)2) P1=(4,8);P2=(-8,-3)A)- 2,52B)6,112C)12,11D)-4,53) P1=(7,1);P2=(-16,-16)A)-92 ,-152B)232 ,172C)-9,-15D) 9,154) P1=(-0.2,-0.4);P2=(-1.1,-2.9)A) (-0.65,-1.65)B) (-1.65,-0.65)C) (-0.45,-1.25)D) (-1.25,-0.45)Page9

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5) P1=(x,6);P2=(0,2)A)x2 ,4B) x,8C)-x2 ,4D) x,46) P1=(3y,1);P2=(4y,2)A)7y2 ,32B) 7y,3C)y,1D)3y2 ,72Solvetheproblem.7) If(5,5)istheendpointofalinesegment,and(7,8)isitsmidpoint,findtheotherendpoint.A) (9,11)B) (9,2)C) (1,-1)D) (11,9)8) If(1,-5)istheendpointofalinesegment,and(0,-7)isitsmidpoint,findtheotherendpoint.A) (-1,-9)B) (-1,-3)C) (3,-1)D) (-3,-7)9) If(-10,7)istheendpointofalinesegment,and(-8,2)isitsmidpoint,findtheotherendpoint.A) (-6,-3)B) (-6,12)C) (-14,17)D) (-20,11)10) If(4,5)istheendpointofalinesegment,and(0,6)isitsmidpoint,findtheotherendpoint.A) (-4,7)B) (-4,4)C) (12,3)D) (6,-3)11) Themediansofatriangleintersectatapoint.Thedistancefromthevertextothepointisexactlytwo-thirdsofthedistancefromthevertextothemidpointoftheoppositeside.FindtheexactdistanceofthatpointfromthevertexA(3,4)ofatriangle,giventhattheothertwoverticesareat(0,0)and(8,0).A) 2173B)173C) 2D) 830.2GraphsofEquationsinTwoVariables;Intercepts;Symmetry1GraphEquationsbyPlottingPointsMULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.Determinewhetherthegivenpointisonthegraphoftheequation.1) Equation:y=x4-xPoint:(-9,6558)A) NoB) Yes2) Equation:x2-y2=36Point:( 32,32)A) NoB) YesPage10

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Graphtheequationbyplottingpoints.3) y=x+ 6x-10-5510y105-5-10x-10-5510y105-5-10A)x-10-5510y105-5-10x-10-5510y105-5-10B)x-10-5510y105-5-10x-10-5510y105-5-10C)x-10-5510y105-5-10x-10-5510y105-5-10D)x-10-5510y105-5-10x-10-5510y105-5-10Page11

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4) y=2x- 6x-10-5510y105-5-10x-10-5510y105-5-10A)x-10-5510y105-5-10x-10-5510y105-5-10B)x-10-5510y105-5-10x-10-5510y105-5-10C)x-10-5510y105-5-10x-10-5510y105-5-10D)x-10-5510y105-5-10x-10-5510y105-5-10Page12

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5) y=x2 - 9x-10-5510y105-5-10x-10-5510y105-5-10A)x-10-5510y105-5-10x-10-5510y105-5-10B)x-10-5510y105-5-10x-10-5510y105-5-10C)x-10-5510y105-5-10x-10-5510y105-5-10D)x-10-5510y105-5-10x-10-5510y105-5-10Page13

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6) 5x+3y=15x-10-5510y105-5-10x-10-5510y105-5-10A)x-10-5510y105-5-10x-10-5510y105-5-10B)x-10-5510y105-5-10x-10-5510y105-5-10C)x-10-5510y105-5-10x-10-5510y105-5-10D)x-10-5510y105-5-10x-10-5510y105-5-10Page14

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7) 4x2+4y=16x-10-5510y105-5-10x-10-5510y105-5-10A)x-10-5510y105-5-10x-10-5510y105-5-10B)x-10-5510y105-5-10x-10-5510y105-5-10C)x-10-5510y105-5-10x-10-5510y105-5-10D)x-10-5510y105-5-10x-10-5510y105-5-10Solvetheproblem.8) If(a,3)isapointonthegraphofy=2x-5,whatisa?A) 4B) 1C)-1D)-49) If(3,b)isapointonthegraphof3x-2y=17,whatisb?A)-4B) 4C) 233D) 113Page15

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