Test Bank for Algebra and Trigonometry Enhanced with Graphing Utilities , 7th Edition

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Ch. 1Graphs, Equations, and Inequalities1.1The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations1Use the Distance FormulaMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Find the distance d(P1, P2) between the points P1 and P2.1)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6A)41B) 3C) 10D) 82)x-8-6-4-22468y8642-2-4-6-8x-8-6-4-22468y8642-2-4-6-8A)170B) 62C) 77D) 4Page 1

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3)x-8-6-4-22468y8642-2-4-6-8x-8-6-4-22468y8642-2-4-6-8A) 210B) 322C) 32D) 44)x-8-6-4-22468y8642-2-4-6-8x-8-6-4-22468y8642-2-4-6-8A) 55B) 753C) 75D) 55) P1=(-2,-2); P2=(-2,-5)A) 3B)3C) 4D) 26) P1=(-3,-3); P2=(-8, 9)A) 13B) 169C) 14D) 267) P1=(0,-2); P2=(-4,-2)A) 4B) 2C) 25D) 168) P1=(0, 0); P2=(-6,-9)A) 313B) 117C) 15D) 3i69) P1=(2, 1); P2=(-2,-6)A)65B)33C) 28D) 310) P1=(5,-7); P2=(3,-3)A) 25B) 123C) 12D) 6Page 2

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11) P1=(-6,-4); P2=(4,-6)A) 226B) 966C) 96D) 1212) P1=(-0.9,-0.2); P2=(1.3,-2.8) Round to three decimal places, if necessary.A) 3.406B) 24C) 10.77D) 3.506Decide whether or not the points are the vertices of a right triangle.13) (-4,-1), (5,-1), (5, 4)A) YesB) No14) (8, 12), (10, 16), (12, 15)A) YesB) No15) (-5,-8), (1,-6), (0,-11)A) YesB) No16) (-2, 9), (4, 11), (10, 4)A) YesB) NoSolve the problem.17) Find all values of k so that the given points are29 units apart.(-5, 5), (k, 0)A)-3,-7B)-7C) 3, 7D) 718) Find the area of the right triangle ABC with A=(-2, 7), B=(7,-1), C=(3, 9).A) 29 square unitsB) 58 square unitsC)582square unitsD)292square units19) Find all the points having an x-coordinate of 9 whose distance from the point (3,-2) is 10.A) (9, 6), (9,-10)B) (9, 2), (9,-4)C) (9,-12), (9, 8)D) (9, 13), (9,-7)20) A middle school's baseball playing field is a square, 60 feet on a side. How far is it directly from homeplate to second base (the diagonal of the square)? If necessary, round to the nearest foot.A) 85 feetB) 86 feetC) 84 feetD) 92 feet21) A motorcycle and a car leave an intersection at the same time. The motorcycle heads north at an averagespeed of 20 miles per hour, while the car heads east at an average speed of 48 miles per hour. Find anexpression for their distance apart in miles at the end of t hours.A) 52t milesB) t68 milesC) 52t milesD) 2t13 miles22) A rectangular city park has a jogging loop that goes along a length, width, and diagonal of the park. To thenearest yard, find the length of the jogging loop, if the length of the park is 125 yards and its width is 75yards.A) 346 yardsB) 146 yardsC) 345 yardsD) 145 yardsPage 3

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23) Find the length of each side of the triangle determined by the three points P1, P2, and P3. State whetherthe triangle is an isosceles triangle, a right triangle, neither of these, or both.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)=34isosceles triangleC) d(P1, P2)=217; d(P2, P3)=34; d(P1, P3)=52right triangleD) d(P1, P2)=217; d(P2, P3)=34; d(P1, P3)=52neither2Use the Midpoint FormulaMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Find the midpoint of the line segment joining the points P1 and P2.1) P1=(3, 8); P2=(4, 1)A) ( 72 , 92 )B) (7, 9)C) (-1, 7)D) ( 92 , 72 )2) P1=(5, 4); P2=(4,-9)A)92 ,-52B)12 , 132C) 1, 13D) 9,-53) P1=(7, 1); P2=(-16,-16)A)-92 ,-152B)232 , 172C)-9,-15D) 9, 154) P1=(-0.1, 0.7); P2=(-2.5,-1.5)A) (-1.3,-0.4)B) (-0.4,-1.3)C) (-1.2,-1.1)D) (-1.1,-1.2)5) P1=(b, 5); P2=(0, 9)A)b2 , 7B) b, 14C)-b2 , 4D) b, 76) P1=(6x, 6); P2=(7x, 5)A)13x2, 112B) 13x, 11C) x, 1D)11x2, 132Solve the problem.7) If (-2, 4) is the endpoint of a line segment, and (2, 5) is its midpoint, find the other endpoint.A) (6, 6)B) (6, 3)C) (-10, 2)D) (0, 12)8) If (1, 1) is the endpoint of a line segment, and (-4,-2) is its midpoint, find the other endpoint.A) (-9,-5)B) (-9, 4)C) (11, 7)D) (-5,-9)9) If (8, 2) is the endpoint of a line segment, and (11, 1) is its midpoint, find the other endpoint.A) (14, 0)B) (14, 3)C) (2, 4)D) (6, 8)Page 4

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10) If (-3,-2) is the endpoint of a line segment, and (-4, 0) is its midpoint, find the other endpoint.A) (-5, 2)B) (-5,-4)C) (-1,-6)D) (1,-4)11) The medians of a triangle intersect at a point. The distance from the vertex to the point is exactlytwo-thirds of the distance from the vertex to the midpoint of the opposite side. Find the exact distance ofthat point from the vertex A(3, 4) of a triangle, given that the other two vertices are at (0, 0) and (8, 0).A) 2173B)173C) 2D) 83Page 5

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3Graph Equations by Plotting PointsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Plot the point in the xy-plane. Tell in which quadrant or on what axis the point lies.1) (3, 5)x-55y5-5x-55y5-5A)x-55y5-5x-55y5-5Quadrant IB)x-55y5-5x-55y5-5Quadrant IC)x-55y5-5x-55y5-5Quadrant IID)x-55y5-5x-55y5-5Quadrant IVPage 6

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2) (-6, 1)x-55y5-5x-55y5-5A)x-55y5-5x-55y5-5Quadrant IIB)x-55y5-5x-55y5-5Quadrant IVC)x-55y5-5x-55y5-5Quadrant ID)x-55y5-5x-55y5-5Quadrant IIIPage 7

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3) (2,-4)x-55y5-5x-55y5-5A)x-55y5-5x-55y5-5Quadrant IVB)x-55y5-5x-55y5-5Quadrant IIC)x-55y5-5x-55y5-5Quadrant IIID)x-55y5-5x-55y5-5Quadrant IPage 8

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4) (-5,-1)x-55y5-5x-55y5-5A)x-55y5-5x-55y5-5Quadrant IIIB)x-55y5-5x-55y5-5Quadrant IIIC)x-55y5-5x-55y5-5Quadrant IVD)x-55y5-5x-55y5-5Quadrant IIPage 9

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5) (0,-6)x-55y5-5x-55y5-5A)x-55y5-5x-55y5-5y-axisB)x-55y5-5x-55y5-5x-axisC)x-55y5-5x-55y5-5Quadrant IID)x-55y5-5x-55y5-5y-axisPage 10

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6) (-5, 0)x-55y5-5x-55y5-5A)x-55y5-5x-55y5-5x-axisB)x-55y5-5x-55y5-5y-axisC)x-55y5-5x-55y5-5Quadrant IID)x-55y5-5x-55y5-5x-axisDetermine whether the given point is on the graph of the equation.7) Equation: y=x2-xPoint: (0, 0)A) YesB) No8) Equation: x2-y2=64Point: (8, 8)A) NoB) YesPage 11

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Graph the equation by plotting points.9) y=x-2x-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-10-5510y105-5-10Page 12

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10) y=2x+8x-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-10-5510y105-5-10Page 13

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11) y=-x2+1x-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-10-5510y105-5-10Page 14

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12) 3x+4y=12x-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-10-5510y105-5-10Page 15

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13) x2+4y=4x-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-10-5510y105-5-10Page 16

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4Graph Equations Using a Graphing UtilityMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Determine the coordinates of the point shown. Tell in which quadrant the point lies. Assume the coordinates areintegers.1)A) (-4, 6); quadrant IIB) (-4, 3); quadrant IIC) (-4, 6); quadrant ID) (-4, 3); quadrant ISelect a setting so that each of the given points will lie in the viewing window.2) (8, 3), (5, 1), (9, 19)A)B)C)D)Page 17

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Determine the viewing window used.3)A)B)C)D)Page 18

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Graph the equation using a graphing utility.4) y=2x+1A)B)C)D)5) 2x-3y=3A)B)C)D)Page 19

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6) y=-2x2+9A)B)C)D)7) 3x2-2y=56A)B)C)D)Page 20

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5Use a Graphing Utility to Create TablesMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Use a graphing utility to create a table that displays the points on the graph of the given equation for x= -3,-2,-1,0, 1, 2, and 3.1) y=3x+5A)B)C)D)2) 6x+2y=28A)B)C)D)Page 21

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3) y=-3x2+10A)B)C)D)4) 4x2-2y=16A)B)C)D)Page 22

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6Find Intercepts from a GraphMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.List the intercepts of the graph.1)x-10-5510y105-5-10x-10-5510y105-5-10A) (-1, 0), (1, 0)B) (0,-1), (1, 0)C) (0,-1), (0, 1)D) (-1, 0), (0, 1)2)x-55y5-5x-55y5-5A) (0,-1)B) (0, 0)C) (-1,-1)D) (-1, 0)Page 23

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3)x--22y54321-1-2-3-4-5x--22y54321-1-2-3-4-5A)-π2 , 0 , (0, 3),π2 , 0B)-π2 , 0 , (3, 0),π2 , 0C) 0,-π2 , (3, 0), 0,π2D) 0,-π2 , (0, 3), 0,π24)x-10-5510y105-5-10x-10-5510y105-5-10A) (-4, 0), (0, 8), (2, 0)B) (-4, 0), (0, 8), (0, 2)C) (0,-4), (8, 0), (0, 2)D) (0,-4), (0, 8), (2, 0)5)x-10-5510y105-5-10x-10-5510y105-5-10A) (-4, 0)B) (0,-4)C) (4, 0)D) (0, 4)Page 24

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6)x-10-5510y105-5-10x-10-5510y105-5-10A) (-7, 0), (0,-7), (0, 7), (7, 0)B) (-7, 0), (0, 7)C) (-7, 0), (0,-7), (0, 0), (0, 7), (7, 0)D) (0, 7), (7, 0)7)x-10-5510y105-5-10x-10-5510y105-5-10A) (4, 0), (1, 0) (5, 0), (0,-4)B) (-4, 0), (0, 4), (0, 1), (0, 5)C) (-4, 0), (1, 0), (-5, 0), (0,-4)D) (-4, 0), (0,-4), (0, 1), (0,-5)8)A) (-4, 0), (0, 4), (4, 0)B) (-2, 0), (0, 2), (2, 0)C) (-2, 0), (0, 4), (2, 0)D) (-2, 0), (2, 0)Page 25

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7Use a Graphing Utility to Approximate InterceptsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Graph the equation using a graphing utility. Use a graphing utility to approximate the intercepts rounded to twodecimal places, if necessary. Use the TABLE feature to help establish the viewing window.1) y=-2x+15A) (0, 15), (7.5, 0)B) (0, 15), (-7.5, 0)C) (0,-15), (7.5, 0)D) (0, 15), (-7.5, 0), (7.5, 0)2) y=-4x+15A) (0, 15), (3.75, 0)B) (0, 3.75), (15, 0)C) (0, 15), (-3.75, 0)D) (0,-3.75), (15, 0)3) y=3x2-19A) (0,-19), (-2.52, 0), (2.52, 0)B) (0,-19), (2.52, 0)C) (0, 19), (-2.52, 0), (2.52, 0)D) (0,-19), (-2.51, 0), (2.51, 0)4) y=5x2-13A) (0,-13), (1.61, 0), (-1.61, 0)B) (0, 1.61), (0,-1.61), (-13, 0)C) (0,-13), (2.60, 0), (-2.60, 0)D) (0, 2.60), (0,-2.60), (-13, 0)5) 3x-4y=56A) (0,-14), (18.67, 0)B) (0,-14), (18.66, 0)C) (0,-14), (-18.67, 0), (18.67, 0)D) (0, 14), (18.67, 0)6) 6x-5y=67A) (0,-13.40), (11.17, 0)B) (0, 11.17), (-13.40, 0)C) (0, 13.40), (-11.17,0)D) (0,-13.41), (11.18, 0)7) 3x2-5y=34A) (0,-6.8), (-3.37, 0), (3.37, 0)B) (0,-6.8), (-3.36, 0), (3.36, 0)C) (0, 6.8), (-3.37, 0), (3.37, 0)D) (0,-6.8), (3.37, 0)8) 4x2-5y=68A) (0,-13.60), (4.12, 0), (-4.12, 0)B) (0, 4.12), (0,-4.12), (-13.60, 0)C) (0,-13.59), (4.13, 0), (-4.13, 0)D) (0, 13.60), (4.12, 0), (-4.12, 0)1.2Solving Equations Using a Graphing Utility; Linear and Rational Equations1Solve Equations Using a Graphing UtilityMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Use a graphing utility to approximate the real solutions, if any, of the equation rounded to two decimal places.1) x3-6x+3=0A) {2.15, 0.52,-2.67}B) {-0.48}C) {2.67,-0.52,-2.15}D) no solution2) x4-3x2+4x+15=0A) {-0.84,-1.93}B) {2.11,-2.60}C) {3.94,-1.27}D) no solution3) 2x4-5x2+7x=14A) {-2.31, 1.69}B) {-2.31, 1.70}C) {-2.30, 1.69}D) {-2.32, 1.70}Page 26

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4) x4-5x3+6x-2=0A) {4.75, 1, 0.38,-1.13}B) {0.31,-5.23}C) {4.71, 1.44,-0.38,-0.77}D) no solution5)-x4+3x3+43 x2=92 x+2A) {2.82, 1.61,-0.46,-0.97}B) {-3.34}C) {1.09,-0.44}D) no solution2Solve Linear EquationsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Solve the equation.1) 4x=-24A) {-6}B) {6}C) {4}D) {-4}2) 9x=12A)43B)-43C)34D)-343) 2x+6=0A) {-3}B) {3}C) {2}D) {-2}4) 5x-10=0A)2B)-2C)12D)-125) 7x+2=0A)-27B)27C)72D)-726) 12 x=-59A)-109B)-910C)109D)1037) 13x=-13+12xA) {-13}B) {13}C) {-12}D) {-1}8) 10x-18=4x+30A) {8}B) {-8}C) {5}D) {-5}9)-3x-49=4x+7A) {-8}B) {8}C) {-7}D) {7}10) 35-2x=-14+5xA) {7}B) {-7}C) {5}D) {-5}11) 7x-(2x-1)=2A)15B)19C)-15D)-19Page 27

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12) 3(4x-1)=12A)54B)34C)1312D)111213) 14(5x-2)=9x-7A)2161B)3561C)-2161D)217914) 6(x+5)=7 x-(3-x)A)518B)-154C)154D)-51815) 3(x+2)=4(x-8)A) {38}B) {-38}C) {-26}D) {4}16) 4(2x-2)=7(x+5)A) {43}B) {-27}C) {-43}D) {31}17) 3(x+4)=(3x+12)A) {24}B) {0}C) all real numbersD) no solution18)-5x-6-7(x+1)=7x+2A)-1519B)-58C)310D) {7}19)-9x+6+7x=-2x+11A) {5}B) {-6}C) all real numbersD) no solution20) x2-4=1A) {10}B) {-10}C) {6}D) {-6}21) x2-12=-3A) {-5}B) {5}C) {-7}D) {7}22) 2x5=2+x3A) {30}B) {-30}C) {60}D) {-60}23) x3+1=x4+3A)24B)-24C)16D)-1624) 15-x2=1710A)-3B)3C)-152D)152Page 28

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25)-9.6x+1.7=-83-1.9xA) {11}B) {-92}C) {8.8}D) {9}26)-3x+57+37=-7x3A)-35B)-320C)320D)122927) (x+2)(x-1)=(x+1)2A)-3B)-2C)32D) {3}28) x(3x-4)=(3x+1)(x-2)A)-2B)-1C)2D) {5}29) x(1+3x)=(3x-1)(x-3)A)311B)-311C)3121D)-312130) x(x2+4)=9+x3A)94B) {4}C) {9}D)49Solve the problem.31) If (a, 3) is a point on the graph of y=2x-5, what is a?A) 4B) 1C)-1D)-432) If (3, b) is a point on the graph of 3x-2y=17, what is b?A)-4B) 4C) 233D) 113Solve the equation. The letters a, b, and c are constants.33) ax-b=c, a≠0A) x=b+caB) x=b-caC) x=c-baD) x=-b+ca34) xa+xb=c, a≠0, b≠0, a≠-bA) x=abca+bB) x=abcC) x=cabD) x=a+babc3Solve Rational EquationsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Solve the equation.1) 1-34x=2A)-34B)34C)-127D)-74Page 29

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2) 5x+25=7xA) {5}B) {-5}C) {2}D) {-2}3)-8x+5x=5A)-35B)-53C)35D)534)3x+5+22x+1=4x-2A)-4647B)4647C)-4746D)47465) 5-xx+34=7xA) {-8}B)-87C) {8}D) {-4}6)xx-9-4=9x-9A) {9,-9}B) {9}C) {-9}D) no solution7)x2x+2=2x-3x+1-2x4x+4A) {3}B)32C) {-3}D) no solution8) 1x+1x+6=x+7x+6A) {1}B) {-6}C) {-1}D) {6}9)62x-3=42x+5A)-212B)212C)-221D)22110)2xx2-4=1x2-4-4x+2A)32B)-76C)72D)-3811) x-2x-5=x+6x-7A)225B)-157C) {-4}D)85Page 30

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