Geometry Find the volume of each rectangular prism.

C Challenge

Multiply or divide.

66. 3 m 3 − 3 m 4 m 2 + 4 m − 8 ⋅ ( 6 m 2 + 12 m ) fraction 3 , m cubed , minus 3 m , over 4 , m squared , plus 4 m minus 8 end fraction . dot . open . 6 , m squared , plus 12 m . close
67. t 2 − r 2 t 2 + t r − 2 r 2 ⋅ t 2 + 3 t r + 2 r 2 t 2 + 2 t r + r 2 fraction t squared , minus , r squared , over t squared , plus t r minus 2 , r squared end fraction . dot . fraction t squared , plus 3 t r plus 2 , r squared , over t squared , plus 2 t r plus , r squared end fraction
68. 5 x 2 y 2 − 25 ÷ 5 x y − 25 x y 2 − 10 y + 25 fraction 5 , x squared , over y squared , minus 25 end fraction . divides . fraction 5 x y minus 25 x , over y squared , minus 10 y plus 25 end fraction
69. 2 a 2 − a b − 6 b 2 2 b 2 + 9 a b − 5 a 2 ÷ 2 a 2 − 7 a b + 6 b 2 a 2 − 4 b 2 fraction 2 , eh squared , minus eh b minus 6 , b squared , over 2 , b squared , plus 9 eh b minus 5 , eh squared end fraction . divides . fraction 2 , eh squared , minus 7 eh b plus 6 , b squared , over eh squared , minus 4 , b squared end fraction

Standardized Test Prep

SAT/ACT

70. What is the simplified form of ( 2 x − 5 ) ⋅ 2 x 2 x 2 − 9 x + 10 ? open 2 x minus 5 close dot . fraction 2 x , over 2 , x squared , minus 9 x plus 10 end fraction . question mark
    1. 1
    2. 2 x x − 2 fraction 2 x , over x minus 2 end fraction
    3. x − 5 − 4 x + 5 fraction x minus 5 , over negative 4 x plus 5 end fraction
    4. 2 x − 5 − 8 x − 10 fraction 2 x minus 5 , over negative 8 x minus 10 end fraction
71. The volume of the rectangular prism is 4 x 3 + 6 x 2 . 4 , x cubed , plus 6 , x squared , .  What is the width w of the prism?

    

    6. 4 x 3 + 6 x 2 − 2 x 4 , x cubed , plus 6 , x squared , minus 2 x
    7. 2 x + 3 2 x plus 3
    8. 2 x + 4 2 x plus 4
    9. 2 x + 6 2 x plus 6
72. What is the vertex of the parabola with the equation y = 2 x 2 + 3 x − 1 ? y equals 2 , x squared , plus 3 x minus 1 question mark
    1. ( − 0.75 , − 2.125 ) open negative , 0.75 , comma negative , 2.125 , close
    2. ( 0.75 , 2.125 ) open , 0.75 , comma , 2.125 , close
    3. ( − 2.125 , − 0.75 ) open negative , 2.125 , comma negative , 0.75 , close
    4. ( − 0.75 , 2.125 ) open negative , 0.75 , comma , 2.125 , close

Short Response

73. A soccer ball is kicked with an initial upward velocity of 35 ft/s from a starting height of 2.5 ft. If no one touches the ball, how long will it be in the air? Use the formula h = − 16 t 2 + v t + c , h equals negative 16 , t squared , plus v t plus c comma  where h is the ball's height at time t, v is the initial upward velocity, and c is the starting height. Show your work.

Mixed Review

See Lesson 11-1.

Simplify each expression. State any excluded values.

74. 7 m − 14 3 m − 6 fraction 7 m minus 14 , over 3 m minus 6 end fraction
75. 5 a 2 10 a 4 − 15 a 2 fraction 5 , eh squared , over 10 , eh to the fourth , minus 15 , eh squared end fraction
76. 4 c 2 − 36 c + 81 4 c 2 − 2 c − 72 fraction 4 , c squared , minus 36 c plus 81 , over 4 , c squared , minus 2 c minus 72 end fraction

Get Ready! To prepare for Lesson 11-3, do Exercises 77–79.

See Lesson 8-3.

Find each product.

77. ( 2 x + 4 ) ( x + 3 ) open 2 x plus 4 close open x plus 3 close
78. ( − 3 n − 4 ) ( n − 5 ) open negative 3 n minus 4 close open n minus 5 close
79. ( 3 a 2 + 1 ) ( 2 a − 7 ) open 3 , eh squared , plus 1 close open 2 eh minus 7 close

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