50. Packaging The diagram below shows a piece of cardboard that makes a box when sections of it are folded and taped. The ends of the box are x inches by x inches, and the body of the box is 10 in. long.

    

    1. Write an equation for the volume V of the box.
    2. Solve the equation in part (a) for x.
    3. Find the integer values of x that would give the box a volume between 40  in . 3 40 , in , . cubed  and 490  in . 3 , 490 , in , . cubed , comma  inclusive.

C Challenge

51. Reasoning Explain the difference between squaring x − 1 square root of x minus 1 end root  and x − 1. square root of x minus 1.
52. 1. Reasoning What is the solution of 7 y + 18 = y ? square root of 7 y plus 18 end root . equals y question mark  What is the extraneous solution?
    2. Multiply one side of 7 y + 18 = y square root of 7 y plus 18 end root . equals y  by − 1 . negative 1 .  What is the solution of the new equation? What is an extraneous solution of the new equation?
    3. What do you think will happen to the solutions and extraneous solutions of y + 2 = y square root of y plus 2 end root , equals y  if you multiply one side by − 1 ? negative 1 question mark  Explain.

Standardized Test Prep

SAT/ACT

53. What are the solutions of c 2 − 17 = 8 ? square root of c squared , minus 17 end root . equals 8 question mark
    1. 6, 9
    2. 8 ,   − 8 8 comma minus 8
    3. 8, 0
    4. 9 ,   − 9 9 comma minus 9

54. Sam is building a fence around a triangular flower garden. What is the perimeter of the garden? Round your answer to the nearest tenth of a meter.

    

    6. 14.1 m
    7. 20.0 m
    8. 24.1 m
    9. 50.0 m
55. What is the slope-intercept form of the equation 2 x + 5 y = 40 ? 2 x plus 5 y equals 40 question mark
    1. y = − 2 x + 8 y equals negative 2 x plus 8
    2. y = − 2 5 x + 8 y equals negative , 2 fifths , x plus 8
    3. y = 2 5 x + 8 y equals , 2 fifths , x plus 8
    4. y = 2 x + 8 y equals 2 x plus 8
56. Short Response Write the equation of the line passing through ( 1 ,   − 1 ) open 1 comma minus 1 close  with a slope of 1 2 1 half  in three different forms. When would each of the forms be useful?

Mixed Review

See Lesson 10-3.

Simplify each expression.

57. 8 + 3 2 square root of 8 plus 3 square root of 2
58. ( 2 5 − 6 ) ( 9 + 3 5 ) open . 2 square root of 5 minus 6 . close . open . 9 plus 3 square root of 5 . close
59. 2 3 + 8 fraction 2 , over square root of 3 plus square root of 8 end fraction

See Lesson 9-6.

Use the quadratic formula to solve each equation.

60. 3 a 2   +   4 a   +   3   =   0 3 , eh squared , plus 4 eh plus 3 equals 0
61. 2 f 2   −   8   =   0 2 , f squared , minus 8 equals 0
62. 6 m 2   +   13 m   +   6   =   0 6 , m squared , plus 13 m plus 6 equals 0

Get Ready! To prepare for Lesson 10-5, do Exercises 63–65.

See Lesson 5-8.

Graph each function by translating y = | x |.

63. y = | x + 2 | y equals vertical line x plus 2 vertical line
64. y = | x | − 3 y equals vertical line x vertical line negative 3
65. y = | x − 4 | y equals vertical line x minus 4 vertical line

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