38. Sports You throw a softball into the air with an initial upward velocity of 38 ft/s and an initial height of 5 ft.
    1. Use the vertical motion model to write an equation that gives the ball's height h, in feet, at time t, in seconds.
    2. The ball's height is 0 ft when it is on the ground. Solve the equation you wrote in part (a) for h = 0 h equals 0  to find when the ball lands.

Solve each cubic equation by factoring out the GCF first.

39. x 3 − 10 x 2 + 24 x = 0 x cubed , minus . 10 x squared , plus 24 x equals 0
40. x 3 − 5 x 2 + 4 x = 0 x cubed , minus . 5 x squared , plus 4 x equals 0
41. 3 x 3 − 9 x 2 = 0 3 x cubed , minus , 9 x squared , equals 0

C Challenge

42. Find an equation that has the given numbers as solutions. For example, 4 and − 3 negative 3  are solutions of x 2 − x − 12 = 0 . x squared , minus , x minus 12 equals 0 .
    1. − 5 , 8 negative 5 comma 8
    2. 3 , − 2 3 comma negative 2
    3. 1 2 , − 10 1 half , comma , minus 10
    4. 2 3 , − 5 7 2 thirds , comma , minus , 5 sevenths

Solve. Factor by grouping.

43. x 3 + 5 x 2 − x − 5 = 0 x cubed , plus . 5 x squared , minus x minus 5 equals 0
44. x 3 + x 2 − 4 x − 4 = 0 x cubed , plus . x squared , minus 4 . x minus 4 equals 0
45. x 3 + 2 x 2 − 9 x − 18 = 0 x cubed , plus . 2 x squared , minus 9 x minus 18 equals 0

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

46. What is the negative solution of the equation 2 x 2 − 13 x − 7 = 0 ? 2 x squared , minus 13 x minus 7 equals 0 question mark  Round to the nearest thousandth.

47. Phil, Toby, and Sam bowled four games last weekend. Their scores are shown in the Venn diagram below. What is the highest score that only Toby and Sam have in common?

    

48. What is the y-intercept of the line with equation 3 y − 4 x = 9 ? 3 y minus 4 x equals 9 question mark
49. How many elements are in the union of the two sets M = { 1 , 2 , − 3 , 4 } m equals left brace 1 comma 2 comma negative 3 comma 4 right brace  and N = { 1 , − 2 , 3 , 5 } ? n equals left brace 1 comma negative 2 comma 3 comma 5 right brace question mark
50. A rectangular card has a length 1 in. longer than twice the width and an area of 15  in. 2 . 15 , in. squared , .  What is the width of the card, in inches?

Mixed Review

See Lesson 9-3.

Solve each equation by finding square roots. If the equation has no real-number solution, write no solution.

51. t 2 = 144 t squared , equals 144
52. w 2 − 8 = − 17 w squared , minus 8 equals . minus 17
53. b 2 + 100 = 100 b squared , plus 100 equals 100
54. 5 h 2 − 80 = 0 5 h squared , minus 80 equals 0
55. 49 − m 2 = 0 49 minus . m squared , equals 0
56. 3 q 2 = 27 3 q squared , equals 27

Get Ready! To prepare for Lesson 9-5, do Exercises 57–59.

See Lesson 8-7.

Factor each expression.

57. y 2 − 10 y + 25 y squared , minus 10 . y plus 25
58. g 2 − 14 g + 49 g squared , minus 14 . g plus 49
59. m 2 + 18 m + 81 m squared , plus 18 . m plus 81

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