52. Given u = 〈 − 4 , 3 〉 negative 4 comma 3 right pointing angle bracket and v = 〈1, − 2 negative 2 〉, find w if u · w = 7 u middle dot w equals 7  and v · w = − 8 . v middle dot w equals negative 8 .
53. Physics When an object is not moving, all the forces acting on it must sum to 0. The object is said to be in equilibrium. Two cables of different lengths hold a stoplight over an intersection. The force vectors being applied along the two cables are 〈20, 18〉 and 〈 − 20 , 12 〉 . negative 20 comma 12 right pointing angle bracket . The magnitude of each vector is measured in pounds. A third force vector in this situation is the force due to gravity, and is straight downward. How much does the stoplight weigh?

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

54. Let u = 〈 − 2 , 2 〉 negative 2 comma 2 right pointing angle bracket and v = 〈9, − 3 negative 3 〉. What is | u + v u plus v |?
55. If x [ − 2 1 3 − 1 ] − [ 5 − 1 − 2 4 ] = [ 1 − 2 − 7 − 1 ] , x . matrix with 2 rows and 2 columns , row1 column 1 , negative 2 , column 2 1 , row2 column 1 , 3 , column 2 negative 1 , end matrix . minus . matrix with 2 rows and 2 columns , row1 column 1 , 5 , column 2 negative 1 , row2 column 1 , negative 2 , column 2 4 , end matrix . equals . matrix with 2 rows and 2 columns , row1 column 1 , 1 , column 2 negative 2 , row2 column 1 , negative 7 , column 2 negative 1 , end matrix . comma  what is x?
56. What is the determinant of [ 3 10 1 5 1 8 1 3 ] ? . matrix with 2 rows and 2 columns , row1 column 1 , 3 tenths , column 2 1 fifth , row2 column 1 , 1 eighth , column 2 1 third , end matrix . question mark  Enter your answer as a fraction.
57. If B = [ 4 − 1 2 0 ] , b equals . matrix with 2 rows and 2 columns , row1 column 1 , 4 , column 2 negative 1 , row2 column 1 , 2 , column 2 0 , end matrix . comma  what is det B − 1 ? b super negative 1 end super , question mark
58. What is the rotation in degrees that transforms a triangle with vertices (2, 0), ( − 3 , 5 ) , open negative 3 comma 5 close comma  and ( 1 , − 2 ) open 1 comma negative 2 close  into a triangle with vertices (0, 2), ( − 5 , − 3 ) , open negative 5 comma negative 3 close comma  and (2, 1)?
59. Given u = 〈x, 3〉, v = 〈 − 3 , 2 〉 , negative 3 comma 2 right pointing angle bracket comma and u · v = − 9 , u middle dot v equals negative 9 comma  what is x?

Mixed Review

See Lesson 12-5.

Graph each figure and its image after reflection across the given line.

60. [ 1 5 3 1 − 2 3 ] ; y = x . matrix with 2 rows and 3 columns , row1 column 1 , 1 , column 2 5 , column 3 3 , row2 column 1 , 1 , column 2 negative 2 , column 3 3 , end matrix . semicolon y equals x
61. [ − 3 0 2 − 1 2 3 0 − 2 ] ; . matrix with 2 rows and 4 columns , row1 column 1 , negative 3 , column 2 0 , column 3 2 , column 4 negative 1 , row2 column 1 , 2 , column 2 3 , column 3 0 , column 4 negative 2 , end matrix . semicolon  the x-axis

See Lesson 3-3.

Solve each system of inequalities by graphing.

62. { 2 + y < 3 − x − y ≥ 1 left brace . table with 2 rows and 1 column , row1 column 1 , 2 plus y less than 3 , row2 column 1 , negative x minus y greater than or equal to 1 , end table
63. { 2 x ≤ 0 − x + y > − 1 left brace . table with 2 rows and 1 column , row1 column 1 , 2 x less than or equal to 0 , row2 column 1 , negative x plus y greater than negative 1 , end table
64. { x < 3 y ≥ − 4 − x + y < 5 left brace . table with 3 rows and 1 column , row1 column 1 , x less than 3 , row2 column 1 , y greater than or equal to negative 4 , row3 column 1 , negative x plus y less than 5 , end table

See Lesson 2-4.

Write in point-slope form an equation of the line through each pair of points.

65. (0, 1) and ( 2 , − 5 ) open 2 comma negative 5 close
66. ( − 9 , 3 ) open negative 9 comma 3 close  and ( − 4 , − 4 ) open negative 4 comma negative 4 close
67. (1, 8) and (7, 2)

Get Ready! To prepare for Lesson 13-1, do Exercises 68–71.

See Lesson 2-1.

Determine whether each relation is a function.

68. {(2, 4), (1, 3), ( − 3 , − 1 ) , open negative 3 comma negative 1 close comma  (4, 6)}
69. {(2, 6), ( − 3 , 1 ) , ( open negative 3 comma 1 close comma open 2, 2), (0, 4)}
70. {(5, 3), (1, 3), ( − 3 , 3 ) , ( open negative 3 comma 3 close comma open 4, 3)}
71. {(8, 4), (8, 3), ( 8 , − 1 ) , ( open 8 comma negative 1 close comma open 8, 6)}

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