Victory for the ACT Student Text 15e

V ICTORY P RACTICE T EST A NSWERS AND E XPLANATIONS • 465

To eliminate the variable y ,

—Ž–‹’Ž› –Š‡ ϐ‹”•– ‡“—ƒ–‹‘ „› 1 and add the equations: ax y b ax y b 2 2 − − = − + + = ax b x =

58. (H) (p. 392) Mathematics/Algebra and Functions/Solving Simultaneous Equations .

a b

= Substitute a b

for x

‹ –Š‡ ϐ‹”•– ‡“—ƒ–‹‘ ƒ† •‘Ž˜‡ ˆ‘” y :

a d n The solution set { x a b y b b y b y Ͳ + = + = =

, y . 59. (A) (p. 392) Mathematics/Geometry/Trigonometry/Determining Trigonometric Values and Triangles/Pythagorean Ȕ ‹• , a b 0 ( 2

Since sin

, we have:

i

side opposite

Theorem .

i

hypotenuse

The third side of the triangle, x x r 4 2 2 2

, is found using the Pythagorean theorem:

+ = =

16

16 = − = !

x

r

2

2

−

x

r

2

16

= −

r

2

16 (length is positive)

Since cos . 60. (G) (p. 392) Mathematics/Number and Quantity/Rates and Proportions. The number of sheets is directly proportional to the number of machines, as well as directly proportional to the amount of time. Thus: sheets sheets hypotenuse side adjacent to i i , cos 4 16 r 2 = − i

d

d n

n

:

:

# of machines time

# of machines time

1

2

300

600

( ) ( ) t 6

3 3

300

600

t

9

6

100 100

t

3

t t

100 300

3