Victory for the ACT Student Text 15e

V ICTORY P RACTICE T EST A NSWERS AND E XPLANATIONS • 453 A central angle is equal to its intercepted arc, so . An inscribed angle is equal to one-half the measure of its intercepted arc. Therefore, the measure c

2. (J) (p. 378) Mathematics/Geometry/Lines and Angles and Circles .

$

AC AOC + of ABC + equation: x x 2 is Therefore, x ( x x

70 c

$

AC 2 2 70

c

35

.

Factor the quadratic

3. (D) (p. 378) Mathematics/Algebra and Functions/Solving Quadratic Equations and Relations .

) + + = + + = + = x

6 8 0

) ( 4 2 0

+ =

x

4 0 or 2 . 4. (F) (p. 379) Mathematics/Geometry/Lines and Angles . 2 0 or Ͷ = −

Fill in the given information and label the remaining angles:

Since b angles form a triangle: r a b 180 + + =

. And a 75

because it is the supplement of y

° is an alternate interior angle with x

° , b 70

° . The three

. Thus:

+ + = =

r

r 75 70 180 35

5. (A) (p. 379) Mathematics/Algebra and Functions/Manipulating Algebraic Expressions/Evaluating Expressions . Substitute the given values for A and r and solve for g : A = 2

g r gr 2 1 + g

( )

=

4

+

g

1

) + = + =

g

g g

( 4 1 2

g

4 4 2

= − = −

g g

2 4

2

V-shaped graphs into the answer

6. (H) (p. 379) Mathematics/Algebra and Functions/Coordinate Geometry/Graphs of Linear Equations . usually indicate absolute value functions. Substitute the given coordinates ( , )2 2 , ( , )0 0 , and ( , )3 3 choices: only y x •ƒ–‹•ϐ‹‡• ƒŽŽ –Š‡ ‘”†‡”‡† ’ƒ‹”•Ǥ 7. (D) (p. 379) Mathematics/Algebra and Functions/Manipulating Algebraic Expressions/Basic Algebraic Manipulations . The distributive property indicates multiplication over addition [ ( ) ] a b c ab ac + = + and multiplication over subtraction [ ( ) ] a b c ab ac − = − . Thus, ( ) x x x x 2 2 2 + = + . 8. (K) (p. 380) Mathematics/Number and Quantity/Percentages . Š‡ •ƒŽ‡• –ƒš ‹• ͹Ψ ‘ˆ ̈́͸ͲͲǣ . ( ) $ 0 07 600 42 . Thus, the total cost is $ $ $ 600 42 642 + = .