Victory for the ACT Student Text 15e

V ICTORY P RACTICE T EST A NSWERS AND E XPLANATIONS • 461

Substitute the root for x

in the equation and evaluate: 12 0 2

40. (F) (p. 387) Mathematics/Algebra and Functions/Solving Quadratic Equations and Relations .

( ) x kx k k + − = + − = + − = + = 16 4 12 0 4 4 0 2 4 12 0

( ) 4

k

= − = −

k k

4 4

1

41. (E) (p. 388) Mathematics/Geometry/Triangles/Properties of Triangles and Number and Quantity/Rates and Proportions . If AB 10 and DB Ͷ , then DA ͸ ; if BC 20 and EC x , then BE x 20 = − .

Since ABC T

and DBE T

are similar triangles, create a proportion between the sides of the two triangles:

AB AD

BC CE

x

6

x 10

20

10 120

x

12

42. (H) (p. 388) Mathematics/Algebra and Functions/Manipulating Algebraic Expressions/Basic Algebraic Manipulations . Expand each of the binomials in the expression by distribution according to the FOIL method (First, Outer, Inner, Last): ( ) ( ) x x x x x x x 2 4 4 2 8 2 8 2 2 + − = − + − = − − And: ( ) ( ) x x x x x x x 4 2 2 4 8 2 8 2 2 + − = − + − = + − ‘™ǡ •—„–”ƒ…– –Š‡ •‡…‘† ‡š’”‡••‹‘ ˆ”‘ –Š‡ ϐ‹”•– ‡š’”‡••‹‘ǣ ( ) x x x x x x x 2 8 2 8 2 2 4 2 2 − − − + − = − − = − 43. (B) (p. 388) Mathematics/Geometry/Lines and Angles . The sum of the measures of the exterior angles of a polygon is ͵͸Ͳι ˆ‘” ƒŽŽ ’‘Ž›‰‘•Ǥ Š‡ •— ‘ˆ –Š‡ ‡ƒ•—”‡• ‘ˆ –Š‡ ‹–‡”‹‘” ƒ‰Ž‡• ‘ˆ ƒ ’‘Ž›‰‘…ƒ „‡ ‡š’”‡••‡† ƒ• ( ) n 180 2 c , where n is the number of sides. Therefore: ( ) n 180 2 360 − =

n = n 2 2 − = 4