Victory for the ACT Student Text 15e

V ICTORY P RACTICE T EST A NSWERS AND E XPLANATIONS • 459

The median to the hypotenuse of a right

30. (H) (p. 385) Mathematics/Geometry/Triangles/Properties of Triangles . triangle is equal in length to half the hypotenuse ( BE AE CE ):

31. (E) (p. 385) Mathematics/Number and Quantity/Rates and Proportions . Since y

varies directly as x

, x y

.

y

Therefore:

1

2

x

1

2

y

10

1

1

5

y 2

( ) ( ) 10 5 2

y

50 2

y

25

Cancel like terms in the numerator

ƒ† †‡‘‹ƒ–‘” —–‹Ž –Š‡ ‰‹˜‡ ‡š’”‡••‹‘ ‹• •‹’Ž‹ϐ‹‡†ǣ 1 = = − ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 5 4 3 2 1 1 2 3 4 5 1 1 1 1 1 − − − − − − − − − −

32. (G) (p. 385) Mathematics/Number and Quantity/Basic Arithmetic Manipulations .

33. (B) (p. 386) Mathematics/Number and Quantity/Properties of Numbers . Š‡ ˆƒ…–‘”• ‘ˆ ͵͸ ƒ”‡ǣ ͳ ƒ† ͵͸ǡ ʹ ƒ† ͳͺǡ ͵ ƒ† ͳʹǡ Ͷ ƒ† ͻǡ ͸ ƒ† ͸Ǥ ˆ –Š‘•‡ ˆƒ…–‘”•ǡ ‘Ž› ʹ ƒ† ͵ ƒ”‡ ’”‹‡ —„‡”•Ǥ Š‡”‡ˆ‘”‡ǡ ͵͸ Šƒ• ‘Ž› –™‘ ’‘•‹–‹˜‡ ’”‹‡ factors. 34. (H) (p. 386) Mathematics/Geometry/Triangles/Properties of Triangles and Lines and Angles . An isosceles triangle has two equal sides and two equal base angles:

x x + + =

50

180

x x 50 2 180 2 130 + = =

=

x

65

35. (B) (p. 386) Mathematics/Statistics and Probability/Measures of Center . The median is the “middle” data element ™Š‡ –Š‡ †ƒ–ƒ ƒ”‡ ƒ””ƒ‰‡† ‹ —‡”‹…ƒŽ ‘”†‡”Ǥ Š‡”‡ ƒ”‡ ͳͷ –‘–ƒŽ –‡”•ǡ •‘ –Š‡ ‡†‹ƒ ‹• –Š‡ ͺ–Š –‡”Ǥ ‹…‡ –Š‡ Š‹‰Š‡•– •…‘”‡ ‹ –Š‡ –ƒ„Ž‡ ‹• ͷͲ ƒ† –Š‡”‡ ƒ”‡ ͹ •…‘”‡• ‘ˆ ͷͲǡ –Š‡ ‡š– Ž‘™‡•– •…‘”‡ ™‹ŽŽ „‡ –Š‡ ͺ–Š –‡” ȋ…‘—–‹‰ –‡”• ˆ”‘ ‰”‡ƒ–‡•– –‘ Ž‡ƒ•–Ȍ ƒ† –Š‡ ‡†‹ƒǣ ͵ͲǤ