Victory for the ACT Student Text 15e

R EVIEW • 275

18. PTS is an equilateral triangle. What is the degree measure of TRS + ? F. 60 G. 75 H. 80 J. 90 K. Cannot be determined from the given information 19. A line segment in the ( x , y ) coordinate plane has endpoints ( , ) 4 2 and ( , )6 7 . What is the midpoint of the line segment? A. (2, 5) B. (10, 9) C. ( , ) 10 9 D. (1, 2.5) E. (1.5, 5) 20. Paul can paint a fence in 2 hours and Fred can paint the same fence in 3 hours. If Paul and Fred work together, how many hours will it take them to paint the fence? F. 5 G. 2 2 1 H. 1 5 1 J. 1 K. 6 5  –Š‡ ϐ‹‰—”‡ „‡Ž‘™ǡ PQRS is a square and

A motorist drives 60 miles to her destination at an average speed of 40 miles per hour and makes the return trip at an average speed of 30 miles per hour. What is her average speed, in miles per hour, for the entire trip? A. 17 B. 34 7 2 C. 35 D. 43 3 1 E. 70

21.

If log value of log F. xy 2 G. x y 2 H. x + 2 y J. a b 2 K. a + 2 b a x 3

and log ab 2 ^ h

, what is the

?

22.

b y

3

3

Throwback to Math Class Memorize these properties: ( ) log a + =

A sphere with a diameter of 18 feet sits inside of a cylinder. It is tangent to the top and bottom of the cylinder and has the same diameter as the cylinder. What is the volume of the space outside of the sphere but inside of the cylinder? A. 486 B. 486 r C. 972 r D. 1, 458 r E. 2, 430 r Which of the following values of x •ƒ–‹•ϐ‹‡• the equation log x 3 6 ?

23.

y

x y a x =

=

( ) ( ) xy x

log

a a

+

y

log

log

( )

b

x

( ) e o Be careful: a common mistake students make is assuming that ( ) ( ) ( ) . log log log x y x y + = + This is incorrect! ( ) log log log y x y a a b = − a a b

24.

F. 9 G. 18 H. 36 J. 216 K. 729