9. c. Factor the numerator and denominator and
cancel like factors:
x 2
+ 2
x – 15 = (
x + 5)(
x – 3)
x 2
+ 4
x – 21 = (
x + 7)(
x – 3)
Cancel the (
x – 3) term from the numerator
and the denominator. The fraction reduces to
x x +
+
5
7
.
10. d. The midpoint of a line is equal to the average
x -coordinates and the average
y -coordinates of
the line’s endpoints:
–5
2
+
x = 2, –5 +
x = 4,
x = 9
3 +
2
y = 1, 3 +
y = 2,
y = –1
The other endpoint of this line is at (9,–1).
11. e. The number of roses, 5
x , plus the number of
tulips, 6
x , is equal to 242 total flowers: 5
x + 6
x = 242, 11
x = 242,
x = 22. There are 5(22) = 110
roses and 6(22) = 132 tulips in Lindsay’s garden.
12. c. There is an inverse relationship between the
number of people and the time needed to clean
the office. Multiply the number of people by
the hours needed to clean the office: (8)(12) =
96. Divide the total number of hours by the new
number of people, 6:
9
6
6
= 16. It takes six people
16 hours to clean the office.
– P R A C T I C E T E S T 1 – 1 9 1
13. c. Be careful not to count the same set of three
paintings more than once—order is not impor-
tant. A nine-choose-three combination is equal
to
(
(
9
3
)
)
(
(
8
2
)
)
(
(
7
1
)
)
=
50
6
4
= 84.
