Intermediate Algebra (11th edition)

CHAPTER 7 Test 423

Solve each problem.

59.The strength of a contact lens is given in units called diopters and also in millimeters

of arc. As the diopters increase, the millimeters of arc decrease. The rational function

defined by

relates the arc measurement to the diopter measurement x. (Source:Bausch and

Lomb.)

(a)What arc measurement will correspond to 40.5-diopter lenses?

(b)A lens with an arc measurement of 7.51 mm will provide what diopter strength?

60.The hot-water tap can fill a tub in 20 min. The cold-water tap takes 15 min to fill the

tub. How long would it take to fill the tub with both taps open?

61.At a certain gasoline station, 3 gal of unleaded gasoline cost $8.37. How much would

13 gal of the same gasoline cost?

62.The area of a triangle varies jointly as the lengths of the base and height. A triangle

with base 10 ft and height 4 ft has area Find the area of a triangle with base

and height 8 ft.

63.If Dr. Dawson rides his bike to his office, he averages 12 mph. If he drives his car, he

averages 36 mph. His time driving is hr less than his time riding his bike. How far is

his office from home?

64.A private plane traveled from San Francisco to a secret rendezvous. It averaged 200 mph.

On the return trip, the average rate was 300 mph. If the total traveling time was 4 hr,

how far from San Francisco was the secret rendezvous?

65.Johnny averages 30 mph when he drives on the old highway to his favorite fishing hole,

and he averages 50 mph when he takes the interstate. If both routes are the same length,

and he saves 2 hr by traveling on the interstate, how far away is the fishing hole?

1

4

20 ft^2. 3 ft

ƒ 1 x 2

ƒ 1 x 2 =

337

x

1.Find all real numbers excluded from the domain of Then give the

domain, using set-builder notation.

2.Write in lowest terms.

Multiply or divide.

3. 4.

5. 6.

7.Find the least common denominator for the following group of denominators:

t^2 +t-6, t^2 + 3 t, t^2.

x^2 - 9

x^3 + 3 x^2

,

x^2 +x- 12

x^3 + 9 x^2 + 20 x

3 - t

5

,

t- 3

10

y^2 - 16

y^2 - 25

#y

(^2) + 2 y- 15
y^2 - 7 y+ 12
1 x+ 322
4
#^6
2 x+ 6
6 x^2 - 13 x- 5
9 x^3 - x
ƒ 1 x 2 =
x+ 3
3 x^2 + 2 x- 8

.

TEST

CHAPTER 7

View the complete solutions to
all Chapter Test exercises on
the Video Resources on DVD.

Step-by-step test solutions are found on the Chapter Test Prep Videos

available via the Video Resources on DVD, in , or on

VIDEOS (search “LialIntermediateAlg”).

CHAPTER