Pop Quiz 9.5

1. Identify the type of function represented by each graph.

2. Match each graph with an equation at the right. 3. Identify the type of function represented by each equation.

4.

9.6 Solving Rational Equations

Solve Check your solution.

The LCD for the three denominators is Original equation Multiply each side by

24(3 –

x

)

.

1 1 1 1 6 1 Simplify.

Simplify.

Add.

Check

Original equation Simplify.

Simplify.

The solution is correct.

Answer:

The solution is

–45

.

Solve Answer:

Solve

The LCD is

Check your solution.

p

– 1 1 1 1 Original equation Multiply by the LCD,

(

p

2

– 1)

.

Distributive Property Simplify.

Simplify.

Add

(2

p

2

– 2

p

to each side.

+ 1)

or Divide each side by

3

.

Factor.

Zero Product Property Solve each equation.

Check

Original equation Simplify.

Simplify.

Original equation Simplify.

Since

p

–1

.

= –1

results in a zero in the denominator, eliminate

Answer:

The solution is

p

= 2

.

Solve Answer:

Mowing Lawns work together? Tim and Ashley mow lawns together. Tim working alone could complete the job in 4.5 hours, and Ashley could complete it alone in 3.7 hours. How long does it take to complete the job when they

In 1 hour, Tim could complete In 1 hour, Ashley could complete of the job.

of the job.

In

t

hours, Tim could complete In

t

hours, Ashley could complete or of the job.

or of the job.

Part completed by Tim plus part completed by Ashley equals entire job.

1

Solve the equation.

Original equation Multiply each side by

16.65

.

Distributive Property Simplify.

Answer:

It would take them about 2 hours working together. Simplify.

Divide each side by

8.2

.

Cleaning Libby and Nate clean together. Nate working alone could complete the job in 3 hours, and Libby could complete it alone in 5 hours. How long does it take to complete the job when they work together? Answer:

about 2 hours

Swimming Janine swims for 5 hours in a stream that has a current of 1 mile per hour. She leaves her dock and swims upstream for 2 miles and then back to her dock. What is her swimming speed in still water?

Words

The formula that relates distance, time, and rate is

Variables

Let

r

be her speed in still water. Then her speed with the current is

r +

1

and her speed against the current is

r –

1

.

Time going with the current plus time going against the current equals total time.

Equation

Solve the equation.

5

Original equation

r

+ 1 1

r

– 1 1 Multiply each side by

r

2

– 1

.

Distributive Property Simplify.

Simplify.

Subtract

4

r

from each side.

Use the Quadratic Formula to solve for

r

.

Quadratic Formula

x = r

,

a

= 5

,

b

= –4

, and

c

= –5

Simplify.

Simplify.

Use a calculator.

Answer:

Since the speed must be positive, the answer is about 1.5 miles per hour.

Swimming Lynne swims for 1 hour in a stream that has a current of 2 miles per hour. She leaves her dock and swims upstream for 3 miles and then back to her dock. What is her swimming speed in still water? Answer:

about 6.6 mph

Chapter 9 Test: Tuesday 4/5/11 (next week) HW: Begin working on the study guide