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College Algebra

Name:

Study Guide 6

Class:

Due Date:

Score:

No Work ⇔ No Points

Use Pencil Only ⇔ Be Neat & Organized

1. (3 points) Solve (x + 1)(x − 2) > 0, graph your final answer and in interval notation.

1.

-4

-3

-2

2. (3 points) Solve

-1

0

1

2

3

4

x−2

≤ 0, graph your final answer and in interval notation.

x+1

2.

-4

-3

-2

3. (4 points) Solve

-1

0

1

2

3

4

x2 − 2x − 8

< 0, graph your final answer and in interval notation.
x2 − 9
3.
-4
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-3
-2
-1
0
1
Study Guide 6
2
3
4
5
6
Total Points: 50
7
4. (4 points) Graph and shade the solution for the system given below in the same
coordinate system.
What do you conclude about the solution for this system of inequalities?
y
2
y > x+2

3

y ≤ 2x − 2

3

x

5. (4 points) Find a system of linear inequalities that satisfies the following shaded

region.

y

x

5.

6. (4 points) y varies inversely as cube root of x.

y is 5 when x is 8. Find y when x is 1000.

6.

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Study Guide 6

Total Points: 50

7. (4 points) y varies directly as fourth power of x.

y is 1250 when x is 5. Find y when x is 4.

7.

8. (5 points) The intensity of a light source varies inversely as the square of its

distance from its source. If the intensity is 30 lumens at the distance of 2 ft, Find

its intensity when the distance is 4 feet.

8.

9. (4 points) Assume that y varies directly as z and inversely as the cube of x. y is

3 when z is 4 and x is 2. Find y when z is 2 and x is 4.

9.

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Study Guide 6

Total Points: 50

10. (4 points) The stopping distance of a car is directly proportional to the square

root of its speed. If a car traveling at 36 mph has a stopping distance of 120 ft,

Find the stopping distance of a car that is traveling at 64 mph. Round your answer

to a whole number.

10.

11. (5 points) Assume that z varies directly as the square root of the sum of x2 and

y 2 . z is 10 when x is 4 and y is 3. Find z when x is 6 and y is 8.

11.

12. Algebra Review Problems:

(a) (3 points) Solve x2 + 4x − 21 = 0 by using the quadratic formula.

(a)

2

(b) (3 points) Solve 2x − 7x + 5 = 0 by using the quadratic formula.

(b)

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Study Guide 6

Total Points: 50