algebra study guide 6

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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 Page 1 of 4 -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.
Page 2 of 4
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.
Page 3 of 4
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)
Page 4 of 4
Study Guide 6
Total Points: 50

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