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1. |
The compound inequality 300 < x + y < 1200 and x = 2y is shown in the graph below. List the possibilities of Bobcats and Lions produced to meet the imposed conditions. |
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A. |
All points on the segment of the line 2x = 2y whose endpoints are (200, 100) and (800, 400) and whose coordinates are integers. |
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B. |
All points on the segment of the line 2x = y whose endpoints are (100, 200) and (400, 800) and whose coordinates are integers. |
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C. |
All points on the segment of the line x = 2y whose endpoints are (200, 100) and (800, 400) and whose coordinates are integers. |
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D. |
All points on the segment of the line x = 2y whose endpoints are (100, 200) and (400, 800) and whose coordinates are integers. |
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Hint |
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2. |
If you use the substitution method to solve the system of equations 3x - 2y = 4 and x + y = 5, which of the following would be the best method?
Method I: Solve the second equation for x, and substitute 5 - y for x into the first equation.
Method II: Solve the second equation for y, and substitute 5 - x for y into the first equation.
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A. |
Both Method I and Method II are correct. |
B. |
Method I |
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C. |
Method II |
D. |
Neither Method I nor Method II is correct. |
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Hint |
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3. |
Suppose the triangle ABC with vertices A(1, 2), B(4, 3) and C(-1, 5) is translated 2 units right and 3 units down. Use the translation matrix to find the vertices for A'B'C', the translated image of the triangle. |
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A. |
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B. |
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C. |
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D. |
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Hint |
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4. |
Divide x4 + 2x2 - 1 by x - 1 using synthetic division. The result of synthetic division is ____. |
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A. |
1 3 1 3 | 2 |
B. |
1 1 3 3 | -2 |
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C. |
1 3 1 3 | -2 |
D. |
1 1 3 3 | 2 |
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Hint |
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5. |
Approximate the real zeros of the function f(x) = 2x2 + 4x + 1 to the nearest tenth. |
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A. |
-1.8 and -0.4 |
B. |
-1.8 and -0.2 |
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C. |
-1.6 and -0.2 |
D. |
-1.7 and -0.3 |
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Hint |
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6. |
Choose the angle measure represented by 5.2 rotations counterclockwise. |
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A. |
-1872° |
B. |
-936° |
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C. |
936° |
D. |
1872° |
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Hint |
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7. |
The terminal side of one angle in standard position contains the point with coordinates (3, -2). The terminal side of another angle in standard position contains the point with coordinates (-3, 2). Compare the tangents of these angles. |
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A. |
One does not exist. |
B. |
They are equal. |
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C. |
They are not equal. |
D. |
One is twice the other. |
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Hint |
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8. |
Given and a = 5, b = 2 and A = 115°, find B. |
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A. |
14.6° |
B. |
22.5° |
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C. |
21.3° |
D. |
31.7° |
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Hint |
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9. |
Find cos (Tan-11 - Sin-11). |
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A. |
- |
B. |
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C. |
- |
D. |
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Hint |
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10. |
Simplify cos x tan x. |
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A. |
csc x |
B. |
sin x |
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C. |
cos x |
D. |
1 |
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Hint |
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11. |
Find the magnitude of the vector . |
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A. |
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B. |
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C. |
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D. |
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Hint |
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12. |
Find the magnitude of for T(4, 0, -6) and M(5, -1, 0). |
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A. |
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B. |
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C. |
6 |
D. |
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Hint |
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13. |
Write a matrix that will translate a triangular prism using the vector . |
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A. |
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B. |
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C. |
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D. |
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Hint |
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14. |
What type of relationship does the scatter plot suggest? |
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A. |
a linear relationship with a negative correlation |
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B. |
a linear relationship with a positive correlation |
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C. |
no linear relationship |
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D. |
no correlation |
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Hint |
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15. |
Set up a matrix equation for this chemistry problem. How many liters of 0.25 solution and 0.40 solution should be combined to make 10 liters of 0.35 solution? |
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A. |
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B. |
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C. |
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D. |
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Hint |
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16. |
Sketch the graph of the function f(x) = (x + 1)3 + 2. |
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A. |
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B. |
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C. |
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D. |
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Hint |
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17. |
Which is the graph of y > (x - 3)2? |
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A. |
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B. |
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C. |
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D. |
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Hint |
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18. |
If y varies inversely as the cube of x and y = 8 when x = 2, find x when y = 1. |
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A. |
x = 4 |
B. |
x = 8 |
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C. |
x = 2 |
D. |
x = 1 |
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Hint |
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19. |
Simplify the expression sin x + 4 cos x + 2 sin -x - 2 cos -x |
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A. |
0 |
B. |
3 sin x + 2 cos x |
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C. |
2 cos x - sin x |
D. |
1 |
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Hint |
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20. |
If a rectangular prism represented by the vertex matrix below is translated using the vector , find the vertex matrix for the translated image.
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A. |
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B. |
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C. |
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D. |
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Hint |
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