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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 x = 2y 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 2x = y 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 solve the following system of equations by substitution, which statement is true?
x = z x - 2y + z = 6 2x + y - 2z = 1
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A. |
Both methods will work. |
B. |
Neither method will work. |
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C. |
You can substitute x for z into the second and third equations. |
D. |
You can substitute z for x into the second and third equations. |
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Hint |
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3. |
Determine the slant asymptote for f(x) = . |
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A. |
y = 3x + 2 |
B. |
y = 2x + 3 |
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C. |
y = 3x - 2 |
D. |
y = -2x +3 |
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Hint |
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4. |
State the number of complex roots of the equation x4 - 3x2 - 4 = 0. |
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A. |
1 |
B. |
4 |
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C. |
2 |
D. |
3 |
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Hint |
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5. |
Find the discriminant of x2 - 2x + 20 = 0. |
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A. |
-76 |
B. |
-72 |
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C. |
76 |
D. |
72 |
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Hint |
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6. |
Approximate the real zero(s) of f(x) = x3 - 2x2 + 5x - 5 to the nearest tenth. |
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A. |
1.2 |
B. |
1.4 |
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C. |
1.4, 2.1, and 3.2 |
D. |
1.6 |
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Hint |
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7. |
A regular pentagon is inscribed in a circle with diameter 20 centimeters. The apothem of a regular polygon is the measure of a line segment from the center of the polygon to the midpint of one of its sides. Find the apothem of the pentagon. |
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A. |
about 8.09 cm |
B. |
about 5.30 cm |
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C. |
about 11.79 cm |
D. |
about 18.87 cm |
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Hint |
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8. |
Find the area of if d =14.2, D = 33.6°, and E = 15.2°. |
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A. |
about 71.9 square units |
B. |
about 46.5 square units |
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C. |
about 62.1 square units |
D. |
about 35.9 square units |
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Hint |
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9. |
Solve 2 cos + 1 < 0 for 0 < 2 . |
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A. |
< < 2 |
B. |
< <  |
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C. |
0 < or
< < 2 |
D. |
< <  |
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Hint |
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10. |
Consider the equation -x + 2y - 5 = 0. Find the length of the normal and the angle it makes with the positive x-axis. |
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A. |
; 243° |
B. |
; 63° |
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C. |
; 117° |
D. |
; 297° |
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Hint |
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11. |
Find an equation of the line that bisects the acute angles formed by the lines with equations 3x + 4y = 8 and 5x + 12y = 16. |
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A. |
14x + 8y - 23 = 0 |
B. |
8x + 14y - 23 = 0 |
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C. |
14x + 8y + 23 = 0 |
D. |
8x + 14y + 23 = 0 |
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Hint |
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12. |
What is the distance from the origin to the graph of 3x + 4y + 12 = 0? |
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A. |
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B. |
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C. |
12 |
D. |
5 |
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Hint |
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13. |
A ship leaving port sails for 100 miles in a direction 40° north of due east. Find the magnitude of the vertical and horizontal components. |
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A. |
about 87 miles; about 50 miles |
B. |
about 50 miles; about 87 miles |
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C. |
about 77 miles; about 84 miles |
D. |
about 64 miles; about 77 miles |
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Hint |
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14. |
Write the polar equation in rectangular form. |
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A. |
x + y = 2x2 |
B. |
x + y = 4x |
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C. |
x2 + y2 = 4x |
D. |
x2 + y2 = 2x |
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Hint |
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15. |
Solve the equation x3 - 27 = 0. |
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A. |
3, ,  |
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B. |
3, ,  |
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C. |
3, ,  |
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D. |
3, ,  |
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Hint |
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16. |
A bank charges a $10 fee if the account balance is less than $200. If the balance is in between $200 and $500 there is a $5 fee. If at least $500 is in the account, there is no fee.Graph the fee schedule for different account balances. |
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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. |
Solve the system of inequalities by graphing. 2x + y 3 2x + y -2 y 4 x < 1 |
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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. |
Describe the end behavior of the function: f(x) = x4 - x3 + x2 + x - 1 |
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A. |
f(x) as x , f(x) as x  |
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B. |
f(x) as x , f(x) as x  |
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C. |
f(x) as x , f(x) as x  |
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D. |
f(x) as x , f(x) as x  |
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Hint |
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19. |
The function f(x) = |x - 4| + 2 has a critical point at x = 4. Determine if this is the location of a maximum, a minimum or a point of inflection. |
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A. |
There is a maximum at (4,2) |
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B. |
There is a point of inflection at (4,2) |
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C. |
none of these |
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D. |
There is a minimum at (4,2) |
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Hint |
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20. |
What is the complex conjugate of a - bi, if a and b are real numbers? |
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A. |
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B. |
a - bi |
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C. |
a2 + b2 - abi |
D. |
a + bi |
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Hint |
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