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1. |
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. |
Neither Method I nor Method II is correct. |
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C. |
Method I |
D. |
Method II |
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Hint |
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2. |
If you solve the following system of equations by elimination, which of the following is the best choice for the first step?
2x + y - z = 3
x + y + z = 5
x - 2y + z = 2
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A. |
Neither method will work. |
B. |
Add the first and second equations to eliminate the z variable. |
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C. |
Both methods will work. |
D. |
Subtract the second and third equation to eliminate the z variable. |
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Hint |
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3. |
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A. |
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B. |
The product doesn't exist. |
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C. |
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D. |
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Hint |
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4. |
Suppose a figure is animated to spin around a certain point. If the image has key points as A(2, 1), B(3, 5) and C(6, 2), and the rotation is about the origin, find the location of these points at a 270° counterclockwise rotation. |
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A. |
A'(1, -2), B'(5, -3), C'(2, -6) |
B. |
A'(-1, 2), B'(-5, 3), C'(-2, 6) |
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C. |
A'(-2, -1), B'(-3, -5),
C'(-6, -2) |
D. |
A'(1, -2), B'(-5, 3), C'(-2, 6) |
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Hint |
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5. |
Find the image of  after Rot90 · Ry-axis if the vertices are
A(2, -3), B(6, -3), and C(2, 5). |
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A. |
A'(3, -2), B'(3, -6),
C'(-5, -2) |
B. |
A'(-3, 2), B'(-3, 6),
C'(5, 2) |
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C. |
A'(-3, -2), B'(-3, -6),
C'(-5, -2) |
D. |
A'(3, 2), B'(3, 6), C'(5, -2) |
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Hint |
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6. |
Find the inverse of  . |
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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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7. |
Which of the following is a graph of the inequalities
l + g > 100 and l > 70? |
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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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8. |
The graph of the system of inequalities is shown below. Name the coordinates of the vertices of the polygonal set. |
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A. |
(1, -4), (3, 0), and (0, 1) |
B. |
(-1, 1), (-1, 4), and (2, 1) |
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C. |
(0, 0), (2, 0), and (2, 6) |
D. |
(1, -1), (-1, 3), and (2, 1) |
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Hint |
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9. |
Suppose a lumber mill can turn out up to 900 units of product each week. The mill must produce at least 100 units of lumber and 400 units of plywood. Write the constraints as a system of inequalities where x = the number of units of lumber and y = the number of units of plywood. |
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A. |
x  100, y  400, and
x + y 900 |
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B. |
x 100, y 400, and
x + y 900 |
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C. |
x 100, y 400, and
x + y 900 |
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D. |
x 100, y 400, and
x + y 900 |
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Hint |
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10. |
Choose the best method to solve the system of equations 4x + y = 6
and 2x - y = 10. |
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A. |
Graphing |
B. |
Substitution |
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C. |
Eliminate x |
D. |
Eliminate y |
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Hint |
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11. |
If you are solving this system of equations by elimination, which of the following is the best choice for the first step? 2x + 3y - z = 4
-x + y + 2z = 3
3x + y + z = 1 |
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A. |
both methods are correct |
B. |
Method I |
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C. |
Method II |
D. |
neither method is correct. |
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Hint |
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12. |
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A. |
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B. |
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C. |
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D. |
impossible |
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Hint |
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13. |
Find the inverse of  . |
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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. |
Find the maximum value of f(x, y) = 2x + y - 4 for the system of inequalities:
y -3x + 1
y  x - 4
x 0
y 0 |
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A. |
2 |
B. |
unbounded |
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C. |
alternate optimal solutions |
D. |
infeasible |
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Hint |
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