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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. |
Method I |
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C. |
Neither Method I nor Method II is correct. |
D. |
Method II |
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Hint |
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2. |
Solve the system of equations by elimination.
2x + y - z = 3
x + y + z = 5
x - 2y + z = 2
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A. |
(1, 2, 1) |
B. |
(2, 2, 1) |
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C. |
(2, 1, 2) |
D. |
(1, 1, 2) |
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Hint |
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3. |
Three planes can |
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A. |
intersect in a line. |
B. |
All of the choices are true. |
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C. |
have no points in common. |
D. |
intersect at one point. |
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Hint |
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4. |
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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5. |
Solve the system of inequalities by graphing. |
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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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6. |
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. |
(0, 0), (2, 0), and (2, 6) |
B. |
(1, -4), (3, 0), and (0, 1) |
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C. |
(-1, 1), (-1, 4), and (2, 1) |
D. |
(1, -1), (-1, 3), and (2, 1) |
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Hint |
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7. |
Use the function P(x, y) = 40x + 60y to determine how many of each item should be produced in order to maximize profit. |
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A. |
(300, 500) |
B. |
(100, 400) |
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C. |
(100, 800) |
D. |
(500, 400) |
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Hint |
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8. |
Which of the following describes the system of equations x - 3y + 2 = 0 and
2x - 6y + 4 = 0? |
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A. |
Consistent and dependent |
B. |
Consistent and independent |
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C. |
Inconsistent |
D. |
none of these |
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Hint |
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9. |
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A. |
[-1 1 18] |
B. |
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C. |
[4 5 6] |
D. |
impossible |
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Hint |
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10. |
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A. |
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B. |
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C. |
impossible |
D. |
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Hint |
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11. |
The quadrilateral with vertices A(-1,5), B(2,7), C(4,5) and D(3,3) is reflected over the line y = x . Find the image of the quadrilateral after the reflection. |
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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 value of the determinant  . |
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A. |
-25 |
B. |
-43 |
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C. |
-3 |
D. |
-29 |
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Hint |
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13. |
Solve this problem using matrix equations.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. |
3.33 L of the 0.25 solution and 6.66 L of the 0.40 solution. |
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B. |
2.5 L of the 0.25 solution and 7.5 L of the 0.40 solution. |
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C. |
4.5 L of the 0.25 solution and 5.5 L of the 0.40 solution. |
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D. |
6.66 L of the 0.25 solution and 3.33 L of the 0.40 solution. |
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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. |
alternate optimal solutions |
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C. |
infeasible |
D. |
unbounded |
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Hint |
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