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1. |
Triangle FGH has vertices F(12, 6), G(8, 1), and H(-4, 4). If the triangle is reduced so that the resulting perimeter is half the original perimeter, what are the coordinates of F'? |
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A. |
(-2, -2) |
B. |
(4, 2) |
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C. |
(6, 3) |
D. |
(6, 6) |
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Hint |
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2. |
Triangle PQR with vertices P(-8, 9), Q(-3, -1), and R(2, 5) is translated so that P' is at (-12, 0). Find the translation matrix. |
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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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3. |
Find  |
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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. |
The product gives the coordinates of two points on line AB that has been rotated 90° counterclockwise about the origin. Name the coordinates of A' and B'. |
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A. |
A'(1, 1), B'(-1, -3) |
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B. |
A'(-1, 1), B'(1, -3) |
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C. |
A'(1, -3), B'(1, 1) |
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D. |
A'(-1, -3), B'(1, 1) |
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Hint |
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5. |
For the determinant , which is the minor of -4? |
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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. |
Find the determinant of  |
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A. |
-21 |
B. |
0 |
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C. |
-11 |
D. |
-16 |
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Hint |
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7. |
Does the inverse of exist? If it does not exist, explain why not. |
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A. |
No; the elements of the principal diagonal are not 1. |
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B. |
No; the matrix is not square. |
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C. |
No; the determinant equals 0. |
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D. |
Yes |
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Hint |
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8. |
What are the dimensions of matrix A if  |
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A. |
4 × 4 |
B. |
4 × 3 |
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C. |
3 × 4 |
D. |
3 × 3 |
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Hint |
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9. |
Which of the following is an example of a column matrix? |
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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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10. |
Find A – B if and  |
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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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11. |
State whether the product of A3 × 4 and B3 × 4 is defined, and if it is defined, state the dimensions. |
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A. |
defined, 3 × 4 |
B. |
defined, 9 × 16 |
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C. |
undefined |
D. |
defined, 4 × 3 |
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Hint |
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12. |
Solve 2.4x + 1.7y = 8.2, 3.8x – 0.8y = 5.3. Round to the nearest hundredth. |
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A. |
(–1.86, 2.20) |
B. |
(–1.86, –2.20) |
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C. |
(1.86, –2.20) |
D. |
(1.86, 2.20) |
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Hint |
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13. |
Two sides of an angle are contained in lines whose equations are 6x + 4y = 15 and 7x – 9y = 3. Find the coordinates of the vertex of the angle. Round to the nearest hundredth. |
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A. |
(1.79, 1.06) |
B. |
(–1.79, 1.06) |
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C. |
(147, 87) |
D. |
(–147, –87) |
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Hint |
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14. |
Determine whether the pair of matrices are inverses. |
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A. |
no, because A · B I |
B. |
yes, because each entry in the second matrix is the reciprocal of its corresponding entry in the first matrix. |
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C. |
no, because fractions cannot be a part of an inverse |
D. |
yes, because A · B = I. |
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Hint |
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15. |
Which of the following is a matrix equation for the system 5x – 3y =11, –3x + 2y = 7? |
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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. |
Solve the system of equations 7x – 14y =4, 3x – 6y =17. |
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A. |
(3, –2) |
B. |
no unique solution |
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C. |
infinite solutions |
D. |
(2, 1) |
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Hint |
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