algebra 40
alehea1
algebra_no.7.docx|
1 of 40 |
2.5 Points |
Use Cramer’s Rule to solve the following system.
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x + 2y = 3 3x - 4y = 4 |
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A. {(3, 1/5)} |
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B. {(5, 1/3)} |
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C. {(1, 1/2)} |
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D. {(2, 1/2)} |
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2 of 40 |
2.5 Points |
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.
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x + y - z = -2 2x - y + z = 5 -x + 2y + 2z = 1 |
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A. {(0, -1, -2)} |
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B. {(2, 0, 2)} |
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C. {(1, -1, 2)} |
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D. {(4, -1, 3)} |
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3 of 40 |
2.5 Points |
Use Cramer’s Rule to solve the following system.
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2x = 3y + 2 5x = 51 - 4y |
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A. {(8, 2)} |
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B. {(3, -4)} |
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C. {(2, 5)} |
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D. {(7, 4)} |
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4 of 40 |
2.5 Points |
Use Cramer’s Rule to solve the following system.
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4x - 5y = 17 2x + 3y = 3 |
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A. {(3, -1)} |
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B. {(2, -1)} |
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C. {(3, -7)} |
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D. {(2, 0)} |
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5 of 40 |
2.5 Points |
Use Cramer’s Rule to solve the following system.
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4x - 5y - 6z = -1 x - 2y - 5z = -12 2x - y = 7 |
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A. {(2, -3, 4)} |
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B. {(5, -7, 4)} |
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C. {(3, -3, 3)} |
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D. {(1, -3, 5)} |
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6 of 40 |
2.5 Points |
Use Cramer’s Rule to solve the following system.
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3x - 4y = 4 2x + 2y = 12 |
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A. {(3, 1)} |
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B. {(4, 2)} |
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C. {(5, 1)} |
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D. {(2, 1)} |
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7 of 40 |
2.5 Points |
Use Cramer’s Rule to solve the following system.
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x + y + z = 0 2x - y + z = -1 -x + 3y - z = -8 |
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A. {(-1, -3, 7)} |
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B. {(-6, -2, 4)} |
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C. {(-5, -2, 7)} |
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D. {(-4, -1, 7)} |
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8 of 40 |
2.5 Points |
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.
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3x1 + 5x2 - 8x3 + 5x4 = -8 x1 + 2x2 - 3x3 + x4 = -7 2x1 + 3x2 - 7x3 + 3x4 = -11 4x1 + 8x2 - 10x3+ 7x4 = -10 |
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A. {(1, -5, 3, 4)} |
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B. {(2, -1, 3, 5)} |
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C. {(1, 2, 3, 3)} |
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D. {(2, -2, 3, 4)} |
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9 of 40 |
2.5 Points |
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.
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x + y + z = 4 x - y - z = 0 x - y + z = 2 |
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A. {(3, 1, 0)} |
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B. {(2, 1, 1)} |
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C. {(4, 2, 1)} |
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D. {(2, 1, 0)} |
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10 of 40 |
2.5 Points |
Solve the system using the inverse that is given for the coefficient matrix.
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2x + 6y + 6z = 8 2x + 7y + 6z =10 2x + 7y + 7z = 9 |
The inverse of:
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2 2 2 |
6 7 7 |
6 6 7 |
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is
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7/2 -1 0 |
0 1 -1 |
-3 0 1 |
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A. {(1, 2, -1)} |
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B. {(2, 1, -1)} |
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C. {(1, 2, 0)} |
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D. {(1, 3, -1)} |
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11 of 40 |
2.5 Points |
Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.
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2w + x - y = 3 w - 3x + 2y = -4 3w + x - 3y + z = 1 w + 2x - 4y - z = -2 |
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A. {(1, 3, 2, 1)} |
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B. {(1, 4, 3, -1)} |
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C. {(1, 5, 1, 1)} |
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D. {(-1, 2, -2, 1)} |
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12 of 40 |
2.5 Points |
Use Cramer’s Rule to solve the following system.
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x + y = 7 x - y = 3 |
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A. {(7, 2)} |
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B. {(8, -2)} |
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C. {(5, 2)} |
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D. {(9, 3)} |
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13 of 40 |
2.5 Points |
Use Gaussian elimination to find the complete solution to each system.
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x1 + 4x2 + 3x3 - 6x4 = 5 x1 + 3x2 + x3 - 4x4 = 3 2x1 + 8x2 + 7x3 - 5x4 = 11 2x1 + 5x2 - 6x4 = 4 |
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A. {(-47t + 4, 12t, 7t + 1, t)} |
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B. {(-37t + 2, 16t, -7t + 1, t)} |
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C. {(-35t + 3, 16t, -6t + 1, t)} |
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D. {(-27t + 2, 17t, -7t + 1, t)} |
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14 of 40 |
2.5 Points |
Find values for x, y, and z so that the following matrices are equal.
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2x z |
y + 7 4 |
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= |
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-10 6 |
13 4 |
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A. x = -7; y = 6; z = 2 |
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B. x = 5; y = -6; z = 2 |
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C. x = -3; y = 4; z = 6 |
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D. x = -5; y = 6; z = 6 |
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15 of 40 |
2.5 Points |
Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.
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5x + 8y - 6z = 14 3x + 4y - 2z = 8 x + 2y - 2z = 3 |
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A. {(-4t + 2, 2t + 1/2, t)} |
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B. {(-3t + 1, 5t + 1/3, t)} |
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C. {(2t + -2, t + 1/2, t)} |
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D. {(-2t + 2, 2t + 1/2, t)} |
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16 of 40 |
2.5 Points |
If AB = -BA, then A and B are said to be anticommutative.
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Are A = |
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0 1 |
-1 0 |
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and B = |
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1 0 |
0 -1 |
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anticommutative? |
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A. AB = -AB so they are not anticommutative. |
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B. AB = BA so they are anticommutative. |
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C. BA = -BA so they are not anticommutative. |
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D. AB = -BA so they are anticommutative |
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17 of 40 |
2.5 Points |
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.
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2x - y - z = 4 x + y - 5z = -4 x - 2y = 4 |
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A. {(2, -1, 1)} |
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B. {(-2, -3, 0)} |
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C. {(3, -1, 2)} |
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D. {(3, -1, 0)} |
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18 of 40 |
2.5 Points |
Use Gauss-Jordan elimination to solve the system.
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-x - y - z = 1 4x + 5y = 0 y - 3z = 0 |
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A. {(14, -10, -3)} |
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B. {(10, -2, -6)} |
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C. {(15, -12, -4)} |
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D. {(11, -13, -4)} |
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19 of 40 |
2.5 Points |
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.
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x - 2y + z = 0 y - 3z = -1 2y + 5z = -2 |
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A. {(-1, -2, 0)} |
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B. {(-2, -1, 0)} |
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C. {(-5, -3, 0)} |
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D. {(-3, 0, 0)} |
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20 of 40 |
2.5 Points |
Find the products AB and BA to determine whether B is the multiplicative inverse of A.
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A = |
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0 0 1 |
1 0 0 |
0 1 0 |
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B = |
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0 1 0 |
0 0 1 |
1 0 0 |
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A. AB = I; BA = I3; B = A |
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B. AB = I3; BA = I3; B = A-1 |
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C. AB = I; AB = I3; B = A-1 |
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D. AB = I3; BA = I3; A = B-1 |
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21 of 40 |
2.5 Points |
Find the standard form of the equation of each hyperbola satisfying the given conditions. Endpoints of transverse axis: (0, -6), (0, 6) Asymptote: y = 2x
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A. y2/6 - x2/9 = 1 |
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B. y2/36 - x2/9 = 1 |
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C. y2/37 - x2/27 = 1 |
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D. y2/9 - x2/6 = 1 |
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22 of 40 |
2.5 Points |
Convert each equation to standard form by completing the square on x or y. Then find the vertex, focus, and directrix of the parabola. y2 - 2y + 12x - 35 = 0
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A. (y - 2)2 = -10(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 9 |
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B. (y - 1)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 6 |
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C. (y - 5)2 = -14(x - 3); vertex: (2, 1); focus: (0, 1); directrix: x = 6 |
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D. (y - 2)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 8 |
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23 of 40 |
2.5 Points |
Convert each equation to standard form by completing the square on x and y. 9x2 + 16y2 - 18x + 64y - 71 = 0
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A. (x - 1)2/9 + (y + 2)2/18 = 1 |
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B. (x - 1)2/18 + (y + 2)2/71 = 1 |
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C. (x - 1)2/16 + (y + 2)2/9 = 1 |
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D. (x - 1)2/64 + (y + 2)2/9 = 1 |
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24 of 40 |
2.5 Points |
Find the focus and directrix of each parabola with the given equation. y2 = 4x
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A. Focus: (2, 0); directrix: x = -1 |
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B. Focus: (3, 0); directrix: x = -1 |
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C. Focus: (5, 0); directrix: x = -1 |
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D. Focus: (1, 0); directrix: x = -1 |
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Reset Selection Mark for Review What's This?
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25 of 40 |
2.5 Points |
Find the vertex, focus, and directrix of each parabola with the given equation. (y + 1)2 = -8x
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A. Vertex: (0, -1); focus: (-2, -1); directrix: x = 2 |
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B. Vertex: (0, -1); focus: (-3, -1); directrix: x = 3 |
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C. Vertex: (0, -1); focus: (2, -1); directrix: x = 1 |
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D. Vertex: (0, -3); focus: (-2, -1); directrix: x = 5 |
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26 of 40 |
2.5 Points |
Find the standard form of the equation of the ellipse satisfying the given conditions. Major axis vertical with length = 10 Length of minor axis = 4 Center: (-2, 3)
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A. (x + 2)2/4 + (y - 3)2/25 = 1 |
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B. (x + 4)2/4 + (y - 2)2/25 = 1 |
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C. (x + 3)2/4 + (y - 2)2/25 = 1 |
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D. (x + 5)2/4 + (y - 2)2/25 = 1 |
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27 of 40 |
2.5 Points |
Find the vertices and locate the foci of each hyperbola with the given equation. x2/4 - y2/1 =1
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A. Vertices at (2, 0) and (-2, 0); foci at (√5, 0) and (-√5, 0) |
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B. Vertices at (3, 0) and (-3 0); foci at (12, 0) and (-12, 0) |
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C. Vertices at (4, 0) and (-4, 0); foci at (16, 0) and (-16, 0) |
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D. Vertices at (5 |
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28 of 40 |
2.5 Points |
Locate the foci of the ellipse of the following equation. 25x2 + 4y2 = 100
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A. Foci at (1, -√11) and (1, √11) |
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B. Foci at (0, -√25) and (0, √25) |
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C. Foci at (0, -√22) and (0, √22) |
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D. Foci at (0, -√21) and (0, √21) |
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29 of 40 |
2.5 Points |
Find the vertex, focus, and directrix of each parabola with the given equation. (x - 2)2 = 8(y - 1)
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A. Vertex: (3, 1); focus: (1, 3); directrix: y = -1 |
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B. Vertex: (2, 1); focus: (2, 3); directrix: y = -1 |
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C. Vertex: (1, 1); focus: (2, 4); directrix: y = -1 |
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D. Vertex: (2, 3); |
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30 of 40 |
2.5 Points |
Convert each equation to standard form by completing the square on x and y. 4x2 + y2 + 16x - 6y - 39 = 0
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A. (x + 2)2/4 + (y - 3)2/39 = 1 |
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B. (x + 2)2/39 + (y - 4)2/64 = 1 |
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C. (x + 2)2/16 + (y - 3)2/64 = 1 |
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D. (x + 2)2/6 + (y - 3)2/4 = 1 |
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31 of 40 |
2.5 Points |
Convert each equation to standard form by completing the square on x or y. Then find the vertex, focus, and directrix of the parabola. x2 - 2x - 4y + 9 = 0
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A. (x - 4)2 = 4(y - 2); vertex: (1, 4); focus: (1, 3) ; directrix: y = 1 |
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B. (x - 2)2 = 4(y - 3); vertex: (1, 2); focus: (1, 3) ; directrix: y = 3 |
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C. (x - 1)2 = 4(y - 2); vertex: (1, 2); focus: (1, 3) ; directrix: y = 1 |
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D. (x - 1)2 = 2(y - 2) |
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32 of 40 |
2.5 Points |
Find the vertices and locate the foci of each hyperbola with the given equation. y2/4 - x2/1 = 1
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A. Vertices at (0, 5) and (0, -5); foci at (0, 14) and (0, -14) |
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B. Vertices at (0, 6) and (0, -6); foci at (0, 13) and (0, -13) |
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C. Vertices at (0, 2) and (0, -2); foci at (0, √5) and (0, -√5) |
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D. Vertices at (0, 1) and (0, -1); foci at (0, 12) and (0, -12) |
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33 of 40 |
2.5 Points |
Find the standard form of the equation of the following ellipse satisfying the given conditions. Foci: (0, -4), (0, 4) Vertices: (0, -7), (0, 7)
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A. x2/43 + y2/28 = 1 |
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B. x2/33 + y2/49 = 1 |
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C. x2/53 + y2/21 = 1 |
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D. x2/13 + y2/39 = 1 |
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33 of 40 |
2.5 Points |
Find the standard form of the equation of the following ellipse satisfying the given conditions. Foci: (0, -4), (0, 4) Vertices: (0, -7), (0, 7)
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A. x2/43 + y2/28 = 1 |
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B. x2/33 + y2/49 = 1 |
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C. x2/53 + y2/21 = 1 |
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D. x2/13 + y2/39 = 1 |
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35 of 40 |
2.5 Points |
Find the standard form of the equation of the following ellipse satisfying the given conditions. Foci: (-5, 0), (5, 0) Vertices: (-8, 0), (8, 0)
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A. x2/49 + y2/ 25 = 1 |
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B. x2/64 + y2/39 = 1 |
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C. x2/56 + y2/29 = 1 |
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D. x2/36 + y2/27 = 1 |
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36 of 40 |
2.5 Points |
Find the standard form of the equation of the ellipse satisfying the given conditions. Endpoints of major axis: (7, 9) and (7, 3) Endpoints of minor axis: (5, 6) and (9, 6)
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A. (x - 7)2/6 + (y - 6)2/7 = 1 |
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B. (x - 7)2/5 + (y - 6)2/6 = 1 |
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C. (x - 7)2/4 + (y - 6)2/9 = 1 |
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D. (x - 5)2/4 + (y - 4)2/9 = 1 |
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37 of 40 |
2.5 Points |
Locate the foci and find the equations of the asymptotes. 4y2 – x2 = 1
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A. (0, ±√4/2); asymptotes: y = ±1/3x |
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B. (0, ±√5/2); asymptotes: y = ±1/2x |
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C. (0, ±√5/4); asymptotes: y = ±1/3x |
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D. (0, ±√5/3); asymptotes: y = ±1/2x |
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38 of 40 |
2.5 Points |
Locate the foci of the ellipse of the following equation. x2/16 + y2/4 = 1
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A. Foci at (-2√3, 0) and (2√3, 0) |
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B. Foci at (5√3, 0) and (2√3, 0) |
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C. Foci at (-2√3, 0) and (5√3, 0) |
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D. Foci at (-7√2, 0) and (5√2, 0 |
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39 of 40 |
2.5 Points |
Locate the foci and find the equations of the asymptotes. x2/9 - y2/25 = 1
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A. Foci: ({±√36, 0) ;asymptotes: y = ±5/3x |
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B. Foci: ({±√38, 0) ;asymptotes: y = ±5/3x |
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C. Foci: ({±√34, 0) ;asymptotes: y = ±5/3x |
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D. Foci: ({±√54, 0) ;asymptotes: y = ±6/3x |
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40 of 40 |
2.5 Points |
Find the standard form of the equation of each hyperbola satisfying the given conditions. Foci: (0, -3), (0, 3) Vertices: (0, -1), (0, 1)
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A. y2 - x2/4 = 0 |
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B. y2 - x2/8 = 1 |
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C. y2 - x2/3 = 1 |
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D. y2 - x2/2 = 0 |
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