Question 1 of 40

Question 1 of 40 2.5 Points Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. x + y - z = -2 2x - y + z = 5 -x + 2y + 2z = 1 A. {(0, -1, -2)} B. {(2, 0, 2)} C. {(1, -1, 2)} D. {(4, -1, 3)} Question 2 of 40 2.5 Points Use Gaussian elimination to find the complete solution to each system. x - 3y + z = 1 -2x + y + 3z = -7 x - 4y + 2z = 0 A. {(2t + 4, t + 1, t)} B. {(2t + 5, t + 2, t)} C. {(1t + 3, t + 2, t)} D. {(3t + 3, t + 1, t)} Question 3 of 40 2.5 Points Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. 2x - y - z = 4 x + y - 5z = -4 x - 2y = 4 A. {(2, -1, 1)} B. {(-2, -3, 0)} C. {(3, -1, 2)} D. {(3, -1, 0)} Question 4 of 40 2.5 Points Use Cramer’s Rule to solve the following system. x + 2y + 2z = 5 2x + 4y + 7z = 19 -2x - 5y - 2z = 8 A. {(33, -11, 4)} B. {(13, 12, -3)} C. {(23, -12, 3)} D. {(13, -14, 3)} Question 5 of 40 2.5 Points Give the order of the following matrix; if A = [aij], identify a32 and a23. 1 0 -2 -5 7 1/2 ? -6 11 e -? -1/5 A. 3 * 4; a32 = 1/45; a23 = 6 B. 3 * 4; a32 = 1/2; a23 = -6 C. 3 * 2; a32 = 1/3; a23 = -5 D. 2 * 3; a32 = 1/4; a23 = 4 Question 6 of 40 2.5 Points Use Cramer’s Rule to solve the following system. 2x = 3y + 2 5x = 51 - 4y A. {(8, 2)} B. {(3, -4)} C. {(2, 5)} D. {(7, 4)} Question 7 of 40 2.5 Points Find values for x, y, and z so that the following matrices are equal. 2x z y + 7 4 = -10 6 13 4 A. x = -7; y = 6; z = 2 B. x = 5; y = -6; z = 2 C. x = -3; y = 4; z = 6 D. x = -5; y = 6; z = 6 Question 8 of 40 2.5 Points Use Cramer’s Rule to solve the following system. 3x - 4y = 4 2x + 2y = 12 A. {(3, 1)} B. {(4, 2)} C. {(5, 1)} D. {(2, 1)} Question 9 of 40 2.5 Points Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 5x + 8y - 6z = 14 3x + 4y - 2z = 8 x + 2y - 2z = 3 A. {(-4t + 2, 2t + 1/2, t)} B. {(-3t + 1, 5t + 1/3, t)} C. {(2t + -2, t + 1/2, t)} D. {(-2t + 2, 2t + 1/2, t)} Question 10 of 40 2.5 Points Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. x + 3y = 0 x + y + z = 1 3x - y - z = 11 A. {(3, -1, -1)} B. {(2, -3, -1)} C. {(2, -2, -4)} D. {(2, 0, -1)} Question 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. 8x + 5y + 11z = 30 -x - 4y + 2z = 3 2x - y + 5z = 12 A. {(3 - 3t, 2 + t, t)} B. {(6 - 3t, 2 + t, t)} C. {(5 - 2t, -2 + t, t)} D. {(2 - 1t, -4 + t, t)} Question 12 of 40 2.5 Points Use Gaussian elimination to find the complete solution to each system. x1 + 4x2 + 3x3 - 6x4 = 5 x1 + 3x2 + x3 - 4x4 = 3 2x1 + 8x2 + 7x3 - 5x4 = 11 2x1 + 5x2 - 6x4 = 4 A. {(-47t + 4, 12t, 7t + 1, t)} B. {(-37t + 2, 16t, -7t + 1, t)} C. {(-35t + 3, 16t, -6t + 1, t)} D. {(-27t + 2, 17t, -7t + 1, t)} Question 13 of 40 2.5 Points Use Gaussian elimination to find the complete solution to each system. 2x + 3y - 5z = 15 x + 2y - z = 4 A. {(6t + 28, -7t - 6, t)} B. {(7t + 18, -3t - 7, t)} C. {(7t + 19, -1t - 9, t)} D. {(4t + 29, -3t - 2, t)} Question 14 of 40 2.5 Points Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. x + y + z = 4 x - y - z = 0 x - y + z = 2 A. {(3, 1, 0)} B. {(2, 1, 1)} C. {(4, 2, 1)} D. {(2, 1, 0)} Question 15 of 40 2.5 Points Use Cramer’s Rule to solve the following system. x + y + z = 0 2x - y + z = -1 -x + 3y - z = -8 A. {(-1, -3, 7)} B. {(-6, -2, 4)} C. {(-5, -2, 7)} D. {(-4, -1, 7)} Question 16 of 40 2.5 Points If AB = -BA, then A and B are said to be anticommutative. Are A = 0 1 -1 0 and B = 1 0 0 -1 anticommutative? A. AB = -AB so they are not anticommutative. B. AB = BA so they are anticommutative. C. BA = -BA so they are not anticommutative. D. AB = -BA so they are anticommutative. Question 17 of 40 2.5 Points Use Cramer’s Rule to solve the following system. x + y = 7 x - y = 3 A. {(7, 2)} B. {(8, -2)} C. {(5, 2)} D. {(9, 3)} Question 18 of 40 2.5 Points Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination. x + 2y = z - 1 x = 4 + y - z x + y - 3z = -2 A. {(3, -1, 0)} B. {(2, -1, 0)} C. {(3, -2, 1)} D. {(2, -1, 1)} Question 19 of 40 2.5 Points Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 3x + 4y + 2z = 3 4x - 2y - 8z = -4 x + y - z = 3 A. {(-2, 1, 2)} B. {(-3, 4, -2)} C. {(5, -4, -2)} D. {(-2, 0, -1)} Question 20 of 40 2.5 Points Use Cramer’s Rule to solve the following system. 4x - 5y - 6z = -1 x - 2y - 5z = -12 2x - y = 7 A. {(2, -3, 4)} B. {(5, -7, 4)} C. {(3, -3, 3)} D. {(1, -3, 5)} Question 21 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 A. (x - 4)2 = 4(y - 2); vertex: (1, 4); focus: (1, 3) ; directrix: y = 1 B. (x - 2)2 = 4(y - 3); vertex: (1, 2); focus: (1, 3) ; directrix: y = 3 C. (x - 1)2 = 4(y - 2); vertex: (1, 2); focus: (1, 3) ; directrix: y = 1 D. (x - 1)2 = 2(y - 2); vertex: (1, 3); focus: (1, 2) ; directrix: y = 5 Question 22 of 40 2.5 Points Find the focus and directrix of the parabola with the given equation. 8x2 + 4y = 0 A. Focus: (0, -1/4); directrix: y = 1/4 B. Focus: (0, -1/6); directrix: y = 1/6 C. Focus: (0, -1/8); directrix: y = 1/8 D. Focus: (0, -1/2); directrix: y = 1/2 Question 23 of 40 2.5 Points Locate the foci and find the equations of the asymptotes. x2/9 - y2/25 = 1 A. Foci: ({±v36, 0) ;asymptotes: y = ±5/3x B. Foci: ({±v38, 0) ;asymptotes: y = ±5/3x C. Foci: ({±v34, 0) ;asymptotes: y = ±5/3x D. Foci: ({±v54, 0) ;asymptotes: y = ±6/3x Question 24 of 40 2.5 Points Find the vertex, focus, and directrix of each parabola with the given equation. (y + 1)2 = -8x A. Vertex: (0, -1); focus: (-2, -1); directrix: x = 2 B. Vertex: (0, -1); focus: (-3, -1); directrix: x = 3 C. Vertex: (0, -1); focus: (2, -1); directrix: x = 1 D. Vertex: (0, -3); focus: (-2, -1); directrix: x = 5 Question 25 of 40 2.5 Points Find the standard form of the equation of each hyperbola satisfying the given conditions. Foci: (-4, 0), (4, 0) Vertices: (-3, 0), (3, 0) A. x2/4 - y2/6 = 1 B. x2/6 - y2/7 = 1 C. x2/6 - y2/7 = 1 D. x2/9 - y2/7 = 1 Question 26 of 40 2.5 Points Find the vertex, focus, and directrix of each parabola with the given equation. (x + 1)2 = -8(y + 1) A. Vertex: (-1, -2); focus: (-1, -2); directrix: y = 1 B. Vertex: (-1, -1); focus: (-1, -3); directrix: y = 1 C. Vertex: (-3, -1); focus: (-2, -3); directrix: y = 1 D. Vertex: (-4, -1); focus: (-2, -3); directrix: y = 1 Question 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 A. Vertices at (2, 0) and (-2, 0); foci at (v5, 0) and (-v5, 0) B. Vertices at (3, 0) and (-3 0); foci at (12, 0) and (-12, 0) C. Vertices at (4, 0) and (-4, 0); foci at (16, 0) and (-16, 0) D. Vertices at (5, 0) and (-5, 0); foci at (11, 0) and (-11, 0) Question 28 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 A. (y - 2)2 = -10(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 9 B. (y - 1)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 6 C. (y - 5)2 = -14(x - 3); vertex: (2, 1); focus: (0, 1); directrix: x = 6 D. (y - 2)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 8 Question 29 of 40 2.5 Points Locate the foci and find the equations of the asymptotes. x2/100 - y2/64 = 1 A. Foci: ({= ±2v21, 0); asymptotes: y = ±2/5x B. Foci: ({= ±2v31, 0); asymptotes: y = ±4/7x C. Foci: ({= ±2v41, 0); asymptotes: y = ±4/7x D. Foci: ({= ±2v41, 0); asymptotes: y = ±4/5x Question 30 of 40 2.5 Points Locate the foci of the ellipse of the following equation. 7x2 = 35 - 5y2 A. Foci at (0, -v2) and (0, v2) B. Foci at (0, -v1) and (0, v1) C. Foci at (0, -v7) and (0, v7) D. Foci at (0, -v5) and (0, v5) Question 31 of 40 2.5 Points Locate the foci of the ellipse of the following equation. x2/16 + y2/4 = 1 A. Foci at (-2v3, 0) and (2v3, 0) B. Foci at (5v3, 0) and (2v3, 0) C. Foci at (-2v3, 0) and (5v3, 0) D. Foci at (-7v2, 0) and (5v2, 0) Question 32 of 40 2.5 Points Find the standard form of the equation of the following ellipse satisfying the given conditions. Foci: (-2, 0), (2, 0) Y-intercepts: -3 and 3 A. x2/23 + y2/6 = 1 B. x2/24 + y2/2 = 1 C. x2/13 + y2/9 = 1 D. x2/28 + y2/19 = 1 Question 33 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) A. y2 - x2/4 = 0 B. y2 - x2/8 = 1 C. y2 - x2/3 = 1 D. y2 - x2/2 = 0 Question 34 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) A. x2/43 + y2/28 = 1 B. x2/33 + y2/49 = 1 C. x2/53 + y2/21 = 1 D. x2/13 + y2/39 = 1 Question 35 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) A. (x + 2)2/4 + (y - 3)2/25 = 1 B. (x + 4)2/4 + (y - 2)2/25 = 1 C. (x + 3)2/4 + (y - 2)2/25 = 1 D. (x + 5)2/4 + (y - 2)2/25 = 1 Question 36 of 40 2.5 Points Find the vertex, focus, and directrix of each parabola with the given equation. (x - 2)2 = 8(y - 1) A. Vertex: (3, 1); focus: (1, 3); directrix: y = -1 B. Vertex: (2, 1); focus: (2, 3); directrix: y = -1 C. Vertex: (1, 1); focus: (2, 4); directrix: y = -1 D. Vertex: (2, 3); focus: (4, 3); directrix: y = -1 Question 37 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) A. (x - 7)2/6 + (y - 6)2/7 = 1 B. (x - 7)2/5 + (y - 6)2/6 = 1 C. (x - 7)2/4 + (y - 6)2/9 = 1 D. (x - 5)2/4 + (y - 4)2/9 = 1 uestion 38 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) A. x2/49 + y2/ 25 = 1 B. x2/64 + y2/39 = 1 C. x2/56 + y2/29 = 1 D. x2/36 + y2/27 = 1 Question 39 of 40 2.5 Points Convert each equation to standard form by completing the square on x and y. 9x2 + 25y2 - 36x + 50y - 164 = 0 A. (x - 2)2/25 + (y + 1)2/9 = 1 B. (x - 2)2/24 + (y + 1)2/36 = 1 C. (x - 2)2/35 + (y + 1)2/25 = 1 D. (x - 2)2/22 + (y + 1)2/50 = 1 Question 40 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 A. y2/6 - x2/9 = 1 B. y2/36 - x2/9 = 1 C. y2/37 - x2/27 = 1 D. y2/9 - x2/6 = 1 File #1