Question 594416:
1. What is the formula for the determinant of a 3 x 3 matrix ?
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2. Solve the inequality |2x − 4| < 10. Write the solution in interval notation and graph it.
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3. Find the equation of the boundary line in the graph below. Then give the inequality represented by the shaded area.
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4. Solve the inequality –2 (3 + x) < 4x + 4 < 8x. Give the result in set notation and graph it.
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5. When solving a system of equations using Cramer's Rule, if Dx = 0, Dy = –1, Dz = 1, and D = 0, then what can you conclude?
A. The system has one solution, (0, 0, 0).
B. The system has one solution, (0, –1, 1).
C. The system is inconsistent.
D. The system is dependent
6. Solve the inequality |5x + 10| ≥ 15. Write the solution in interval notation and graph it.
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7. Use matrices to help find a general solution for this system of equations.
2x − y + 3z = 5
–x + 4y + 4z = –1
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8. The first two rows of the following matrix are already in triangular form.
Finish the job by performing Gaussian elimination on row 3.
What are the contents of row 3 after you have done so?
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A. 0 0 3 29
B. 0 0 1 9
C. 0 0 3 –11
D. 0 0 –5 –11
9. Solve the equation |x| = 7.
A. x = –7
B. x = 7 or x = –7
C. Undefined
D. x = 7
10. Convert to a fraction.
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11. Aunt Jane's Pies had a tent at the county fair. Unfortunately their cash register broke, so they have no receipts. They know from counting their left over paper plates that they made 413 sales. They know from the cash box that they made $2,243. If they only sell two kinds of items at the fair tent, a piece of pie for $4 and pie á là mode for $7, help them figure out how many of each kind they sold.
A. They sold 216 pieces of pie and 197 pies á là mode.
B. They sold 355 pieces of pie and 58 pies á là mode.
C. They sold 610 pieces of pie and 4683 pies á là mode.
D. The system of equations is inconsistent, and therefore their plate counting or money counting must have an error.
12. Solve the inequality –6 ≤ 6x < 24. Give the result in set notation and graph it.
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13. Choose the correct ways to fill in the blanks in the following sentence.
To solve a system of equations using the matrix method, use __________ to transform the augmented matrix into one with __________, then proceed to back-substitute.
A. multiplication and addition, zeros in its final column
B. the coefficient matrix, an inverse
C. elementary row operations, zeros below the diagonal
D. the coefficient matrix, Gaussian elimination
14. Find the value of the expression –|–18|.
A. –18
B. 18
C. 0
D. Undefined
15. Solve the system of equations x − 4y = –8 and –3x + 12y = 24.
A. There is one solution, and it is (0, 2).
B. There is no solution.
C. There is one solution, and it is (–4, 1).
D. There are infinitely many solutions.
16. Solve the system of equations 2x − 2y − 2z = 3, x + 4y − z = 2, and –2x − 8y + 2z = –4.
A. There are infinitely many solutions, of the form (x, 0.1, x −1.6).
B. There is one solution, (0.1, 0.1, –1.5).
C. There are infinitely many solutions, of the form (0.1, 0.1, –1.5).
D. There is no solution.
17. Consider two ships, one on a course described by the equation 0.6x + 0.3y = 2.1 and the other on a course described by the equation –0.3x + 0.1y = –1.8. Which of the following sentences best describes the possibility of a collision?
A. There is a possibility of a collision at the point (5, –3) but a collision is not a certainty.
B. There is no possibility for a collision.
C. There is a possibility of a collision at the point (0, 7) but a collision is not a certainty.
D. There will certainty be a collision at the point (6, 0).
18. Solve the system of equations x + y + z = 9, –x + y + z = 1, and x − y − z = 5.
A. There is no solution.
B. There are infinitely many solutions.
C. There is one solution, x = 4, y = 2, and z = 3.
D. There is not enough information to solve the problem.
19. Which of the following ordered pairs is a solution to the system of equations y = x − 6 and 2y = –x + 14?
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20. Which of the following phrases correctly describes the graph of the system of equations and y = 2 − x?
A. The graph is of two lines that intersect at a single point.
B. The graph is of a line and a parabola, which intersect at two points.
C. The graph is of two lines that coincide.
D. The graph is of two parallel lines that do not intersect.
21. Are the two equations –6 + y = 2x and 2y − 4x = 12 dependent?
A. Yes, because both are the equations of straight lines.
B. No, because they are not parallel.
C. Yes, because they have the same graph.
D. No, because the equations are not written the same.
Solve the inequality . Give the result in set notation and graph it.
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B.
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D.
Answer by richard1234(7193)   (Show Source):
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