# Questions on Algebra: Inequalities, trichotomy answered by real tutors!

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 Algebra: Inequalities, trichotomy Solvers Lessons Answers archive Quiz In Depth

 Question 594416: 1. What is the formula for the determinant of a 3 x 3 matrix ? A. B. C. D. 2. Solve the inequality |2x − 4| < 10. Write the solution in interval notation and graph it. A. B. C. D. 3. Find the equation of the boundary line in the graph below. Then give the inequality represented by the shaded area. A. B. C. D. 4. Solve the inequality –2 (3 + x) < 4x + 4 < 8x. Give the result in set notation and graph it. A. B. C. D. 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. A. B. C. D. 7. Use matrices to help find a general solution for this system of equations. 2x − y + 3z = 5 –x + 4y + 4z = –1 A. B. C. D. 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? . 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. A. B. C. D. 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. A. B. C. D. 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? A. B. C. D. 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. A. B. C. D. Click here to see answer by richard1234(5390)

 Question 594693: 1.Find all roots of x3 + 2x2 + 2x + 1. Hint: Find the rational one(s) first. 2.Solve 2x = 5x2 for x. 3.Which of the following is not a property of logarithms? 4.A falling object has velocity 37(1 − e–0.4t) meters per second after t seconds of free fall. Which of the following statements is true? 5.How many roots does x6 = 3x5 + 1 have? Click here to see answer by edjones(7569)

 Question 594938: -8 - 11(3x+7) less than equal to -40x - 9 Click here to see answer by jim_thompson5910(28595)

 Question 595196: Which of the following is not a property of logarithms? A falling object has velocity 37(1 − e–0.4t) meters per second after t seconds of free fall. Which of the following statements is true? How many roots does x6 = 3x5 + 1 have?''. Click here to see answer by richard1234(5390)

 Question 595611: Describe two real-life examples where inequalities are used either at home or on the job? Click here to see answer by math-vortex(472)

 Question 595644: A parabola contains the points (2,0)and(-3,0).What is the equation of its axis of symmetry Click here to see answer by scott8148(6628)

 Question 596122: The formula for converting Fahrenheit temperature, F, to Celsius temperature, C is C= 5/9(F-32). If Celsius temperature ranges from 15 to 35, inclusive, what is the range for the Fahrenheit temperature? teacher said inequality problem, answer will finish in the middle Click here to see answer by math-vortex(472)

 Question 596431: Solve the following inequality (3x-4)/(x+5) <= 2 so far i've done: subtract the 2 from both sides (3x-4)/(x+5) - 2 Common denominator -2 * (x + 5) (3x-4 - 2x + 10)/(x+5) <= 0 Now I simplify (x+6)/(x+5) <= 0 Finally graph [-6,-5] im not sure if that's correct I haven't touched this subject in a while. Click here to see answer by stanbon(57337)

 Question 597424: what is the solution set of the inequality 5-|x+4| Click here to see answer by stanbon(57337)

 Question 597495: I'm trying to help my daughter with her homework, but am clueless on how to solve the problem. She's working on inequality word problems. Here is the problem: Paula ran a 15 kilometer race in 1 1/2 hours. Write an inequality to describe the average speeds s of runners who were faster than Paula. Graph the inequality. Click here to see answer by KMST(1868)

 Question 597653: what is the solution of the inequality -6x-17>or equal to 8x+25? Click here to see answer by stanbon(57337)
 Question 597653: what is the solution of the inequality -6x-17>or equal to 8x+25? Click here to see answer by josmiceli(9674)

 Question 598069: What is the correct solution for the inequality? -13x + 13 > 78 i don't get this and this has been puzzling me for a while. help? Click here to see answer by Alan3354(30993)

 Question 598373: How do you solve the Inequality of -2/5x -9 < 9/10 I know that you add 9 to both sides but then I'm stuck. I don't know how to do fractions. Click here to see answer by josmiceli(9674)

 Question 599305: what is the inequality of no less than 3,000 and no more than 12,000? Click here to see answer by jim_thompson5910(28595)

 Question 599403: a + 18< 37 solve the inequality a: a > 18 b: a > 19 c: a < 19 d: a < 18 Click here to see answer by Alan3354(30993)
 Question 599403: a + 18< 37 solve the inequality a: a > 18 b: a > 19 c: a < 19 d: a < 18 Click here to see answer by jim_thompson5910(28595)

 Question 599647: i cant figure out the circle part out if it shade what does it mean if it not what does it mean Click here to see answer by math-vortex(472)

 Question 600320: Hi! I Hope you've had a wonderful day! I need help on this problem! Please answer and show step by step!Thanks! 3+|8j-5|>=6 the problem in words: three plus the absolute value of eight j minus five is greater or equal to six Reply ASAP! :) Click here to see answer by jim_thompson5910(28595)

 Question 600335: SOlve the following inequality x+17/x-1 less than or equal to 1 with steps please Click here to see answer by stanbon(57337)

 Question 601434: Hi can you please help me figure this problem. I am solving for x and y. the equation is {(3x+4y=48,x-y=2) this is how the teacher wrote it out on my assignment. The answers given were x=40 and y=42 I need to understand how these numbers were gotten and the book is no help. I am visual and there are no examples close to this problem. Click here to see answer by Alan3354(30993)
 Question 601434: Hi can you please help me figure this problem. I am solving for x and y. the equation is {(3x+4y=48,x-y=2) this is how the teacher wrote it out on my assignment. The answers given were x=40 and y=42 I need to understand how these numbers were gotten and the book is no help. I am visual and there are no examples close to this problem. Click here to see answer by bucky(2189)