Tutors Answer Your Questions about Inequalities (FREE)
Question 591229: A shuttle service taking skiers to a ski area charges $8 per person each way. Four skiers are debating whether to take the shuttle bus or rent a car for $45 plus $.25 per mile. Assuming that the skiers will share the cost of the car and that they want the least expensive method of transportation, how far away is the ski area if they choose to take the shuttle service? I know the answer is more than 38 miles.
8*2*4<45 + .25X
64<45 +.25X
I don't understand how you get 9.5<.25X and not 19 <.25X?? Please Help!
Click here to see answer by scott8148(6628)   |
Question 591463: I am in dire need of help with this extreme elimination problem.
I have tried multiplying top and bottom by 2 as well as 2 and 3 but have not been able to find a way to equal out the x or y to cancel either out and continue with the equation.
Click here to see answer by derangoj(14) |
Question 592118: (Find the equation)well I found the slope of (-4,1)and(2,-2). which is -3/6= -1/2. that is in fraction form for rise over run. my computer does not have the fraction symbol. anyways im not sure if im suppose to change the -1/2 to 2/-1 than Divide.
Click here to see answer by scott8148(6628) |
Question 594419: 1. Find all roots of x3 + 2x2 + 2x + 1. Hint: Find the rational one(s) first.
A.
B.
C.
D.
2. Solve 2x = 5x2 for x.
A. 2.322
B. 0 and 2.322
C. 0 and 0.431
D. 0.431
3. Which of the following is not a property of logarithms?
A.
B.
C.
D.
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?
A. Its initial velocity was 0 meters per second and its velocity after 10 seconds is –12.2 meters per second.
B. Its initial velocity was –1 meter per second and its velocity after 10 seconds is –36.3 meters per second.
C. Its initial velocity was 0 meters per second and its velocity after 10 seconds is 36.3 meters per second.
D. Its initial velocity was 1 meter per second and its velocity after 10 seconds is 12.2 meters per second.
5. How many roots does x6 = 3x5 + 1 have?
A. 6
B. 5
C. 11
D. 1
6. If 2 − i is a root of 3x3 − 11x2 + 11x + 5, then what are its other roots?
A.
B.
C.
D.
7. On which interval does the Intermediate Value Theorem guarantee that the polynomial x4 + 7x2 − 9x − 1 has a root?
A.
B.
C.
D.
8. If 1 and –6 are two of the roots of 6x4 + 31 x3 − 33x2 − 16x + 12, then what are the other two?
A.
B.
C.
D.
9. Which of these graphs could be the graph of y = ex + 1?
A.
B.
C.
D.
10. Why do we use the Intermediate Value and Bisection Theorems to find only the irrational roots of polynomials?
A. It is the only method available for finding irrational roots of any polynomial.
B. The Rational Roots Theorem is better for finding the rational roots.
C. Those theorems are unable to find rational roots.
D. No polynomial has rational roots.
11. A population of 2000 snakes is released into a marshland and grows according to the formula P = 2000 • 1.5t, where t is the number of months after the release. Find the population 10 months after the release.
A. 63,246
B. 115,330
C. 5.9 x 1034
D. 30,000
12. Write in terms of ln a, ln b, and ln c. You may assume that all variables are positive.
A.
B.
C.
D.
13. Which of these is the result of (x5 − x3 + 2x2 − 9x + 5) ÷ (x + 2)?
A.
B.
C.
D.
14. Evaluate .
A. 2
B. 4
C. ¼
D. ½
15. Find the point (x, y) on the parabola y = 9 − x2 such that the shaded rectangle in the figure below has area 20 square units.
A.
B.
C.
D.
16. Solve ln t = log 50 for t.
A. t = 5.47
B. t = 8166.3
C. t = 13.6
D. t = 50
17. Which of the following is the conclusion you can draw using Descartes' Rule of Signs applied to 2x4 − 6x3 + x2 + 7x − 4?
A. Zero is not a root.
There are either 1 or 3 positive real roots.
There are 3 negative real roots.
There are either 0 or 2 complex roots.
B. Zero is not a root.
There are either 1 or 3 positive real roots.
There are 3 negative real roots.
No information is available about the number of complex roots.
C. Zero is not a root.
There are either 1 or 3 positive real roots.
There is 1 negative real root.
There are either 0 or 2 complex roots.
D. Zero is not a root.
There are either 1 or 3 positive real roots.
There is 1 negative real root.
No information is available about the number of complex roots.
18. Which of these is the remainder when 4x4 − 5x3 + 9 is divided by x − 3?
A.
B.
C.
D.
19. Which of these could be the graph of y = 7x − 2?
A.
B.
C.
D.
20. Simplify .
A.
B. 216
C.
D. is already in simplified form.
21. Which of the following is a reason for why the trace function on a graphing calculator can sometimes be better than the Bisection Theorem for finding roots?
A. The trace function always finds an exact root.
B. The Intermediate Bisection Theorem applies only to continuous functions, and not all polynomials are continuous.
C. Some roots aren't surrounded by one positive and one negative value of the polynomial
D. The Bisection Theorem can't find roots to more than 3 decimal places.
22. If a cubic polynomial has roots –5 and 6 − 2i, what is its third root?
A. 1 − 2i
B. –30 + 10i
C. 6 + 2i
D. 5
23. Which of the following is a correct description of the expression logbx?
A. It is the power to which b must be raised to yield x.
B. It is the xth power of b.
C. It is the bth power of x.
D. It is the power to which x must be raised to yield b.
24. Which of the following is equal to log6(t + 1) − log6(t2 − 1)?
A. log6(t + 1)
B. log6t − log6t2
C. log6t
D. –log6(t − 1)
25. Which are upper and lower bounds for the real roots of 3x4 − 2x3 + x − 9 = 0?
A. –3 and –1, 1, and 3
B. –2 and 2
C. –2 and –1, 1, and 2
D. 0 and 3
Click here to see answer by Alan3354(69443)  |
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(7193)  |
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(8007)  |
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(7193) |
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(648)  |
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(75887) |
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(5328)  |
|
Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205
|
