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

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Question 1126439: Mr chows car consumes petrol at an average rate of 8 litres daily. before Mr Chow begins his journey he top up the petrol in his car to 100 litres. given that he will next top of the petrol in his car when there are 20 litres left, form an in equality and solve it to find the maximum number of days he can travel before he has to top up the petrol in car.
Click here to see answer by Theo(13342)

Question 1126671: 4(x-4)≤-4(x-6)
Click here to see answer by josgarithmetic(39614)

Question 1126800: 5(x + 6) ≤ 2(x + 21)
Click here to see answer by Boreal(15235)

Question 1126815: you plug a microwave own into a 20-ampere (amp) electrical circuit. The microwave uses as much as 12.5 amp. How many amps are available on this circuit for other appliances?
Click here to see answer by MathLover1(20849)

Question 1126831: There are 157 students and 8 teachers going on a field trip. Each bus can seat at most 48 passengers. How many buses should the school reserve?
Click here to see answer by ikleyn(52759)

Question 1126836: write and solve an inequality:
There are 157 students and 8 teachers going on a field trip. Each bus can seat at most 48 passengers. How many buses should the school reserve?
Click here to see answer by josmiceli(19441)

Question 1127181: Given that coordinates of P amd Q are (-2,6) and (9,3) , find
a) cooridantes of point R that lies on y axis such that PR =QR
b) coordinates of point S that lies on x axis such as PS=QS
Click here to see answer by MathLover1(20849)

Question 1127185: A line segmemt has 2 end points M(3,7) and N (11,-6). find coordinates of point W that lies in yaxis such that W is equidistant (same distance) from M and from N
Click here to see answer by josmiceli(19441)

Question 1127269: Max scored 71 and 65 on his first two tests in Biology 101. What is the lowest he must score on the third test to get an average for the three tests above 77?
Click here to see answer by math_helper(2461)

Question 1127303: Your goal is to take at least 11,100 steps per day. According to your pedometer, you have walked 7103 steps. Write and solve an inequality to find the possible numbers of steps you can take to reach your goal.
Click here to see answer by stanbon(75887)

Question 1127496: The sun of a number and 81 is greater than the product of -3 and that number

Click here to see answer by Boreal(15235)

Question 1127854: how do i find the value of r in this equation.
A line passes through the point r,5 and -2,r and has a slope of -2/9

Click here to see answer by ikleyn(52759)

Question 1128340: translate two thirds of a number is less than negative fifteen
Click here to see answer by Boreal(15235)

Question 1128347: A family decides to rent a boat for the day while on vacation. The boat's rental rate is $500 for the first two hours and $50 for each additional half hour. Suppose the family can spend $700 for the boat. What inequality represents the number of hours for which they can rent the boat?
Click here to see answer by josmiceli(19441)

Question 1128713: A parking lot has a surface of 720 m^2. Each car occupies an area of 6m^2 and each bus occupies an area of 18m^2
How do I make this an equation ? Like an inequality
Also, how would I identify the variables?
Click here to see answer by ikleyn(52759)

Question 1128720: The perimeter of a rectangle field is less than 60m
How do I make this an inequality equation?
Click here to see answer by MathLover1(20849)

Question 1128721: Tickets at a concert cost $10 per adult and 6$ per child. The total revenue from ticket sales is greater than 600
How do I make this an inequality? And how do I solve?
Click here to see answer by josmiceli(19441)

Question 1128842: Tell whether −3
is a solution of the inequality.
3−4x≥15
Click here to see answer by ikleyn(52759)

Question 1128862: Use the given functions to find all values of x that satisfy the inequality f(x)≥ g(x).
f(x)= 5x� g(x)=23x-12
A. The solution set is____________
Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)
B. The solution set is �.

ASAP Please and thank you in advance!

Click here to see answer by josmiceli(19441)

Question 1128929: Hi, I need your help with a couple of story problems. Here it is I have been trying to figure it out but I need some help.

Mr. and Mrs. Vance will spend no more than $300 for two bicycles and a bicycle carrier for their car. They plan to spend the same amount for each bicycle. If they buy a rack for $65 how much will they spend on each bicycle? I need to solve an inequality and express the answer using inequality notation. I am not a lazy student i just need some help. Thank you so much

Click here to see answer by MathLover1(20849)

Question 1129169: the length of a rectangle is 6cm longer than th width. The perimeter of the rectangle is 92 cm. What is the length and the width of the rectangle?
Click here to see answer by ikleyn(52759)

Question 1129273: Find the discriminant as a function of k, and hence find the values of k for which is positive definite.
Please explain the reasoning behind > and <, as they don't seem to follow conventional rules when using a discriminant.
Click here to see answer by rothauserc(4718)

Question 1129342: Find the maximum or minimum value of the function.
f(x) = 3x^2 − 43
Click here to see answer by Alan3354(69443)

Question 1129341: Find the maximum or minimum value of the function.
f(x) = 2x^2 + 3x + 2
Click here to see answer by Alan3354(69443)

Question 1129340: The fuel efficiency for a certain midsize car is given by
E(v) = −0.016v2 + 1.376v + 3.8
where
E(v)
is the fuel efficiency in miles per gallon for a car traveling v miles per hour.
(a) What speed will yield the maximum fuel efficiency? Round to the nearest mile per hour.______mph
(b) What is the maximum fuel efficiency for this car? Round to the nearest mile per gallon.____mpg
Click here to see answer by rothauserc(4718)

Question 1129343: Determine the number of units x that produce a maximum revenue, in dollars, for the given revenue function.
R(x) = 312x − 0.2x2
x = units
Determine the maximum revenue.____$
Click here to see answer by MathLover1(20849)

Question 1129339: When a softball player swings a bat, the amount of energy E(t), in joules, that is transferred to the bat can be approximated by the function
E(t) = −279.67t2 + 82.86t
where 0 ≤ t ≤ 0.3 and t is measured in seconds. According to this model, what is the maximum energy of the bat? Round to the nearest tenth of a joule.____joule
Click here to see answer by MathLover1(20849)

Question 1129469: The total revenues (in dollars) for a company to sell x blank audiocassette tapes per week is given by the polynomial function R(x)=2x. Find the total revenue from selling 10,000 tapes per week. The total revenue from selling 10,000 tapes per week is $____________.
Click here to see answer by josmiceli(19441)

Question 1129778: Solve the inequality and write the solution in interval notation.
I am confused how to do this problem
x^2-3x-10 less than or equal to 0

please help
Click here to see answer by josgarithmetic(39614)

Question 1129787: solve the inequality and write the solution in interval notation
3/x-5<0
please help

Click here to see answer by MathLover1(20849)

Question 1129787: solve the inequality and write the solution in interval notation
3/x-5<0
please help

Click here to see answer by MathTherapy(10549)

Question 1129806: A graphing calculator is recommended.
The data in the table below show the distance, in feet, a ball travels for various swing speeds, in miles per hour, of a bat.
Bat speed (mph) Distance (ft)
40 199
45 217
50 237
60 280
70 298
75 326
80 334
(a) Find the linear regression equation for these data. (Round all numerical values to three decimal places.)
y = ___________
(b) Using the regression model, what is the expected distance a ball will travel when the bat speed is 58 miles per hour? Round to the nearest foot.
___________ft

Click here to see answer by MathLover1(20849)

Question 1129969: a standard school day will average at least 5 1/2 hours, excluding meal breaks. for the first four days of one week school, bad weather resulted in school days of four hours, 6 1/2 hours, 3 1/2 hours and 6 1/2 hours. how long must the friday school day be in order to average at least 5 1/2 hours for the week
Click here to see answer by josgarithmetic(39614)

Question 1130029: Eight less a number is less than or equal to seventeen
Click here to see answer by josgarithmetic(39614)

Question 1130088: Rewrite the statement so that is uses < instead
15>-21
Click here to see answer by Boreal(15235)

Question 1130088: Rewrite the statement so that is uses < instead
15>-21
Click here to see answer by MathLover1(20849)

Question 1130092: 4 8/9 + (-5 2/3) find the sum
Click here to see answer by MathLover1(20849)

Question 1130092: 4 8/9 + (-5 2/3) find the sum
Click here to see answer by MathTherapy(10549)

Question 1130163: Write an inequality and solve each problem:
Four more than a number is no more than thirteen.
The difference of a number and -6 is less than 9.
Eleven less than a number is more than seventeen.
Click here to see answer by Edwin McCravy(20054)

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