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

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Question 1174921: The total profit function, P(x), for a company producing x thousand units is given by P(x)=−2x^2+38x−120. Find the values of x for which the company makes a profit. [Hint: The company makes a profit when P(x)>0.] Explain and justify your answer.
Click here to see answer by ewatrrr(24785)

Question 1175261: Troy is landscaping his yard.
He spends a total of $500.
Troy spends $160 on bricks.
He spends the rest of the money on trees that cost $20 each.
Troy uses the equation 500 = 20t + 160 to find the number of trees, t, he can buy.
How many trees can Troy buy?
Click here to see answer by ewatrrr(24785)

Question 1175469: Compound Inequality
the length of a rectangle is 9 times its width. If the perimeter of the rectangle is not to exceed 240 feet, what are the possible values for x?
Click here to see answer by ikleyn(52781)

Question 1175710: The sum of two counting numbers is 45. One of the number exceeds the other by 7. What are the two numbers?
Click here to see answer by ikleyn(52781)

Question 1175706: A lab technician needs to make 12 liters of 45% alcohol. How much of 40% alcohol and 60% alcohol must he mix to produce this?
Click here to see answer by josgarithmetic(39617)

Question 1175706: A lab technician needs to make 12 liters of 45% alcohol. How much of 40% alcohol and 60% alcohol must he mix to produce this?
Click here to see answer by MathTherapy(10552)

Question 1175706: A lab technician needs to make 12 liters of 45% alcohol. How much of 40% alcohol and 60% alcohol must he mix to produce this?
Click here to see answer by ikleyn(52781)

Question 1175706: A lab technician needs to make 12 liters of 45% alcohol. How much of 40% alcohol and 60% alcohol must he mix to produce this?
Click here to see answer by ewatrrr(24785)

Question 1175706: A lab technician needs to make 12 liters of 45% alcohol. How much of 40% alcohol and 60% alcohol must he mix to produce this?
Click here to see answer by greenestamps(13200)

Question 1175711: In a wallet are one-peso and five-peso coins. The number of coins sum up to 22 but its value sums up to 50. How many one-peso and five-peso coins are in it?
Click here to see answer by ikleyn(52781)

Question 1175828: four children earn money for a charity, dauda earns #y, obi earns half as much as dauda, chidi earns three times as much as Obi and Wale earns #250 less than all the other three

Click here to see answer by ikleyn(52781)

Question 1170830: Solve and graph the following inequalities. If there is no solution, write DNE. If all real numbers are solutions, write ARS. Show all your works (5 points each)
1) 3x - 5<_ 13 ( 3x minus 5 is less than or equal to 13)
2) 3(2x - 3) < 12x + 14 / 2
3) -3x + 7 >_ 16 ( negative 3x plus 7 is greater than or equal to 16)
Click here to see answer by CubeyThePenguin(3113)

Question 1173212: Jane is buying squid balls and noodles. Each cup of noodles costt 15.0 while each stick of squid balls costs 10. She only has 70.0 but needs to buy at least 3 sticks of squid balls. Solve the system graphically.
Click here to see answer by CubeyThePenguin(3113)

Question 1175999: The point (-2,5) satisfies the inequality y + 2x ≥ -7.
sometimes
never
always
Click here to see answer by Boreal(15235)

Question 1175999: The point (-2,5) satisfies the inequality y + 2x ≥ -7.
sometimes
never
always
Click here to see answer by ikleyn(52781)

Question 1176090: A mortgage of 100,000 for a set of appliances is to be amortized with equal payments every quarter for one year at 10%. How much will be his quarterly payment?
Click here to see answer by Theo(13342)

Question 1176237: farmer ted goes to the auction each week and buys lots of hay bales. last week he bought 3 truck and 10 wagons full of hay... for a total of 946 bales. this week he bought 9 trucks and 6 wagons full of hay... for a total of 798 bales. how many bales of hay are on each truck, and same for each wagon.
Click here to see answer by Boreal(15235)

Question 1176236: coach sue bought milkshakes for her field hockey team. the number of large shakes was just 1 less than twice the number of small shakes. she bought small shakes for $1.75 each and large shakes for $3 each and spent a total of $82.25. how many of each size shake did coach sue buy?
Click here to see answer by ewatrrr(24785)

Question 1171424: A polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coefficients that are irreducible over ℝ.
1, −5 − 4i; degree 3
Click here to see answer by CubeyThePenguin(3113)

Question 1096289: You are designing a container in the shape of a cylinder. The radius is 6 inches. You want the container to hold at least 324π cubic inches. What is the least possible height of the container?

Click here to see answer by CubeyThePenguin(3113)

Question 1177098: Grace is more than 20 years old when her first son was born. Today the sum of their ages is no less than 60. How old are they now?
Click here to see answer by Solver92311(821)

Question 1177547: graph 2y-4x<8
Click here to see answer by MathLover1(20849)

Question 1177550: y>=-2x-1, y>=x+2

Click here to see answer by Edwin McCravy(20055)

Question 1177684: Let a and b be positive real numbers(That is a≥0, b≥0). Prove that a⁴+b⁴≥a³b+ab³

Click here to see answer by ikleyn(52781)

Question 1177684: Let a and b be positive real numbers(That is a≥0, b≥0). Prove that a⁴+b⁴≥a³b+ab³

Click here to see answer by math_helper(2461)

Question 1177686: Solve|x²-9|>7

Click here to see answer by ikleyn(52781)

Question 1177685: Solve (x²-4)(11-2x)≤0

Click here to see answer by MathLover1(20849)

Question 1177785: https://gyazo.com/29e8bd90c8086740705e6fcc5559b6d7
Click here to see answer by MathLover1(20849)

Question 1177785: https://gyazo.com/29e8bd90c8086740705e6fcc5559b6d7
Click here to see answer by greenestamps(13200)

Question 1178210: A yoga class has space for at most 30 students. There are already 16 students who have signed up for the class.

Click here to see answer by ikleyn(52781)

Question 1178210: A yoga class has space for at most 30 students. There are already 16 students who have signed up for the class.

Click here to see answer by josgarithmetic(39617)

Question 1178290: Which of the following describes the graph of {x | x ≤ 1} {x | x ≥ 4}?

Click here to see answer by MathLover1(20849)

Question 1178290: Which of the following describes the graph of {x | x ≤ 1} {x | x ≥ 4}?

Click here to see answer by ikleyn(52781)

Question 1178280: To rent a certain meeting room, a college charges a reservation fee of $17 and an additional fee of $6 per hour. The chemistry club wants to spend at most $65 on renting the room. What are the possible numbers of hours the chemistry club could rent the meeting room?
Use t for the number of hours.
Write your answer as an inequality solved for t.
Click here to see answer by ikleyn(52781)

Question 1178686: An open box is to be made from a rectangular piece of tin by cutting 2-inch squares out of the corners and folding up the sides. The length of the finished box is to be twice the width. The volume of the box will be 100 cubic inches. Find the dimensions of the rectangular piece of tin.
Click here to see answer by josgarithmetic(39617)

Question 1178729: Let r, s, and t be the roots of the equation x^3 - 2x + 1 = 0 in some order. What is the maximal value of r^3 - s- t?
Click here to see answer by MathLover1(20849)

Question 1178729: Let r, s, and t be the roots of the equation x^3 - 2x + 1 = 0 in some order. What is the maximal value of r^3 - s- t?
Click here to see answer by ikleyn(52781)

Question 1178757: Show that 1/x <= 3 - 2sqrt(x) for all positive real numbers x. Describe when we have equality.
Click here to see answer by Edwin McCravy(20055)

Question 1178910: A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The trick ski requires labor-hours for fabricating and labor-hour for finishing. The slalom ski requires labor-hours for fabricating and labor-hour for finishing. The maximum labor-hours available per day for fabricating and finishing are and , respectively. Find the set of feasible solutions graphically for the number of each type of ski that can be produced.
If x is the number of trick skis and y is the number of slalom skis produced per day, write a system of linear inequalities that indicates appropriate restraints on x and y.
Write an inequality for the constraint on fabricating time. Complete the inequality below.
_ _ _ 204
Can you please explain this to me step-by-step?

Click here to see answer by mananth(16946)

Question 1179143: What is the inequalities of -2x > 0?
Click here to see answer by MathLover1(20849)

Question 1179380: One number is 4 less than a second number. Twice the second number is 2 less than 3 times the first. Find the two numbers.
a) 11 and 15
b) 9 and 13
c) 10 and 14
d) -14 and -10
Click here to see answer by josgarithmetic(39617)

Question 1179366: Let x, a, b, c be nonnegative real numbers. Prove that
(x + cuberoot{abc})^3 <= (x + a)(x + b)(x + c) <= ( x + {(a+b+c)/(3)}^3)
Click here to see answer by math_helper(2461)

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