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

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Question 1163650: Prove lim x^3 = 1 as x approaches 1 using precise definition of limits
This is how far I got and my line of thought not sure if I am making any conceptual errors.
Basically the question wants me to show that whenever they give me a e>0 value, I can return a &>0 value whereby
0<|x-1|<& --> |x^3 - 1| I tried to express the right hand inequality in terms of |x-1| so that I can relate to the left hand inequality.
|(x-1)(x^2 + x + 1)| |(x-1)((x-1)^2 + 3(x-1) - 3)| If I were to modulus all the x-1, I will get this inequality
||x-1|(|x-1|^2 + 3|x-1| - 3)| >= |(x-1)((x-1)^2 + 3(x-1) - 3)|
And if I were to convert it further to & terms,
&(&^2 + 3& - 3) > ||x-1|(|x-1|^2 + 3|x-1| - 3)| < e
&(&^2 + 3& -3) < e
So from here I am not too sure how to go about it. Please advise
Click here to see answer by Edwin McCravy(20054)

Question 1164234: The numbers 1,2,3,4,5,6,7,8,9,10 are to be entered into the 10 boxes shown below, so that each number is used exactly once:
P = (blank + blank + blank + blank+ blank)(blank + blank + blank + blank + blank)
What is the maximum value of P? What is the minimum value of P?

Blank stands for the empty boxes that were in the original problem.

Click here to see answer by Edwin McCravy(20054)

Question 1164246: The numbers 1,2,3,4,5,6,7,8,9,10 are to be entered into the 10 boxes shown below, so that each number is used exactly once:
P = (blank + blank + blank + blank+ blank)(blank + blank + blank + blank + blank)
What is the maximum value of P? What is the minimum value of P?
Blank stands for the empty boxes that were in the original problem.
Click here to see answer by Edwin McCravy(20054)

Question 1164230: 2x-1/3+3 <= -4
or
8x-2/2-1>= 6

Click here to see answer by greenestamps(13198)

Question 1164322: The numbers 1,2,3,4,5,6,7,8,9,10 are to be entered into the 10 boxes shown below, so that each number is used exactly once:
P = (blank + blank + blank + blank+ blank)(blank + blank + blank + blank + blank)
What is the maximum value of P? What is the minimum value of P?
Blank stands for the empty boxes that were in the original problem.
Can you solve with the AM GM inequality? I don't really get it.
Click here to see answer by solver91311(24713)

Question 1164459: Determine whether the statement is true or false. If the statement is false, give a reason.
{x|x is in N} = {x|x is in W and x > 0}
1 True. The set of natural numbers is equal to the set of whole numbers greater than 0.
2 False. The set of natural numbers is the same as the set of whole numbers.
3 False. The set of whole numbers is equal to the set of natural numbers greater than 0.
4 False. The set of integers is equal to the set of whole numbers greater than 0.
Click here to see answer by solver91311(24713)

Question 1164458: Use set-builder notation to write the following set.
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
1 {x | x is in N and x < 13}
2 {x | x is in N and x < 12}
3 none of these
4 {x | x is in N and x > 1}
5 {x | x is in N and x > 0}

Click here to see answer by solver91311(24713)

Question 1164457: Insert either ⊆ or is not a subset of in the blank space between the sets to make a true statement.
{c, d, e, f} _____ {a, b, c, d, e, f, g}
Click here to see answer by solver91311(24713)

Question 1164455: Let U = {p, q, r, s, t}, D = {p, r, s, t}, E = {q, s}, F =
{p, r},
and G = {s}. Determine whether the statement is true or false.
F ⊂ D
Click here to see answer by solver91311(24713)

Question 1164455: Let U = {p, q, r, s, t}, D = {p, r, s, t}, E = {q, s}, F =
{p, r},
and G = {s}. Determine whether the statement is true or false.
F ⊂ D
Click here to see answer by Edwin McCravy(20054)

Question 1164515: Jacinta says the product of a rational number and an irrational number is always irrational. is that true, does it work for 0?

Click here to see answer by jim_thompson5910(35256)

Question 1164520: Four times a number is less than or equal to the sum of three times the number and negative two
Click here to see answer by ikleyn(52775)

Question 1164531: Write an equation in slope-intercept form that is perpendicular to -4x+10y=-5 and passes through the point (6,-7).
Click here to see answer by josgarithmetic(39616)

Question 1164531: Write an equation in slope-intercept form that is perpendicular to -4x+10y=-5 and passes through the point (6,-7).
Click here to see answer by ikleyn(52775)

Question 1164703: a gym charges a 20 dollar fee plus 25 dollars per month.you have a 120 dollar gift card for the gym. when does the total spent on your gym membership exceed the amount of your gift card

Click here to see answer by Boreal(15235)

Question 1164456: Use the roster method to write the given set. You may need to consult a reference, such as the Internet or an encyclopedia. (Enter EMPTY for the empty set.)
The set of whole numbers less than 9.
Click here to see answer by solver91311(24713)

Question 1164997: The total profit P(x) for a company producing x thousand of pens is given by P(x)= -2x^2 + 26x + 44.
Find the values of x for which the company makes a profut when P(x)>0
Click here to see answer by Boreal(15235)

Question 1165002: Rex is doing a physics experiment with a steel ball. He throws it upwards with a velocity of 11m/s from a height of 1.2m. For what times is the height of the steel ball greater than 3m? Use height formula h = -16t^2 + Velocity(t) + height and round your answers to the nearest hundrendths of a second.
Click here to see answer by Alan3354(69443)

Question 1165072: A balloon is being inflated. If its radius is increasing at a speed of 2cm/s, determine its surface area as a function of time t. Begin with A(x)=4(pi)x^2.
This is the exact question on my assignment and I have no idea how to approach it. I think I am overthinking the question.
Click here to see answer by solver91311(24713)

Question 1165249: Change the math sentence, 25 + 27+ 29 > 81, into a verbal phrase using the terminology of
consecutive integers. Is there more than one way to write the phrase? If so, give another example.

Click here to see answer by ikleyn(52775)

Question 1165457: Can you please help me with this problem:
Write an inequality to compare the two numbers
Let a>0, b<0, c>0, a>c
Two numbers:
-a,|b|
I answered
-a < b
Click here to see answer by ikleyn(52775)

Question 1165641: What is the result of subtracting the second equation from the first?
-2x+y=0 and -7x+3y=2
Click here to see answer by Theo(13342)

Question 1165692: Three times the sum of a number and three is greater than the number decreased by two. Find all solutions.

Click here to see answer by josgarithmetic(39616)

Question 1165692: Three times the sum of a number and three is greater than the number decreased by two. Find all solutions.

Click here to see answer by ikleyn(52775)

Question 1165723: What is the interval notation 5n - 22 < - 13.2 + 3n in decimal form?
Click here to see answer by Boreal(15235)

Question 1165723: What is the interval notation 5n - 22 < - 13.2 + 3n in decimal form?
Click here to see answer by MathTherapy(10551)

Question 1165942: Which ordered pairs represent solutions to the linear inequality below
x - 4y < - 12
(1,-8)
(-8,-3)
(-12,0)
(3,5)
(-7,9)
(-4,2)
Click here to see answer by ikleyn(52775)

Question 1166074: I'm trying to solve this problem, and I'm not sure if I should change the inequality sign when (-x+5) is multiplied to the numerators. (These are fractions):
1/x+3 > 1/-x+5
Click here to see answer by Theo(13342)

Question 1166057: Y Greater than or equal to-5x-2
Click here to see answer by Alan3354(69443)

Question 1166092: I'm trying to check my answer. Can anyone please solve this too? (Absolute Inequality):
|x^2-9| > 0
Click here to see answer by ikleyn(52775)

Question 1166203: 3x - 8 less than or equal to 23 and -4x 26 greater than or equal to 6

Click here to see answer by josgarithmetic(39616)

Question 1166394: 2/5h-7=12/5h-2h+3
Click here to see answer by josgarithmetic(39616)

Question 1166539: between 15.000 yd 3 and 16.000 yd 3 of earth must be tucked away from a construction site . the trucks can remove 1000 yd 3 per day and 10.500 yd3 has already been removed how many days are needed
Click here to see answer by ikleyn(52775)

Question 1166565: The sum of twelve and a number is not greater than the sum of twice the number and -8
Click here to see answer by solver91311(24713)

Question 1166640: Jaunice is redecorating her room. She wants to paint a design on a
rectangular section of her wall that is at least 76.5 square feet. The height of the design will be 8.5 feet. What is the minimum length of the design Juanice will paint on the wall?
A. 8 feet
B. 8.5 feet
C. 9 feet
D. 9.5 feet
Click here to see answer by Boreal(15235)

Question 1166655: A company makes backpacks and briefcases. Daily output cannot exceed a total of 40 backpacks and briefcases. A maximum of 20 backpacks can be made in one day. The maximum daily output of briefcases is 30. How many of each bag can the company produce in a single day?
write a written inequality to express the answer
Click here to see answer by Edwin McCravy(20054)

Question 1167158: A volunteer is buying 10 blankets for the animal shelter. Shipping the blankets is a one time fee of $10.50. At most the volunteer has $75 to spend. What is the maximum amount the volunteer can spend for each blanket? Use b to represent the cost of each blanket, then write an inequality that would represent the situation. Solve the inequality and show your work to justify your answer.
Click here to see answer by Boreal(15235)

Question 1167262: what is
1.-4(x+10)-6=-3(x-2)
2.2/3(x-4)=2x
3.slove for h: A= l times W times H
Click here to see answer by Boreal(15235)

Question 1167350: A baker is making cakes.
She starts with 48 eggs.
She makes 10 cakes.
She has 18 eggs left over.
Which equation can be used to find the number of eggs, x, the baker uses in each cake?
Click here to see answer by josgarithmetic(39616)

Question 1167402: Solve the inequality: 2x^2+x<0
Click here to see answer by josgarithmetic(39616)

Question 1167405: What is the inverse function of f(x)=x^2-6x if x is less than or equal to 3?
Click here to see answer by josgarithmetic(39616)

Question 1167821: solve each polynomial inequality. Approximately to three decimal places if necessary?
(x + 4)(3x - 9) (x - 1) < 0
Click here to see answer by josgarithmetic(39616)

Question 1167831: The product of 4 and a number, decreased by 6, is at least the sum of 8 and twice the number. Write and solve an inequality to find the numbers that satisfy this condition.
Click here to see answer by josgarithmetic(39616)

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