Questions on Algebra: Expressions involving variables, substitution answered by real tutors!

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Question 421830: -4x-2y=-8 y=-2x+4
Click here to see answer by ikleyn(53339)

Question 730274: A company manufactures an alarm clock. Three weeks ago the had 250 on hand. Two weeks from now it will have 500. Assume the company will continue to make the clocks at this same rate

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Question 733492: how would i solve this equation : (2t)^4*3^3
Click here to see answer by josgarithmetic(39675)

Question 733492: how would i solve this equation : (2t)^4*3^3
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Question 737462: The width of a rectangle is 18 feet less than the perimeter. the area of the rectangle is 2,040 square feet. What are the dimensions of the rectangle?
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Question 612274: I have two algebra I word problems i need help setting up. I would like if you can explain the steps of setting up.
Here it is:
Problem #1
The length of a rectangle is 2 1/2 times its width. Its area is 90 square units. What are its dimensions? (Hint: length times width = area)
Let w= width in units.
L=(2 1/2)w= 5w/2 = length in units

Click here to see answer by MathTherapy(10579)

Question 747745: Some of Aaron's friends are planning to buy him a gift worth 270, dividing the cost equally among themselves. Six more of his friends decided to share in the expenses and so each one's share is decreased by 12. How many friends were originally part of the plan?
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Question 869743: The sum of 4 times a number and 2 is 18. What is the number?
Click here to see answer by timofer(132)

Question 479860: I am working on my math packet for school. I came across a section in it, in which i completely forgot how to do. i asked my family and they helped me on most of the problems but they couldn't help me figure this one out.
I am suppose to determine the answer for each problem. Simplify when possible:
Here is the equation:
I've tried combining the "x"s and I have also tried using the order of operations but no matter what i use, it seems like i can't solve it.
If you could go through each step and explain what you did and why you did it, i would make it much easier for me to understand and i would greatly appreciate it.

Click here to see answer by ikleyn(53339)

Question 500890: please help me with this question.
Express in terms of odd and even numbers why the number 286 would not appear in the series 4, 12, 24, 40... ?

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Question 553434: solve the system of equations using the substitution method
x+z=8
y-z=5
x-y=9
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Question 553434: solve the system of equations using the substitution method
x+z=8
y-z=5
x-y=9
Click here to see answer by ikleyn(53339)

Question 1160143: How would I write the following so the coefficient is in front?
1. (3y)8
2. 3(4b)
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Question 1209923: Let x, y, and z be real numbers. If x^2 + y^2 + z^2 = 1, then find the maximum value of
3x + 4y + 5z + x^3 + \frac{4x^2*y)/{z} + \frac{z^5}{xy^2}
Click here to see answer by ikleyn(53339)

Question 1210272: (-9x + 57)^x = 729,
find x.
Click here to see answer by Edwin McCravy(20077)

Question 1209973: Let a and b be positive real numbers. Let
m = \min \left\{ a, \frac{1}{b}, b^2 + \frac{1}{a + 1} \right\}.
Find the largest possible value of m.

Click here to see answer by mccravyedwin(417)

Question 1209926: (a) Let x, y, and z be positive real numbers. Find the largest possible value of
\sqrt{\frac{3x + 5y + 2z}{6x + 5y + 4z}} + \sqrt{\frac{2x + 5y + z}{6x + 5y + 5z}} + \sqrt{\frac{9x + y + 4z}{6x + 5y + 4z}}.

(b) Find \frac{z}{x} if (x,y,z) is a triple that gives the maximum value in Part (a).

Click here to see answer by mccravyedwin(417)

Question 1209935: Let a, b, and c be positive real numbers. If a + b + c = 1, then find the minimum value of
\frac{1}{a} + \frac{1}{b} + \frac{1}{c*a^2} + \frac{2}{ab^2} + \frac{8}{c^3}.
Click here to see answer by CPhill(2138)

Question 1209936: Let a, b, and c be positive real numbers. If a + b + c = 1, then find the minimum value of
\frac{1}{a} + \frac{1}{b} + \frac{4}{c*a^2} + \frac{16}{b^4*a} + \frac{32}{a*b^3}
Click here to see answer by CPhill(2138)

Question 1209927: The real numbers x_1, x_2, x_3, x_4, and x_5 satisfy
x_1 + x_2 + x_3 + x_4 + x_5 = 8,
x_1^2 + x_2^2 + x_3^2 + x_4^2 + x_5^2 = 12,
x_1^3 + x_2^3 + x_3^3 + x_4^3 + x_5^3 = 16.

Let m be the smallest possible value of x_5, and let M be the largest possible value of x_5. Enter the ordered pair (m,M).

Click here to see answer by CPhill(2138)

Question 1209925: Let x_1, x_2, \dots, x_{100} be real numbers. If
x_1^2 + 2x_2^2 + \dots + 100x_{100}^2 = 1,
then find the maximum value of x_1/1 + x_2/2 + \dots + x_{100}/100.
Click here to see answer by CPhill(2138)

Question 1209918: Let x_1, x_2, \dots, x_n be real numbers. If
x_1 + 2x_2 + \dots + nx_n = 1,
then find the minimum value of x_1^2/1 + x_2^2/2 + \dots + x_n^2/n, in terms of n.

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Question 1209919: Let x_1, x_2, \dots, x_n be real numbers. If
x_1^2 + 2x_2^2 + \dots + nx_n^2 = 1,
then find the maximum value of (x_1 + x_2/2 + \dots + x_n/n)^2, in terms of n.
Click here to see answer by CPhill(2138)

Question 1209917: Let a, b, and c be positive real numbers. Find the minimum value of
(a + 1)^2 + \left( \frac{b}{a} + a + 1 \right)^2 + \left( \frac{c}{b} + abc \right)^2 + \left( \frac{4}{c} + \frac{c}{a} \right)^2.
Click here to see answer by CPhill(2138)

Question 1209912: Let x and y be positive real numbers. If x + y = 1, then find the maximum value of xy + y^3.

Click here to see answer by mccravyedwin(417)

Question 1209912: Let x and y be positive real numbers. If x + y = 1, then find the maximum value of xy + y^3.

Click here to see answer by math_tutor2020(3827)

Question 1209912: Let x and y be positive real numbers. If x + y = 1, then find the maximum value of xy + y^3.

Click here to see answer by greenestamps(13248)

Question 1209914:
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Question 1209913:
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Question 1209908: Let w, x, y, and z be positive real numbers. If w + 2x + 3y + 6z = 8 - w^2 - x^2 - y^2 - z^2, then what is the maximum value of wxyz?
Click here to see answer by ikleyn(53339)

Question 1209908: Let w, x, y, and z be positive real numbers. If w + 2x + 3y + 6z = 8 - w^2 - x^2 - y^2 - z^2, then what is the maximum value of wxyz?
Click here to see answer by CPhill(2138)

Question 1209906: Let a and b be positive real numbers. Find the minimum value of
(a + b) \left( \frac{1}{a + 1} + \frac{1}{b + 1} \right)

Click here to see answer by ikleyn(53339)

Question 1209906: Let a and b be positive real numbers. Find the minimum value of
(a + b) \left( \frac{1}{a + 1} + \frac{1}{b + 1} \right)

Click here to see answer by CPhill(2138)

Question 1209892: Find the smallest positive real number x such that
\lfloor x^2 \rfloor - x \lfloor x \rfloor = \lfloor x^3 \rlfoor/x

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Question 1179440: In Exercises 1 - 3, Monica is at a bowling center. By becoming a member for
$30, she gets a 15% discount on her bowling cost.
Build a function-machine network using the nonmember bowling cost as
the input. The output is Monica’s bowling cost with membership.
Suppose b is the cost of one night’s bowling for nonmembers. Find a rule
for M(b), Monica’s discounted cost. Do not include the membership fee.
Click here to see answer by ikleyn(53339)

Question 1185331: Find the inverse Laplace transform f(t)=L^(−1){F(s)} of the function
F(s)=(e^(−s)(6s−5))/(s^2+64)
You may use h(t) for the Heaviside step function.
f(t)=L^(−1){(e^(−s)(6s−5))/(s^2+64)}=
My answer is h(t-1)(6cos(8h(t-1)))-5/8sin(8h(t-1)) , wrong
Click here to see answer by CPhill(2138)

Question 1209353: Find all values of c such that 3(2c+1) = 28*3c - 9. If you find more than one value of c, then list your values in increasing order, separated by commas.
Click here to see answer by josgarithmetic(39675)

Question 1209333: How many pairs of integers (a,b) satisfy the equation ab^a = 648?
Click here to see answer by greenestamps(13248)

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, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390