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# Recent problems solved by 'scott8148'

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 Human-and-algebraic-language/331683: I have a word problem that I would like help simplifying. The sum of 2 numbers is 20,and the sum of their squares is 218.Find the numbers. I have created equations of x+y=20 and x*x+y*y= 218. but I am assuming I need to break down the second equation to substitute the value of 20 for the term x+y. Any help would be great Thanks Steve1 solutions Answer 237762 by scott8148(6628)   on 2010-08-13 20:19:11 (Show Source): You can put this solution on YOUR website!x + y = 20 ___ y = 20 - x substituting ___ x^2 + (20 - x)^2 = 218 ___ x^2 + 400 - 40x + x^2 = 218 x^2 - 20x + 91 = 0 ___ (x - 13)(x - 7) = 0 x = 13 (or 7) and y equals the other one
 Polynomials-and-rational-expressions/331450: A rectangular storage bin is to be made from a rectangular piece of sheet metal 12 cm by 10 cm, by cutting out equal corners of side x and bending up the sides. Find x if the storage bin is to hold 90cm³(volume). I got up to here and I am stuck 4x³ - 44x²+ 120x + 90 = 0 However, my question is worth 8marks and I dont think i am allowed to use a graphic calculator to work it out. How do i answer this question properly? 1 solutions Answer 237759 by scott8148(6628)   on 2010-08-13 19:06:15 (Show Source): You can put this solution on YOUR website!4x^3 - 44x^2 + 120x = 90 2x^3 - 22x^2 + 60x - 45 = 0 test for roots using [(factors of -45) / (factors of 2)] doesn't seem to be an integer value (maybe not rational) , so Guess-Divide-Average might be the way to solution
 Quadratic_Equations/331207: 60-16w+w^2 : please factor1 solutions Answer 237531 by scott8148(6628)   on 2010-08-12 19:28:54 (Show Source): You can put this solution on YOUR website!(10 - w)(6 - w)
 test/331298: factor: x to the second power minus ax minus bx plus ab1 solutions Answer 237528 by scott8148(6628)   on 2010-08-12 19:16:19 (Show Source): You can put this solution on YOUR website!(x - a)(x - b)
 Polynomials-and-rational-expressions/331304: please help me factor the following completely: 2x^2+5x+3 thanks!1 solutions Answer 237527 by scott8148(6628)   on 2010-08-12 19:14:21 (Show Source): You can put this solution on YOUR website!(2x + 3)(x + 1)
 Rate-of-work-word-problems/331397: Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together? 1 solutions Answer 237524 by scott8148(6628)   on 2010-08-12 19:10:55 (Show Source): You can put this solution on YOUR website!they each fill some FRACTION of the pool based on their individual rates ___ the fractions sum to ONE (the whole pool) (x / 30) + (x / 45) + (x / 90) = 1 3x + 2x + x = 90 ___ 6x = 90 ___ x = 15
 Linear-equations/330965: I have worked this problem several times and just want to be sure I did it correctly. I am supposed to solve with elimination. 2r-5s=-7 5r-2s=55 I came up with the solution of (289/21, 145/21) Can anyone tell me if this is correct?1 solutions Answer 237295 by scott8148(6628)   on 2010-08-11 17:09:44 (Show Source): You can put this solution on YOUR website!multiplying 1st equation by -5 ___ -10r + 25s = 35 multiplying 2nd equation by 2 ___ 10r - 4s = 110 adding resulting equations (eliminating r) ___ 21s = 145 ___ s = 145/21 substituting ___ 2r - 5(145/21) = -7 ___ 42r - 725 = -147 ___ 42r = 578 ___ r = 289/21
 Quadratic_Equations/330866: 4x(x-6)-5x(x-5)=2 sovle for x. I must admit on this one I'm totaly lost.1 solutions Answer 237290 by scott8148(6628)   on 2010-08-11 16:36:06 (Show Source): You can put this solution on YOUR website!distributing ___ 4x^2 - 24x - 5x^2 + 25x = 2 collecting terms ___ -x^2 + x = 2 ___ 0 = x^2 - x + 2 use quadratic formula to find x
 Equations/330725: 1/5 is greater than 3/16, but why? How do I do the math to figure out the answer myself? The problem that was given was: which number is smallest? A. 1/5 or B. 3/16 ? and I saw the answer but I want to know how they came up with that.1 solutions Answer 237094 by scott8148(6628)   on 2010-08-10 20:56:49 (Show Source): You can put this solution on YOUR website!make the denominators of the fractions the same , and then compare the numerators the LCD is 80 1/5 = 16/80 ___ multiplying numerator and denominator by 16 3/16 = 15/80 ___ multiplying numerator and denominator by 5
 Volume/330713: I have the following question Shown below. I really need help with it please. I have tried working it out but don't know if its right. I tried multiplying 8.3 x 10^13 square feet and 200 feet. then divide by 1.3 x 10^-9 but my answer does not show in my choices for the question. Any help will be greatly appreciated. The sahara desert covers about 8.3 x 10^13 square feet. The average depth of the sand is 200 ft A grain of sand has a volume of approxemately 1.3 x 10^-9 best estimate of the number of grains of sand in the sahara desert? Thank you1 solutions Answer 237090 by scott8148(6628)   on 2010-08-10 20:50:31 (Show Source): You can put this solution on YOUR website!(8.3 x 10^13)(200) = 1660 x 10^13 = 1.66 x 10^16 (1.66 x 10^16) / (1.3 x 10^-9) = 1.28 x 10^25 (approx) FYI: there may be an issue with significant figures ___ 200 (no decimal point) has one significant figure ___ "technically" , the answer should have only one significant figure also , what are the dimensions for the sand grain volume? ___ there may be a units conversion issue
 Quadratic_Equations/330706: how do i factor 9x^4+42 x^3+49x^21 solutions Answer 237088 by scott8148(6628)   on 2010-08-10 20:19:39 (Show Source): You can put this solution on YOUR website!x^2 (9x^2 + 42x + 49) x^2 (3x + 7) (3x + 7)
 Polynomials-and-rational-expressions/330704: Not sure how to write this equation. It is calculus fundamental concept review with real numbers. We have tried it a number of ways. Here goes. The answer is . We have tried it anumber of ways and can not get there from here. LOL. My book does not show me how to work through it. Can you? kizerfamily7@yahoo.com 1 solutions Answer 237085 by scott8148(6628)   on 2010-08-10 20:14:55 (Show Source): You can put this solution on YOUR website!multiplying any quantity by one does not change the value ___ one is anything divided by itself starting with the fraction ___ gives multiplying the first term "a" by to get a common denominator ___ adding the fractions ___ factoring the "a" in the numerator ___
 Equations/330671: Brenda can do a job in 10 days; Adam does the same job in 15 days. After Adam works alone for 3 days, Adam and Brenda work together and finish the job. How many days did Brenda work. (Answer is decimal)1 solutions Answer 237059 by scott8148(6628)   on 2010-08-10 18:23:32 (Show Source): You can put this solution on YOUR website!in the 3 days he works alone , Adam completes 3/15 or 1/5 of the job ___ Adam and Brenda then work together to complete the remaining 4/5 ___ Brenda's days are the same as the together days (t / 10) + (t / 15) = 4/5 multiplying by 30 (LCD) ___ 3t + 2t = 24 ___ 5t = 24
 Travel_Word_Problems/330052: Plane X leaves airport 1 and heads for airport 2 which is a distance of 2,700 km. At the same time, plane Y leaves airport 2 and heads for airport 1. Due to headwinds and tailwinds, Plane X's average speed is 100 kph greater than that of plane Y. If the two planes pass each other after 3 hours, find the speed of each plane.1 solutions Answer 237058 by scott8148(6628)   on 2010-08-10 18:12:31 (Show Source): You can put this solution on YOUR website!they close the distance of 2700 km in 3 hr , so the sum of their speeds is 2700/3 or 900 kph X + Y = 900 ___ and ___ X = Y + 100 substitute to solve the system
 Polynomials-and-rational-expressions/329908: x^3 + 5x^2 - 4x - 20 = 0 i know that's the cubic equation, but i seriously can't find a good equation to find the roots. I NEED HELP! x^4 + 9x^3 + 18x^2 = 0 i know this is a quartic trinomial, but i don't know how to solve this and the paper expects 4 roots. (3x + 1)(2x + 7) = 0 i think i set these equal to zero, but am i supposed to get a fraction?1 solutions Answer 237054 by scott8148(6628)   on 2010-08-10 17:32:40 (Show Source): You can put this solution on YOUR website!grouping ___ (x^3 + 5x^2) - (4x + 20) factoring ___ x^2(x + 5) - 4(x + 5) rearranging ___ (x^2 - 4)(x + 5) factoring (difference of squares) ___ (x + 2)(x - 2)(x + 5) factoring ___ x^2(x^2 + 9x +18) = 0 factoring again ___ (x)(x)(x + 6)(x + 3) = 0 ___ x = 0 is a double root roots do NOT have to be whole numbers (or rational , for that matter)
 Trigonometry-basics/330482: Having trouble understanding the conceopts behind evaluating inverse functions, please help!.. Tan^-1 (Sin pi/6) The book answe is 0.4636 but i don't know how to get there,...1 solutions Answer 237053 by scott8148(6628)   on 2010-08-10 17:21:14 (Show Source): You can put this solution on YOUR website!translation from trig to english ___ the angle whose tangent is the sine of pi/6 2pi rad in a circle , so pi/6 is 30º ___ sin(30º) = .5 .5 is the tangent of 26.57º or .4636 rad
 Human-and-algebraic-language/330435: the number of chipmunks varied directly as the number of acorns in the forest. it took 100 accorns to feed 5 chipmunks, how many acorns will it take to feed 30 chipmunks?1 solutions Answer 236839 by scott8148(6628)   on 2010-08-09 23:33:08 (Show Source): You can put this solution on YOUR website!6 times as many chipmunks means 6 times as many acorns
 Polynomials-and-rational-expressions/330429: factor completely. 9a^2-1001 solutions Answer 236838 by scott8148(6628)   on 2010-08-09 23:31:59 (Show Source): You can put this solution on YOUR website!difference of squares (3a + 10)(3a - 10)
 Radicals/330436: Hello, Need to find the exact and approximate solutions to three decimal places for the following: (x-6)^2=20. I am unable to solve, and have even tried using Algebrator, but cannot interpret. Thanks!1 solutions Answer 236836 by scott8148(6628)   on 2010-08-09 23:30:12 (Show Source): You can put this solution on YOUR website!taking square root ___ x - 6 = ± sqrt(20) = ± 2 sqrt(5) adding 6 ___ x = 6 ± 2 sqrt(5) use calculator to find 2 sqrt(5) , add to and subtract from 6
 test/330348: Julie and Eric row their boat at a constant speed 40 miles downstream for 4 hours helped by the current rowing at the same rate the trip back against the current takes 10 hours find the rate of the cirrent1 solutions Answer 236831 by scott8148(6628)   on 2010-08-09 22:41:39 (Show Source): You can put this solution on YOUR website!b + c = 40 / 4 = 10 b - c = 40 / 10 = 4 subtracting equations ___ 2c = 10 - 4
 Human-and-algebraic-language/330401: the pressure of a quantity of an ideal gas was held constant. the initial volume and volume and temperature were 20 liters and 273 K, respectively. what would be the final temperature if the final volume was 30 liters?1 solutions Answer 236830 by scott8148(6628)   on 2010-08-09 22:35:51 (Show Source): You can put this solution on YOUR website!at constant pressure , the volume and absolute temperature are directly related 20 / 30 = 273 / t t = (30 * 273) / 20
 Inequalities/330388: I need to solve |4x-1|≤4 This is absolute value and inequality but I cannot figure it out. Thanks in advance for your help.1 solutions Answer 236829 by scott8148(6628)   on 2010-08-09 22:29:41 (Show Source): You can put this solution on YOUR website!the absolute value of the quantity must be less than or equal to 4 this means the quantity must be greater than (or equal to) -4 ... (-3 , -2 , -1 ,etc.) ___ AND less than (or equal to) 4 ... (3 , 2 , 1 , etc) -4 ≤ (4x - 1) ≤4 adding 1 ___ -3 ≤ 4x ≤ 5 dividing by 4 ___ (-3/4) ≤ x ≤ (5/4)
 Quadratic_Equations/330287: Jack usually mows his lawn in 4 hours. Marilyn can mow the same lawn in 7 hours. How much time would it take for them to mow the lawn together? It would take tham how many hours of they worked together? 1 solutions Answer 236795 by scott8148(6628)   on 2010-08-09 20:44:22 (Show Source): You can put this solution on YOUR website!they each mow a FRACTION of the lawn , based on their individual times ___ the fractions sum to one , the whole lawn let t="time together" (t / 4) + (t / 7) = 1 multiplying by 28 (the LCD) ___ 7t + 4t = 28 ___ 11t = 28
 Linear_Equations_And_Systems_Word_Problems/330362: A plane with a tail wind makes its 785-mile flight in 2.5 hours. The return flight against the wind takes a half hour longer. What is the wind speed (rounded to the nearest mile per hour)? 1 solutions Answer 236794 by scott8148(6628)   on 2010-08-09 20:36:45 (Show Source): You can put this solution on YOUR website!p + w = 785 / 2.5 p - w = 785 / 3 subtracting equations ___ 2w = (785 / 2.5) - (785 / 3)
 Exponential-and-logarithmic-functions/330357: what is the expontential form of In 5 = r1 solutions Answer 236781 by scott8148(6628)   on 2010-08-09 20:11:34 (Show Source): You can put this solution on YOUR website!guessing it should be ln(5) , natural log of 5 5 = e^r "e" is Euler's Number , the base for natural logs
 Distributive-associative-commutative-properties/330344: Word problem: Jon's father is 3 times as old as Jon. Four years ago he was 4 times older. How old is Jon? Create an algebraic equation and solve by using the distributive law. (I know distributive law, I cannot figure out how to set problem up to solve it) Thanks!1 solutions Answer 236780 by scott8148(6628)   on 2010-08-09 20:07:06 (Show Source): You can put this solution on YOUR website!"Jon's father is 3 times as old as Jon" ___ f = 3j "Four years ago he was 4 times older" ___ f - 4 = 4(j - 4) substituting ___ (3j) - 4 = 4(j - 4)
 Graphs/330209: re: inverse variation (y = k/x) problem: speed of bus inversely proportional to time (t) that it takes to travel fixed distance at 30 mph in 80 minuntes; how fast does bus need to travel to cover same distance in 20 minutes. If speed is inversely proportional to time, do I set speed = 1/time? I am unclear on how to set up equation - thanks for help.1 solutions Answer 236755 by scott8148(6628)   on 2010-08-09 17:54:47 (Show Source): You can put this solution on YOUR website!speed = distance / time the distance is ___ 30 mph times 4/3 hr (80 min) or 40 miles 30 mph = 40 mi / 80 min x = 40 mi / 20 min FYI: this is a REALLY fast bus
 Equations/330290: find the center and the radius of the circle x^2+y^2+8x-10y=51 solutions Answer 236753 by scott8148(6628)   on 2010-08-09 17:43:01 (Show Source): You can put this solution on YOUR website!completing the squares ___ x^2 + 8x + 16 + y^2 - 10y + 25 = 5 + 16 + 25 (x + 4)^2 + (y - 5)^2 = 46 center is (-4 , 5) ___ radius is sqrt(46)
 Expressions-with-variables/330064: Hi! Can you please help me solve: s = -1/2gt^2 + vt for g Thank you so much! 1 solutions Answer 236521 by scott8148(6628)   on 2010-08-08 23:25:39 (Show Source): You can put this solution on YOUR website!subtracting vt ___ s - vt = -(1/2)gt^2 multiplying by -2 ___ -2(s - vt) = gt^2 dividing by t^2 ___ [-2(s - vt)] / t^2 = g
 Probability-and-statistics/330070: The standardized mathematics scores of a certain school district are normally distributed with the mean of 500 and standard deviation 100. Find the probability that a score is less than 300? I have no idea where to start. a clue would be great. Have another homework question just like it.1 solutions Answer 236520 by scott8148(6628)   on 2010-08-08 23:20:14 (Show Source): You can put this solution on YOUR website!a score of 300 is two standard deviations below the mean ___ z = -2 a z-score table will show that the probability of this is ___ .0228
 Polynomials-and-rational-expressions/329999: am trying to help my stepdaughter with this problem if you could please help!! It is not showing ÷m-1 on preview so I will do problem again to verify for you}1 solutions Answer 236497 by scott8148(6628)   on 2010-08-08 21:29:40 (Show Source): You can put this solution on YOUR website!this is like "old style" long division m goes into m^3 , m^2 times ___ m^2 times (m-1) is (m^3 - m^2) ___ (m^3 + 3m^2) minus (m^3 - m^2) is 4m^2 ___ bring down -5m m goes into 4m^2 , 4m times ___ 4m times (m-1) is (4m^2 - 4m) ___ (4m^2 - 5m) minus (4m^2 - 4m) is -m ___ bring down +1 m goes into -m , -1 times ___ -1 times (m-1) is (-m + 1) ___ (-m + 1) minus (-m + 1) is zero (no remainder) (m^3 + 3m^2 - 5m + 1) / (m - 1) = 4m^2 - m - 1