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# Recent problems solved by 'oberobic'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309, >>Next

 percentage/523662: 43.2 is what percent of 1081 solutions Answer 347363 by oberobic(2304)   on 2011-10-30 21:28:17 (Show Source): You can put this solution on YOUR website!To calculate percentage: . 43.2/108 * 100 = 40% . Done.
 Linear_Equations_And_Systems_Word_Problems/523649: sue bought 4 packs of cookies and 3 sacks of potato chips for 5.01. Later she bought 3 pack of cookies and 5 sacks of potato chips for 5.27. what is the price of a pack of cookies? 1 solutions Answer 347362 by oberobic(2304)   on 2011-10-30 21:22:47 (Show Source): You can put this solution on YOUR website!c = cookies p = potato chips . 4c + 3p = 501 cents 3c + 5p = 527 cents . multiply the first equation by 3 and the second equation by 4 and then subtract . 12c + 9p = 1503 12c + 20p = 2108 ------------------ -11p = -605 . p = 55 cents . substitute to find 'c' . 4c + 3(55) = 501 4c = 501 -165 4c = 336 . c = 84 cents . use the other equation to check these values . 3(84) + 5(55) = 527 . Answer: Potato chips cost 55 cents, and cookies cost 84 cents. . Done.
 Linear-systems/523644: the line has a slope of -2/3 and passes through (6,12)1 solutions Answer 347355 by oberobic(2304)   on 2011-10-30 21:00:38 (Show Source): You can put this solution on YOUR website!Given the line has slope -2/3 we can define the equation using slope-intercept form: . y = -2/3x + b . Use the point to find 'b'. . 12 = -(2/3)*6 + b 12 = -4 + b 16 = b . So the equation is: . y = -2/3x + 16 .
 Numbers_Word_Problems/523638: the sum of three numbers is 237. the second number is 9 less than two times the first number. the third number is 6 more than three times the first number. what are the three numbers?1 solutions Answer 347352 by oberobic(2304)   on 2011-10-30 20:52:06 (Show Source): You can put this solution on YOUR website!x + y + z = 237 . y = 2x -9 . z = 3x +6 . substitute . x +2x-9 +3x+6 = 237 . 6x -3 = 237 . 6x = 240 . x = 40 . substitute . y = 2x -9 y = 2*40 -9 y = 71 . z = 3x +6 z = 3*40 +6 z = 126 . Check the sum . 40 + 71 + 126 = 237 . Answer: The three numbers are 40, 71, and 126. . Done.
 Numeric_Fractions/523614: what is 7 1/4 minus 2 3/41 solutions Answer 347348 by oberobic(2304)   on 2011-10-30 20:45:59 (Show Source): You can put this solution on YOUR website!7 1/4 - 2 3/4 = 29/4 - 11/4 = 18/4 = 4 2/4 = 4 1/2
Quadratic-relations-and-conic-sections/523603: graph the following parabola: (x-4)^2=4(y-1)
1 solutions

Answer 347345 by oberobic(2304)   on 2011-10-30 20:40:25 (Show Source):
You can put this solution on YOUR website!
(x-4)^2 = 4(y-1)
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x^2 -8x + 16 = 4y -4
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4y-4 = x^2 -8x + 16
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4y = x^2 -8x +20
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y = (1/4)*x^2 -2x + 5
.

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You will notice the parabola does not cross or touch the x-axis, so there are no solutions with real numbers. You can confirm this with the quadratic equation.
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 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . The discriminant -1 is less than zero. That means that there are no solutions among real numbers. If you are a student of advanced school algebra and are aware about imaginary numbers, read on. In the field of imaginary numbers, the square root of -1 is + or - . The solution is Here's your graph:

 Linear_Algebra/523618: Solve graphically: 3y = 5 - x and 2x = y + 3. Write down the co-ordinates of the point of intersection of the two lines1 solutions Answer 347341 by oberobic(2304)   on 2011-10-30 20:28:25 (Show Source): You can put this solution on YOUR website!3y = 5 -x 3y = -x +5 y = -(1/3)x + 5/3 . 2x = y + 3 2x -3 = y y = 2x -3 . In the graph that follows: The red line is y = -(1/3)x + 5/3 The green line is y = 2x -3 . , It appears the point (2,1) satisfies both equations. . Check: y = -(1/3)*2 + 5/3 y = -2/3 + 5/3 y = 3/3 = 1 . y = 2*2-3 y = 4 -3 y = 1 . Correct.
 Numbers_Word_Problems/523607: What number multiplied by the numerator and added to the denominator of the fraction 2/5 makes the resulting fraction 3/4?1 solutions Answer 347340 by oberobic(2304)   on 2011-10-30 20:19:59 (Show Source): You can put this solution on YOUR website! . . cross multiply . .
 Linear_Algebra/523616: hi..I have a problem that says x=-3, y=9..What do I do?1 solutions Answer 347338 by oberobic(2304)   on 2011-10-30 20:16:55 (Show Source): You can put this solution on YOUR website!That appears to define the point (-3,9). You could graph the point. But if that's all the information you have, there's not much that can be done with.
 Functions/523528: I need to find the domain of this equation: f(x)=4/3x+71 solutions Answer 347325 by oberobic(2304)   on 2011-10-30 18:16:17 (Show Source): You can put this solution on YOUR website!It appears your equation is: so x can range from -infinity to +infinity . However, if your equation in fact is: If so, x cannot = 0 cannot because that would be dividing by 0. So the domain is -infinity to 0, and 0 to +infinity. . In the following graph; the red line is y = (4/3)x+7 the green line is y=4/(3x)+7 .
 Volume/523491: a standard 8/1/2x11. sheet of paper is rolled along its short side to form a cylinder as shown. a second sheet of the same measurements as the first one is rolled along its longer side to forma second cylinde. .there is no overlap .will the taller cylinder have the same volume, greater volume, or less volume than that of the short cylinder?1 solutions Answer 347324 by oberobic(2304)   on 2011-10-30 18:06:13 (Show Source): You can put this solution on YOUR website!One cylinder will have dimensions as follows: circumference = 8.5 = pi*d = pi*2*r r = (8.5)/ (2*pi) height = 11 area of base of cylinder = pi*r^2 = pi * ( 8.5/(2*pi) )^2 volume = 11 *pi * ( 8.5/(2*pi) )^2 = 198.6875/pi . The other cylinder: circumference = 11 r = 11/ (2*pi) height = 8.5 area of base = pi * ( 11/(2*pi) )^2 volume = 8.5* pi * ( 11/(2*pi) )^2 = 257.125/pi .
 Numbers_Word_Problems/523497: the second of two numbers is 6 times the first. Their sum is 77. Find the numbers.1 solutions Answer 347323 by oberobic(2304)   on 2011-10-30 17:26:35 (Show Source): You can put this solution on YOUR website!x = 6y . x + y = 77 so x = 77-y . x = x so . 6y = 77-y . 7y = 77 . y = 11 . x = 6*11 . x = 66 . Answer: The two numbers are 11 and 66.
 Numeric_Fractions/523490: how would i do the following problem 2/3+1/2 divided by 3/4 1 solutions Answer 347322 by oberobic(2304)   on 2011-10-30 17:22:48 (Show Source): You can put this solution on YOUR website!(2/3+1/2) / (3/4) = (4/6 + 3/6) / (3/4) = (7/6)/(3/4) = (7/6)*(4/3) = 28/18 = 14/9
 Rate-of-work-word-problems/523482: working alone jennifer can pick forty bushels of apples in 12 hours . tosakan can pick the same amount in 10 hours .how long would it take them if they worked together1 solutions Answer 347320 by oberobic(2304)   on 2011-10-30 17:10:20 (Show Source): You can put this solution on YOUR website!Work problems like this are solved by using fractions. . Jennifer can pick 40 bushels of apples in 12 hours. We can define "picking 40 bushels of apples" as 1 whole job. She does 1/12 of the job per hour. . Tosakan can do the job in 10 hours. She does 1/10 of the job per hour. . x = number of hours working together to do the job . (1/12 + 1/10)*x hours = 1 whole job . (1/12 + 1/10)*x = 1 . 22/120*x = 1 . 22x = 120 . x = 120/22 = 60/11 . 60/11 = 5 5/11 hours . 5/11 hr * 60 min/hr = 300/11 = 27.27272727272727 or about 27.3 min. . Working together they can do the job in 5 5/11 hr or about 5 hr and 27.3 min. . Always check your solution to see if it is the answer. . How many bushels does Jennifer pick in 60/11 hr? She picks 40 in 12 hr, so she picks 10/3 bushels per hr. 60/11 hr * 10/3 bushels/hr = 600/33 = 200/11 = 18.18181818181818 bushels . How many bushels does Tosakan pick in 60/11 hr? She picks 40 in 10 hr, so she picks 4 bushels per hr. 60/11 hr * 4 bushels/hr = 240/11 = 21.81818181818182 bushels . Answer: They can pick 40 bushels in 5 5/11 hr working together. . Done.
 Numbers_Word_Problems/523463: the sum of two numbers is twelve. the square of the smaller is subtracted from the product the result is ten.Find the numbers1 solutions Answer 347319 by oberobic(2304)   on 2011-10-30 16:52:22 (Show Source): You can put this solution on YOUR website!x + y = 12 so x = 12-y . x*y - x^2 = 10 so x*y = x^2 +10 y = x + 10/x . substitute for x . (12-y)*y -(12-y)^2 = 10 . 12y -y^2 - ( (12-y)(12-y) ) = 10 . 12y - y^2 -144 +24y - y^2 = 10 . -2y^2 +36y -144 = 10 . -2y^2 +36y -154 = 0 . y^2 -18y + 77 = 0 . (y-7)(y-11) = 0 . So y = 7 or 11 . x + y = 12 so If y =7, x = 5 If y = 11, x = 1 . Using ordered pair (x,y) notation, the solutions are: (1,11) and (5,7). . In the following graph: red line is y = -x+12 green line is y = x + 10/x .
 Numbers_Word_Problems/523468: what two consecutive integers sum is 1751 solutions Answer 347318 by oberobic(2304)   on 2011-10-30 16:39:57 (Show Source): You can put this solution on YOUR website!Define the two consecutive integers as follows: x x+1 . x +x+1 = 175 2x = 174 x = 87 x+1 = 88 87+88 =175 . Answer: The two numbers are 87 and 88.
 Numbers_Word_Problems/523469: The mean of five numbers is 10.If a new number is added then the mean becomes 12.Find the value of that number1 solutions Answer 347317 by oberobic(2304)   on 2011-10-30 16:37:53 (Show Source): You can put this solution on YOUR website!The sum of 5 numbers divided by 5 = 10, which is the average (i.e., the arithmetic mean). So, the sum of the 5 numbers is 5*10 = 50. . When we add a number, the average is increased to 12. . (50+x)/6 = 12 . 50+x = 72 . x = 22 . Done.
 Numbers_Word_Problems/523466: One number is twice the other and their product is equal to six times the larger.Find the numbers1 solutions Answer 347315 by oberobic(2304)   on 2011-10-30 16:33:57 (Show Source): You can put this solution on YOUR website!x = 2y . Note that that means x > y. . The product = 6 times the greater number. . x*y = 6x . Substitute x = 2y . 2y*y = 6(2y) . 2y^2 -12y = 0 . 2y(y-6) = 0 . y = 0 or 6 . Zero works quite nicely. Zero times anything is zero. So, x*0 = 6*x is true. In this case, x can be any number from -infinity to +infinity. This means there is no ordered pair. (x,0) for any x. This probably is a spurious solution, which means it is one that is not relevant to the practical problem at hand. . But how about y=6? . x = 2y x = 2(6) x = 12 . Their product = 12*6 = 72. 6*12 = 72. Correct. . Answer: The two numbers are 6 and 12. . Done.
 Numbers_Word_Problems/523457: The perimeter of a triangle is 48. The sides are the sum of three consecutive integers that are multiples of four. Find each side.1 solutions Answer 347314 by oberobic(2304)   on 2011-10-30 16:23:26 (Show Source): You can put this solution on YOUR website!The notion of three consecutive numbers that are divisible by 4 has to be interpreted. On the number, there is no instance where three consecutive numbers are divisible by 4. So it must mean that you are find three numbers that are multiples of 4 in sequence, but not really "consecutive" in the common meaning of the word "consecutive." So, we can define the three numbers a: x = a number that, we hope, is divisible by 4 x + 4 = the next number that would be divisible by 4, given x is divisible by 4 x + 8 = the next number that would be divisible by 4, given x+4 is divisible by 4 . x +(x+4) + (x+8) = 48 3x +12 = 48 3x = 36 x = 12 so x+4 = 16 x+8 = 20 . 12+16+20 = 48 . Answer: The three numbers are 12, 16, and 20. . Done.