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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

 Polygons/531562: The sum of the interior angles of a regular polygon is 2340 degrees. How many sides does the polygon have?1 solutions Answer 350500 by oberobic(2304)   on 2011-11-14 18:26:57 (Show Source): You can put this solution on YOUR website!The sum of the interior angles of a polygon is (n-2)*180, where n = number of sides. . (n-2)*180 = 2340 . (n-2) = 2340/180 = 13 . n - 2 = 13 . n = 15
 Equations/531541: Four times a number minus twice another number is -16. The sum of the two numbers is -1.1 solutions Answer 350497 by oberobic(2304)   on 2011-11-14 18:16:27 (Show Source): You can put this solution on YOUR website!x + y = -1 so x = -y-1 . 4x -2y = -16 . substitute . 4(-y -1) -2y = -16 . -4y -4 -2y = -16 . -6y = -12 . y = 2 . x + y = -1 . x + 2 = -1 . x = -3 . Answer: x = -3, y = 2 . Done.
 Mixture_Word_Problems/531551: The manager of a food store wants to create a blend of herbs that she can sell for \$1 per once. She decides to make 8 ounces of a blend of oregano and sage. What will be the ratio of oregano to sage in the mixture?1 solutions Answer 350492 by oberobic(2304)   on 2011-11-14 18:11:41 (Show Source): You can put this solution on YOUR website!What do oregano and sage cost?
 Travel_Word_Problems/531544: if you drive 40 miles per hour then how long does it take to drive 60 miles1 solutions Answer 350489 by oberobic(2304)   on 2011-11-14 18:10:58 (Show Source): You can put this solution on YOUR website!d = r*t r = 40 mph d = 60 miles t = d/r = 60/40 = 3/2 = 1 1/2 hr
 Graphs/531520: how do you solve 10a-37=6a+511 solutions Answer 350481 by oberobic(2304)   on 2011-11-14 17:55:36 (Show Source): You can put this solution on YOUR website!You have to remember to do the same thing to both sides of the equation, whatever that might be. . 10a-37=6a+51 . Subtract 6a from both sides. That will cancel the 6a on the right side, so that all 'a' terms are on the left side. . 4a -37 = 51 . Add 37 to both sides. That will cancel the -37 on the left. . 4a = 88 . Divide both sides by 4. That will eliminate the coefficient on 'a'. . a = 22 . Always check the solution to make sure it is the correct answer. Substitute 22 for 'a' and check the values. . 10*22 -37 = 220 -37 = 183 6*22 + 51 = 132 + 51 = 183 183 = 183 Correct. . Answer: a = 22 . P.S. In the old days, teachers talked about "moving" factors from one side of the equation to the other. After years of confusion and frustration, I ran into a math teacher who explained that you have to do the same time to both sides. You cannot just "move" anything from one side to the other.
 Equations/531529: -20=-4x-6x can you explain how to solve that equation ? 1 solutions Answer 350477 by oberobic(2304)   on 2011-11-14 17:45:12 (Show Source): You can put this solution on YOUR website!-20 = -4x -6x . combine like terms . -20 = -10x . divide both sides by -10 . 2 = x . x = 2
 Rational-functions/531502: graph y=(x+5)^2+51 solutions Answer 350475 by oberobic(2304)   on 2011-11-14 17:42:21 (Show Source): You can put this solution on YOUR website!y = (x+5)^2 + 5 y = x^2 +10x +25 +5 y = x^2 +10x +30 . You know this is a parabola. So find several values of x to calculate values of y. . The axis of symmetry is where x = -b/2a. -10/2 = -5 . The vertex is where the parabola ends. It occurs on the axis of symmetry. y = (-5)^2 +10(-5) + 30 y = 25 -50 + 30 y = 5 . Pick several points to either side of the vertex. x = -4, y = 6 x = -6, y = 6 x = 0, y = 30 x = -10, y = 30 x = 5, y = 105 x = -15, y = 105 .
 Equations/531510: The perimeter of a rectangle is 50 centimeters. The length of the rectangle is one more than 3 times the width of the rectangle. What are the dimensions of the rectangle? 1 solutions Answer 350472 by oberobic(2304)   on 2011-11-14 17:29:24 (Show Source): You can put this solution on YOUR website!P = 50 P = 2(L+W) L+W = 25 . L = 3W + 1 . 3W+1 +W = 25 4W = 24 W = 6 L = 3W+1 L = 19 . Answer: Length = 19 cm, Width = 6 cm
 Numbers_Word_Problems/531511: what is the expression for six minus the quotient of twenty five and five1 solutions Answer 350470 by oberobic(2304)   on 2011-11-14 17:26:56 (Show Source): You can put this solution on YOUR website!6 - 25/5 = 6-5 =1
 Linear-equations/531426: What is the line(In slope intercept form) that passes through the points (-3,3) and (1,2)?1 solutions Answer 350461 by oberobic(2304)   on 2011-11-14 16:17:33 (Show Source): You can put this solution on YOUR website!m = (3-2)/(-3-1) m = 1/-4 m = -(1/4) . y = -1/4*x + b . use the point (1,2) to find 'b' . 2 = -1/4(1) +b 2 + 1/4 = b b = 9/4 . y = -1/4x +9/4 .
 Inverses/531455: what is 2x-3x=11?1 solutions Answer 350460 by oberobic(2304)   on 2011-11-14 16:11:35 (Show Source): You can put this solution on YOUR website!2x -3x = 11 -x = 11 x = -11
Numbers_Word_Problems/531458: when the sum of 5 and three times a positive number is subtracted from the square of the number, 0 rusults
1 solutions

Answer 350459 by oberobic(2304)   on 2011-11-14 16:07:11 (Show Source):
You can put this solution on YOUR website!
x^2 -(3x +5) = 0
x^2 -3x -5 = 0
 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 : . Discriminant d=29 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4.19258240356725, -1.19258240356725. Here's your graph:

 Numbers_Word_Problems/531454: the sum of three consecutive integers is 18721 solutions Answer 350458 by oberobic(2304)   on 2011-11-14 16:05:01 (Show Source): You can put this solution on YOUR website!Define 3 consecutive integers as: x x+1 x+2 . x +x+1 +x+2 = 1872 3x + 3 = 1872 3x = 1869 x = 623 x+1 = 624 x+2 = 625 . Answer: The three consecutive integers are 623, 624, and 625. . Done.
 Travel_Word_Problems/531453: after driving 136 km, 4/7 of a trip is comleted1 solutions Answer 350456 by oberobic(2304)   on 2011-11-14 16:02:10 (Show Source): You can put this solution on YOUR website!4/7 of trip = 136 km trip = 136*7/4 trip = 34*7 trip = 238 km
 Angles/531446: An angle has a degree measure such that its complement is 1/4 its supplement. Determine this angle's complement.1 solutions Answer 350455 by oberobic(2304)   on 2011-11-14 15:59:36 (Show Source): You can put this solution on YOUR website!Angle 'x' has a complement: 90-x. Angle 'x' has a supplement: 180-x. Angle 'x's' complement is 1/4 its supplement. . 90-x = 1/4(180-x) . Multiply both sides by 4 to eliminate fraction. . 4(90-x) = 180-x . Use distribute property to remove parentheses . 360 -4x = 180 -x . Add 'x' to both sides and subtract 360 from both sides. . -3x = -180 . Divide both sides by -3. . x = 60 . Check this answer to see if it is correct. The complement = 90-60 = 30. The supplement = 180-60 = 120. Is the complement 1/4 of the supplement? Yes. . Answer: The angle is 60 degrees. . Done.
Probability-and-statistics/531441: A code of six letters must be chosen. The letters cannot be repeated. How many different codes are possible?
1 solutions

Answer 350453 by oberobic(2304)   on 2011-11-14 15:52:36 (Show Source):
You can put this solution on YOUR website!
Position     Possible Choices
1 26
2 25
3 24
4 23
5 22
6 21

Total possibilies = 26*25*24*23*22*21 = 165765600
.
Done.

Don't I set this to "0"?
I moved the -12x-5 over to the left (the other side of the =) to read:
5x^2+12x+5=0
Is this the final answer? I get confused on if I need to do anymore or if this should be the end of the problem.
Cheers!
Angela
1 solutions

Answer 350343 by oberobic(2304)   on 2011-11-13 21:47:02 (Show Source):
You can put this solution on YOUR website!
Hint: You cannot "move" anything when dealing with equations. You must do the same thing to both sides of the equation. The notion of "moving" obscures that you are doing something to both sides.
.
5x^2 = -12x + 5
.
.
5x^2 +12x = (-12x+12x) + 5
.
Subtract 5 from both sides.
.
5x^2 +12x -5 = 0
.
 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 : . Discriminant d=244 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.362049935181331, -2.76204993518133. Here's your graph:

 Equations/531113: Caroline's score is 5 less than twice Aikos score. It is also 45 points greater than Aiko's score. What score did the two girls receive?1 solutions Answer 350341 by oberobic(2304)   on 2011-11-13 21:38:49 (Show Source): You can put this solution on YOUR website!C = 2A -5 C = A +45 . C = C so 2A-5 = A+45 A = 50 . C = 2*50 -5 C = 95 . Done.
 test/531086: 6x+6y=-6 5x+y=-131 solutions Answer 350340 by oberobic(2304)   on 2011-11-13 21:37:18 (Show Source): You can put this solution on YOUR website!6x +6y = -6 5x + y = -13 . divide the first equation by 6 and then subtract the second from it . x + y = -1 5x +y = -13 ------------ subtract -4x = 12 . x = -3 . substitute to find y . -3 +y = -1 y = 2 . check these values using the second equation 5(-3) + 2 = -13 correct . Answer: x = -3, y = 2 . Done.
 Sequences-and-series/531095: name two integers whose product is -18 and whose difference between the greatest and least is 91 solutions Answer 350333 by oberobic(2304)   on 2011-11-13 21:19:25 (Show Source): You can put this solution on YOUR website!x and y are two integers. . x*y = -18 . x-y = 9 x = y+9 . (y+9)*y = -18 y^2 +9y + 18 = 0 . (y+3)(y+6) = 0 . y = -3 or -6, which means x = 6 or 3, respectively . The ordered pairs would be: (6,-3) or (3,-6) . Done.
Quadratic_Equations/531094: How do you find the y-Intercept of f(x)= -x^2+4x-1
1 solutions

Answer 350330 by oberobic(2304)   on 2011-11-13 21:08:29 (Show Source):
You can put this solution on YOUR website!
y-intercept occurs where x = 0.
That will be (0,-1).
.
-x^2 +4x -1 = 0
.
 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 : . Discriminant d=12 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.267949192431123, 3.73205080756888. Here's your graph:

 Word_Problems_With_Coins/531081: You have 100 coins in nickels,dimes, and quarters. The value of the coins is \$21.25. You have 3 more nickels than dimes. What are the three equations that you would use to solve this problem?1 solutions Answer 350329 by oberobic(2304)   on 2011-11-13 21:05:20 (Show Source): You can put this solution on YOUR website!n + d + q = 100 . 5n +10d +25q = 2125 . n = d+3 . d+3 +d +q = 100 2d + q = 97 . 5(d+3) + 10d + 25q = 2125 5d +15 +10d + 25q = 2125 15d +25q = 2110 . 2d + q = 97 15d +25q = 2110 . 50d + 25q = 2425 15d + 25q = 2110 ------------------ subtract 35d = 315 . d = 115/35 d = 9 dimes . n = d+3 = 12 nickels . q = 100 -9 -12 q = 79 quarters . Check the values to determine if the answer is correct. 12(5) + 10(9) + 25(79) = 2125 ?? Yes. . Answer: 12 nickels, 9 dimes, and 79 quarters
 Linear-equations/531073: How do I get pairs for the equation y=3/5x ? 1 solutions Answer 350327 by oberobic(2304)   on 2011-11-13 20:47:12 (Show Source): You can put this solution on YOUR website!y = 3/5*x . x=0, y=0 . x=5, y=3 . With two points you can draw a line .
 Mixture_Word_Problems/531060: A Chemist has a mixture that is 10% iodine and another that is 50% iodine. How much of each solution should the druggist use to get 100 ml of a solution that is 20% iodine1 solutions Answer 350324 by oberobic(2304)   on 2011-11-13 20:19:59 (Show Source): You can put this solution on YOUR website!The chemist needs 100 ml of a 20% solution. .2*100 ml = 20 ml of pure iodine in the 100 ml solution. . The chemist has 10% solution and 50% solution. . x = 10% solution y = 50% solution . x + y = 100 ml x = 100-y ml . .1x + .5y = .2*100 . multiply by 10 to eliminate the decimals . 1*x + 5*y = 2*100 . substitute . (100-y) + 5y = 200 100 + 4y = 200 4y = 100 y = 25 ml of 50% iodine . x = 100-25 x = 75 ml of 10% iodine . Check the amount of pure stuff to be sure this is the answer. .5*25 = 12.5 ml .1*75 = 7.5 ml 12.5 + 7.5 = 20 ml, which is the amount we need. Correct. . Done.
 Finance/531061: If you add pure alcohol to a 15% solution, what percent alcohol are you adding, and how do you represent the percentage in decimal form? 1 solutions Answer 350321 by oberobic(2304)   on 2011-11-13 20:10:44 (Show Source): You can put this solution on YOUR website!Pure alcohol is 100% alcohol. 15% alcohol is shown as .15*something. Pure alcohol would be 1*something else.
 Graphs/531062: how to write 2x-3y-14=-6 in standard form1 solutions Answer 350320 by oberobic(2304)   on 2011-11-13 20:09:24 (Show Source): You can put this solution on YOUR website!2x -3y -14 = -6 2x -3y = 8
 Money_Word_Problems/531054: A chlds bank contains \$6.30 in dimes and quarters. There are twice as many dimes as quarters. How many of each kind of coin are in the bank?1 solutions Answer 350317 by oberobic(2304)   on 2011-11-13 20:06:32 (Show Source): You can put this solution on YOUR website!With coin problems you need to keep track of the count of the coins and the value. d = number of dimes 10d = value of the dimes in cents q = number of quarters 25q = value of the quarters in cents . 10d + 25q = 630 cents . d = 2q . substitute . 10(2q) + 25q = 630 20q + 25q = 630 45q = 630 q = 14 . d = 2q d = 2*14 = 28 . Check the values to be sure this answer is right. 25(14) = 350 cents 10(28) = 280 cents total = 630 cents Correct. . Answer: The child has 14 quarters and 28 dimes. . Done.
 Radicals/531050: r^2+16=10r1 solutions Answer 350313 by oberobic(2304)   on 2011-11-13 20:01:06 (Show Source): You can put this solution on YOUR website!r^2 -10r +16 = 0 (r-2)(r-8) = 0 r = 2 or 8 Using the x-axis for r, the following graph shows the plot.
 Polynomials-and-rational-expressions/531041: x(to the fourth) +8x(squared)+15=01 solutions Answer 350311 by oberobic(2304)   on 2011-11-13 19:57:05 (Show Source): You can put this solution on YOUR website!Let u = x^2. . u^2 +8u +15 = 0 . factor . (u+3)(u+5)=0 . substitute u = x^2 . (x^2 + 3)(x^2 + 5) = 0 . So x^2 = -3 or -5. That means there are no real roots. .
 Mixture_Word_Problems/531021: I'm trying to figure out the formula for this word problem. If I can figure out the formula for mixtures I should be able to do the entire worksheet. Sample Problem: A Chemist has a solution that is 12% acid and another solution that is 42% acid. She wants 10L of solution that is 30% acid. How much of each solution should she mix?1 solutions Answer 350306 by oberobic(2304)   on 2011-11-13 19:43:26 (Show Source): You can put this solution on YOUR website!With solution problems you need to determine how much 'pure' stuff you have or need. . The chemist needs 10 liters of a 30% acid. .3*10 = 3 liters of 'pure' acid in a solvent (likely water). . She has 12% acid and 42% acid to mix together. . x = liters of 12% acid y = liters of 42% acid x+y =10 so x = 10-y or y = 10 - x . .12*x + .42*y = .3*10 . multiply by 100 to eliminate decimals . 12x + 42y = 30*10 . substitute for x . 12(10-y) + 42y = 300 120 -12y + 42y = 300 30y = 180 y = 6 . Answer: Mix 6 liters of 42% acid and 4 liters of 12% acid. . Check the amount of pure acid to be sure this answer is correct. .42*6 = 2.52 .12*4 = 0.48 2.52 + .48 = 3.0 Correct. . Done.