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# Recent problems solved by 'nerdybill'

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 Graphs/678572: How do i solve by elimination? -x+2y=-10 5x+4y=81 solutions Answer 421509 by nerdybill(6948)   on 2012-11-10 21:33:22 (Show Source): You can put this solution on YOUR website!-x+2y=-10 5x+4y=8 . Multiply top equation by -2 and combine with second: 2x-4y = 20 5x+4y = 8 -------------- 7x = 28 x = 4 . now, substitute the value found above into either of the two equations to find y: 5x+4y=8 5(4)+4y=8 20+4y=8 4y=-12 y = -3 . answer: x=4 and y=-3
 Miscellaneous_Word_Problems/678456: Alex can complete a work in 5 hours and Ben can complete the same work in 10 hours .How many hours will they both take to complete the job together?1 solutions Answer 421437 by nerdybill(6948)   on 2012-11-10 15:34:38 (Show Source): You can put this solution on YOUR website! Alex can complete a work in 5 hours and Ben can complete the same work in 10 hours .How many hours will they both take to complete the job together? . Let x = time (hours) for both then x(1/5 + 1/10) = 1 multiplying both sides by 10: x(2 + 1) = 10 x(3) = 10 x = 10/3 x = 3 and 1/3 hours or x = 3 hours and 20 minutes
 Exponential-and-logarithmic-functions/678478: Find X so that log base 3 of X + log base 3 of (X-3) = log base 3 of 10.1 solutions Answer 421434 by nerdybill(6948)   on 2012-11-10 15:31:52 (Show Source): You can put this solution on YOUR website! Find X so that log base 3 of X + log base 3 of (X-3) = log base 3 of 10. . x = {-2, 5} we can throw out the -2 (extraneous -- won't work) leaving: x = 5
 Miscellaneous_Word_Problems/678462: A container has 6 litres f a 40% alcohol solution in it. How much pure alcohol should be added to raise it to be a 60% solution?1 solutions Answer 421419 by nerdybill(6948)   on 2012-11-10 14:50:57 (Show Source): You can put this solution on YOUR website!A container has 6 litres f a 40% alcohol solution in it. How much pure alcohol should be added to raise it to be a 60% solution? . Let x = amount (liters) of pure alcohol added then x + .40(6) = .60(x+6) x + 2.4 = .60x+3.6 .40x + 2.4 = 3.6 .40x = 1.2 x = 3 litres
 Polynomials-and-rational-expressions/678473: Find a polynomial function of lowest degree with integer coefficients that has the given zeros. 5, −6, 2 1 solutions Answer 421415 by nerdybill(6948)   on 2012-11-10 14:43:46 (Show Source): You can put this solution on YOUR website!Find a polynomial function of lowest degree with integer coefficients that has the given zeros. 5, −6, 2 . If you have the above zeros, then the factors must be: (x-5)(x+6)(x-2) multiplying them together gives the polynomial. (x-5)(x+6)(x-2) (x^2+x-30)(x-2) x^2(x-2) + x(x-2) - 30(x-2) (x^3-2x^2) + (x^2-2x) - (30x-60) x^3-2x^2 + x^2-2x - 30x+60 x^3-x^2 -2x - 30x+60 x^3-x^2-32x+60
 Polynomials-and-rational-expressions/678195: Find a polynomial f(x) of degree 3 with real coefficients and the following zeros: -2, 3+i Thanks for your help!1 solutions Answer 421210 by nerdybill(6948)   on 2012-11-09 09:26:36 (Show Source): You can put this solution on YOUR website!Find a polynomial f(x) of degree 3 with real coefficients and the following zeros: -2, 3+i . If a zero has an "imaginary" root such as: 3+i then, there must be another imaginary root that is the conjugate: 3-i . so, all the zeros are: -2, 3+i , 3-i . The factors must be: (x - (-2)) , (x - (3+i)) , (x - (3-i)) (x+2) , (x-3-i) , (x-3+i) . Multiply the factors together to get the polynomial: (x+2)(x-3-i)(x-3+i) (x+2)(x(x-3+i)-3(x-3+i)-i(x-3+i)) (x+2)((x^2-3x+xi)-(3x-9+3i)-(xi-3i+i^2)) (x+2)((x^2-3x+xi)-(3x-9+3i)-(xi-3i-1)) (x+2)(x^2-3x+xi-3x+9-3i-xi+3i+1) (x+2)(x^2-6x+xi+9-3i-xi+3i+1) (x+2)(x^2-6x+9-3i+3i+1) (x+2)(x^2-6x+9+1) (x+2)(x^2-6x+10) x(x^2-6x+10)+2(x^2-6x+10) (x^3-6x^2+10x)+(2x^2-12x+20) x^3-6x^2+10x+2x^2-12x+20 x^3-4x^2+10x-12x+20 x^3-4x^2-2x+20
 Mixture_Word_Problems/678166: how many liters of a 10 alcohol solution must be mixed with 80 liters of a 70% solution to get a 30% solution?1 solutions Answer 421194 by nerdybill(6948)   on 2012-11-09 06:40:34 (Show Source): You can put this solution on YOUR website! how many liters of a 10 alcohol solution must be mixed with 80 liters of a 70% solution to get a 30% solution? . Let x = amount (liters) of 10% alcohol added then .10x + .70(80) = .30(x+80) .10x + 56 = .30x+24 56 = .20x+24 32 = .20x 32/.20 = x 160 liters = x
 Quadratic_Equations/678154: How do you write a quadratic equation in the form ax^2 + bx + c = 0 such that c = 4 and the equation has the given solutions of -4 and 3?1 solutions Answer 421193 by nerdybill(6948)   on 2012-11-09 06:37:35 (Show Source): You can put this solution on YOUR website!How do you write a quadratic equation in the form ax^2 + bx + c = 0 such that c = 4 and the equation has the given solutions of -4 and 3? because you are given that c=4 we have two equations and two unknowns: since x= -4 is a solution: a(-4)^2 + b(-4) + 4 = 0 16a - 4b + 4 = 0 (equation 1) . since x= 3 is a solution: a(3)^2 + b(3) + 4 = 0 9a + 3b + 4 = 0 (equation 2) . System of equation: 16a - 4b + 4 = 0 9a + 3b + 4 = 0 . multiply top by 3 and bottom by 4: 48a - 12b + 12 = 0 36a + 12b + 16 = 0 ----------------------- 84a + 28 = 0 84a = -28 a = -28/84 a = -1/3 . plug above into: 9a + 3b + 4 = 0 9(-1/3) + 3b + 4 = 0 -3 + 3b + 4 = 0 3b + 1 = 0 3b = -1 b = -1/3 . our final answer: (-1/3)x^2 - (1/3)x + 4 = 0
 Percentage-and-ratio-word-problems/678163: The amount of water in the leaking tant is inversely proportional to the time is has been leaking. If after 4 hours there are 50 litters left in the tant. How many litters will be left after 5 hours? 1 solutions Answer 421191 by nerdybill(6948)   on 2012-11-09 06:23:12 (Show Source): You can put this solution on YOUR website!The amount of water in the leaking tant is inversely proportional to the time is has been leaking. If after 4 hours there are 50 litters left in the tant. How many litters will be left after 5 hours? "inversely proportional" think: y = k/x to find 'k', use "after 4 hours there are 50 litters left in the tank" 50 = k/4 200 = k . Our relationship then, is y = 200/x Now, we can answer: How many litters will be left after 5 hours? y = 200/5 y = 40 liters
 Travel_Word_Problems/677596: a car travelled a distance of 89 km in 6 hours.What is it's speed1 solutions Answer 420955 by nerdybill(6948)   on 2012-11-08 06:33:24 (Show Source): You can put this solution on YOUR website! a car travelled a distance of 89 km in 6 hours.What is it's speed . That's: 89 km per 6 hours or 89/6 14.83 km per hour (answer)
 Radicals/677598: What is the cube root of 8x^3y^91 solutions Answer 420954 by nerdybill(6948)   on 2012-11-08 06:31:29 (Show Source): You can put this solution on YOUR website!8x^3y^9 can be written as: 2^3x^3(y^3)^3 2xy^3 (answer)
 Travel_Word_Problems/677593: how far could you walk in 20 seconds ? 1 solutions Answer 420953 by nerdybill(6948)   on 2012-11-08 06:16:05 (Show Source): You can put this solution on YOUR website!how far could you walk in 20 seconds ? . Assuming a person can walk 3 mph then 3 mph * 20 secs * 1/60 min/sec * 1/60 hr/min 3 * 20 * 1/60 * 1/60 60 * 1/60 * 1/60 1 * 1/60 1/60 mile or 1/60 mile * 5290 ft/mile = 88 feet
 Inverses/676011: given f(x)= (7/x)-3 find f^-1(x)1 solutions Answer 420156 by nerdybill(6948)   on 2012-11-05 01:12:39 (Show Source): You can put this solution on YOUR website!given f(x)= (7/x)-3 find f^-1(x) . f(x)= (7/x)-3 y= (7/x)-3 switch x for y and y for x: x= (7/y)-3 solve for y: xy = 7-3y xy+3y = 7 y(x+3) = 7 y = 7/(x+3) . so: f^-1(x) = 7/(x+3)
 test/676000: I need help with the following question: "A man has 26 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 485 cents, how many dimes and quarters does he have?"1 solutions Answer 420155 by nerdybill(6948)   on 2012-11-05 01:09:33 (Show Source): You can put this solution on YOUR website!A man has 26 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 485 cents, how many dimes and quarters does he have? . Let x = number of dimes then 26-x = number of quarters . 10x + 25(26-x) = 485 10x + 650-25x = 485 650-15x = 485 -15x = -165 x = -165/(-15) x = 11 (dimes) . quarters: 25-11 = 14
 Mixture_Word_Problems/676013: ok....Suppose that a 12 quart radiator contains a 20% solution of antifreeze. how much solution needs to be drained out and replaced with pure antifreeze to obtain a 40% solution of antifreeze....1 solutions Answer 420154 by nerdybill(6948)   on 2012-11-05 01:05:40 (Show Source): You can put this solution on YOUR website!Suppose that a 12 quart radiator contains a 20% solution of antifreeze. how much solution needs to be drained out and replaced with pure antifreeze to obtain a 40% solution of antifreeze . Let x = amount (quarts) drained and replaced then .20(12-x) + x = .40(12) 2.4-.20x + x = 4.8 2.4 + .80x = 4.8 .80x = 2.4 x = 2.4/.80 x = 3 quarts
 Linear_Equations_And_Systems_Word_Problems/675582: How do I solve a question in 2 variables such as: "Hats cost \$8 each, scarves cost \$7 each. 17 items were sold at a total cost of \$150. How many hats were sold and how may scarves were sold?" Thanks, ANN :-D1 solutions Answer 419936 by nerdybill(6948)   on 2012-11-04 00:35:48 (Show Source): You can put this solution on YOUR website!You have a typo in the problem as stated. Please correct and resubmit.
 Complex_Numbers/675584: How do I find the reciprocal of a complex number, specifically 9i? (Written in standard form)1 solutions Answer 419935 by nerdybill(6948)   on 2012-11-04 00:33:54 (Show Source): You can put this solution on YOUR website!The reciprocal of: 9i is 1/(9i) . But, we don't want i in the denominator so we multiply by: 1/(9i) * i/i i/(9i^2) i/(-9) or (-1/9)i
 Miscellaneous_Word_Problems/675543: Chocolate Confections, Inc. has determined that when x chocolate cakes are made daily, the average cost per chocolate cake is given by C(x)=0.001x^2-0.14x+12.20 a) What is the average cost per cake if 30 chocolate cakes are made daily? b) How many chocolate cakes should be made daily in order to minimize the average cost per cake? Show work1 solutions Answer 419931 by nerdybill(6948)   on 2012-11-03 23:31:15 (Show Source): You can put this solution on YOUR website!Chocolate Confections, Inc. has determined that when x chocolate cakes are made daily, the average cost per chocolate cake is given by C(x)=0.001x^2-0.14x+12.20 a) What is the average cost per cake if 30 chocolate cakes are made daily? set x to 30 and solve for C(x): C(x)=0.001x^2-0.14x+12.20 C(30)=0.001(30)^2-0.14(30)+12.20 C(30)=0.9-4.2+12.20 C(30)=-3.3+12.20 C(30)=\$8.90 . b) How many chocolate cakes should be made daily in order to minimize the average cost per cake? Show work The given equation: C(x)=0.001x^2-0.14x+12.20 is a parabola that opens upwards, therefore the vertex is the minimum: x = -b/(2a) x = -(-0.14)/(2*0.001) x = 0.14/(0.002) x = 70 cakes
 Exponential-and-logarithmic-functions/675067: Find the value of x in the equation 14^x = 0.4285.1 solutions Answer 419525 by nerdybill(6948)   on 2012-11-02 06:41:04 (Show Source): You can put this solution on YOUR website! Find the value of x in the equation 14^x = 0.4285. . 14^x = 0.4285 x = x = x = -0.321
 test/675063: 20%of14 How to Solve this Question1 solutions Answer 419524 by nerdybill(6948)   on 2012-11-02 06:38:34 (Show Source): You can put this solution on YOUR website!20%of14 20/100 * 14 .20 * 14 2.8
 Rectangles/674559: One number is one-third of another. The difference of their squares is ¾. Find the numbers1 solutions Answer 419320 by nerdybill(6948)   on 2012-11-01 06:52:17 (Show Source): You can put this solution on YOUR website! One number is one-third of another. The difference of their squares is ¾. Find the numbers . Let x = one number then x/3 = other number . x^2 - (x/3)^2 = 3/4 x^2 - x^2/9 = 3/4 multiplying both sides by 36: 36x^2 - 4x^2 = 27 32x^2 = 27 x^2 = 27/32 x = x = . other number: x/3 = x/3 =
 Rectangles/674560: Find the length and width of a rectangle if its length is thrice its width and its diagonal is 7.1 solutions Answer 419319 by nerdybill(6948)   on 2012-11-01 06:44:56 (Show Source): You can put this solution on YOUR website! Find the length and width of a rectangle if its length is thrice its width and its diagonal is 7. . Let w = width then 3w = length . applying Pythagorean theorem: w^2 + (3w)^2 = 7^2 w^2 + 9w^2 = 49 10w^2 = 49 w^2 = 4.9 w = 2.2 (width) . length: 3w = 3(2.21) = 6.6
 Numbers_Word_Problems/674562: Using two even consecutive integers where two times the lower integer plus the higher integer equals 50. I have tried: 2x2+4=8, 4x4+6=22, 6x6+8=44, 8x8+10=64 so I can get close but not equal to 50 without going over1 solutions Answer 419318 by nerdybill(6948)   on 2012-11-01 06:40:24 (Show Source): You can put this solution on YOUR website!Using two even consecutive integers where two times the lower integer plus the higher integer equals 50. . Let x = lower even integer then x+2 = higher consecutive even integer . 2x + (x+2) = 50 3x + 2 = 50 3x = 48 x = 16 (lower) . higher: x+2 = 16+2 = 18 . answer: 16 and 18
 Money_Word_Problems/673180: An airline carries 180 passengers and 10 tonnes of freight and earns \$75000 for its owners in fares and freight charges. On the return trip it carries 100 passengers and 20 tonnes of freight, earning \$85000. What is the passenger fare per person and the freight charges per tonne. 1 solutions Answer 418507 by nerdybill(6948)   on 2012-10-29 05:16:22 (Show Source): You can put this solution on YOUR website! An airline carries 180 passengers and 10 tonnes of freight and earns \$75000 for its owners in fares and freight charges. On the return trip it carries 100 passengers and 20 tonnes of freight, earning \$85000. What is the passenger fare per person and the freight charges per tonne. . Let x = cost (\$) per person and y = cost (\$) per ton . from:"180 passengers and 10 tonnes of freight and earns \$75000" 180x + 10y = 75000 . from:"100 passengers and 20 tonnes of freight, earning \$85000" 100x + 20y = 85000 . Our simultaneous equations: 180x + 10y = 75000 100x + 20y = 85000 . multiply top equation by -2 and combine with second: -360x - 20y = -150000 100x + 20y = 85000 ------------------------ -260x = -65000 x = -65000/(-260) x = \$250 (passenger fare per person) . freight charges per tonne: plug above into: 100x + 20y = 85000 100(250) + 20y = 85000 25000 + 20y = 85000 20y = 60000 y = \$3000 (per tonne)
 Quadratic-relations-and-conic-sections/673121: solve the equation 4s^2 + 36s + 81 = 01 solutions Answer 418503 by nerdybill(6948)   on 2012-10-29 04:52:49 (Show Source): You can put this solution on YOUR website! solve the equation 4s^2 + 36s + 81 = 0 . 4s^2 + 36s + 81 = 0 4s^2 + 18s + 18s + 81 = 0 (4s^2 + 18s) + (18s + 81) = 0 2s(2s + 9) + 9(2s + 9) = 0 (2s + 9)(2s + 9) = 0 (2s + 9)^2 = 0 s = -9/2 = -4.5
 Trigonometry-basics/673122: When does cos(x) = 0?1 solutions Answer 418502 by nerdybill(6948)   on 2012-10-29 04:48:32 (Show Source): You can put this solution on YOUR website!When does cos(x) = 0? From the "unit circle" cos(x)=0 when In terms of degrees: 90 and 270 degrees In terms of radians: (pi)/2 and 3(pi)/2 radians
 Miscellaneous_Word_Problems/672738: A bank teller has \$22.55 in quarters and dimes. There are 58 more quarters than dimes. How many dimes does he have? 1 solutions Answer 418306 by nerdybill(6948)   on 2012-10-28 09:01:45 (Show Source): You can put this solution on YOUR website!A bank teller has \$22.55 in quarters and dimes. There are 58 more quarters than dimes. How many dimes does he have? . Let d = number of dimes then because "There are 58 more quarters than dimes" we have d+58 = number of quarters . .10d + .25(d+58) = 22.55 .10d + .25d+14.5 = 22.55 .35d+14.5 = 22.55 .35d = 8.05 d = 23 (number of dimes) . number of quarters: d+58 = 23+58 = 81
 Rate-of-work-word-problems/672511: a man can complete a piece of work in 9 days but with the help of his son, he can do it in 6 days.the taken by his son to do it alone is1 solutions Answer 418125 by nerdybill(6948)   on 2012-10-27 08:39:24 (Show Source): You can put this solution on YOUR website!a man can complete a piece of work in 9 days but with the help of his son, he can do it in 6 days.the taken by his son to do it alone is . Let x = time (days) it takes the son alone then 6(1/9 + 1/x) = 1 multiplying both sides 9x: 6(x + 9) = 9x 6x + 54 = 9x 54 = 3x 18 days = x
 test/672516: how many questions can I get wrong on a 36 question test in order to achieve a score of 68% with a max score of 100?1 solutions Answer 418124 by nerdybill(6948)   on 2012-10-27 08:37:09 (Show Source): You can put this solution on YOUR website!how many questions can I get wrong on a 36 question test in order to achieve a score of 68% with a max score of 100? Let x = number of questions got wrong then (36-x)/36 = .68 multiplying both sides by 36: 36-x = 24.48 36 = 24.48+x 11.52 = x You can miss 11 questions
 Percentage-and-ratio-word-problems/672518: Dan earned money from babysitting. He spent 1/4 of his money on a guitar and gave 1/4 of what was left to charity. He has \$108 left. How much money did he begin with?1 solutions Answer 418122 by nerdybill(6948)   on 2012-10-27 08:33:04 (Show Source): You can put this solution on YOUR website!Dan earned money from babysitting. He spent 1/4 of his money on a guitar and gave 1/4 of what was left to charity. He has \$108 left. How much money did he begin with? Let x = amount (\$) he began with then x - (1/4)x - (1/4)(x - (1/4)x) = 108 x - x/4 - ((1/4)x - (1/4)(1/4)x) = 108 x - x/4 - (x/4 - (1/16)x) = 108 x - x/4 - (x/4 - x/16) = 108 x - x/4 - x/4 + x/16 = 108 multiplying both sides by 16: 16x - 4x - 4x + x = 1728 16x - 8x + x = 1728 8x + x = 1728 9x = 1728 x = \$192