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 Word_Problems_With_Coins/162721: 1. A piggy bank has 250 pieces of assorted coins, 3/4 of which are 10.00 peso coins. The other coins are 5.00 peso, 1.00 peso and .25 cents coins, in the proportion of 3:4:3.Since the owner finds out that .25 cents coins can easili comes out from the piggy hole he decided to extract all these .25 coins. What is the total amount saved?1 solutions Answer 119962 by ankor@dixie-net.com(15660)   on 2008-10-18 10:26:00 (Show Source): You can put this solution on YOUR website! of 250 is not an integer (187.5). What gives here?
 Numbers_Word_Problems/162687: This question is from textbook Hilary has three times as much money as Paul. Jeff has \$4 less than Hilary and \$5 more than Paul. How much money does each have?1 solutions Answer 119929 by ankor@dixie-net.com(15660)   on 2008-10-17 21:22:58 (Show Source): You can put this solution on YOUR website!Hilary has three times as much money as Paul. H = 3P : Jeff has \$4 less than Hilary" J = H - 4 Substitute 3P for H J = 3P - 4 : "and \$5 more than Paul" J = P + 5 : rearrange these two equations J - 3P = -4 J - P = 5 ---------------subtraction eliminates J, find P -2P = -9 P = P = \$4.50 then H = 3(4.5); from the 1st equation H = \$13.50 and J = P + 5 J = 4.50 + 5 J = \$9.50 : Confirm this with the equation J = H - 4 J = 13.50 - 4 J = \$9.50 : Hopefully this made sense to you. Let me know.
 Complex_Numbers/162523: Write the expression as a complex number in standard form: six minus i square roots of 2 divided by six plus i square roots of 21 solutions Answer 119912 by ankor@dixie-net.com(15660)   on 2008-10-17 18:07:03 (Show Source): You can put this solution on YOUR website!six minus i square roots of 2 divided by six plus i square roots of 2 : Multiply by the conjugate of the denominator over itself * = = = = reduce the fraction:
 Travel_Word_Problems/162653: This question is from textbook beginning and intermediate algebra a plane can fly 400 miles downwind in the same amount of time as it can travel 320 miles upwind. If the plane can fly at 360 miles per hour in still air. Find the speed of the wind. I need to revise my exam1 solutions Answer 119906 by ankor@dixie-net.com(15660)   on 2008-10-17 16:34:18 (Show Source): You can put this solution on YOUR website! plane can fly 400 miles downwind in the same amount of time as it can travel 320 miles upwind. If the plane can fly at 360 miles per hour in still air. Find the speed of the wind. : Let x = speed of the wind then (360-x) speed against the wind and (360+x) speed with the wind : It says the times are equal for flying 400 mi and 320 mi. Write a time equation time = : Time with the wind = time against the wind = Cross multiply 320(360+x) = 400(360-x) : 115200 + 320x = 144000 - 400x : 320x + 400x = 144000 - 114200 : 720x = 28800 x = x = 40 mph is the wind : : Check the solution, find out if the times are equal: Using the wind, the speed with 400, speed against 320 400/400 = 1 hr 320/320 = 1 hr
 Problems-with-consecutive-odd-even-integers/162685: One integer is 6 less than another integer. The product of the lesser integer and -7 is 42 more than the greater integer. What are the integers?1 solutions Answer 119905 by ankor@dixie-net.com(15660)   on 2008-10-17 16:07:17 (Show Source): You can put this solution on YOUR website!One integer is 6 less than another integer. The product of the lesser integer and -7 is 42 more than the greater integer. What are the integers? : I don't think there is a solution to this, but let's proceed like there is: : Let x = larger integer Let y = lesser integer : Write an equation for each statement: "One integer is 6 less than another integer." y = x - 6 : " The product of the lesser integer and -7 is 42 more than the greater integer." y * -7 = 42 + x we can write it: -7y = x + 42 : Substitute (x-6) for y (from the 1st statement) -7(x-6) = x + 42 -7x + 42 = x + 42 You can see we are in real trouble here -7x = x; not possible What are the integers? there aren't any
 Human-and-algebraic-language/162645: A homeowner wants to fence a rectangular garden using 120ft of fencing. The side of the garage will be used as one side of the rectangle. Find the dimenstions for which the area is a maximum.1 solutions Answer 119904 by ankor@dixie-net.com(15660)   on 2008-10-17 15:53:40 (Show Source): You can put this solution on YOUR website!A homeowner wants to fence a rectangular garden using 120ft of fencing. The side of the garage will be used as one side of the rectangle. Find the dimensions for which the area is a maximum. : The perimeter equation with one side being the garage: L + 2W = 120 or L = (120 - 2W) ; Area = W * L Substitute (120-2W) for L and you have: A = W(120-2W) A = 120W - 2W^2 This can be arranged as a quadratic equation -2W^2 + 120W = 0 : To find the maximum, find the axis symmetry using x = In this equation: W = W = W = +30 ft is the width for max area Find L L = 120 - 2(30) L = 60 ft is the length ; Find the max area, substitute 30 for W in the equation A = -2(30^2) + 120(30) A = -1800 = 3600 A = +1800 sq/ft is the maximum area : : Check solution by finding the area with the dimensions: 60 * 30 = 1800 sq/ft
 Travel_Word_Problems/162664: During the first part of a trip, a canoeist travels 69 miles at a certain speed. The canoeist travels 2 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 3 hrs. What was the speed on each part of the trip?1 solutions Answer 119893 by ankor@dixie-net.com(15660)   on 2008-10-17 13:33:59 (Show Source): You can put this solution on YOUR website!During the first part of a trip, a canoeist travels 69 miles at a certain speed. The canoeist travels 2 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 3 hrs. What was the speed on each part of the trip? ; Canoing that far in 3 hrs is a fantasy, but anyway: : Let s = speed on the 69 miles then (s-5) = speed on the last to miles of the trip : Write a time equation: Time = dist/speed : 69 mi time + 2 mi time = 3 hrs + = 3 : Multiply equation by s(s-5), results: 69(s-5) + 2s = 3s(s-5) 69s - 345 + 2s = 3s^2 - 15s 71s - 345 = 3s^2 - 15s 0 = 3s^2 - 15s = 71s + 345 A quadratic equation: 3s^2 - 86s + 345 = 0 Use the quadratic formula to solve this The solution that makes sense is s ~ 23.84 mph for the 1st 69mi and 23.84 - 5 = 18.84 mph for the last two mi : : Check solution by finding the times at each speed 69/23.84 = 2.89 hrs 2/18.84 = .106 hr ---------------- total time 2.996 ~ 3 hrs : I suspect there may be a typo in this as written here, but the method should help you.
 Numeric_Fractions/162655: Can someone help me with this problem. I know that it is simple but I have drawn a blank. And, can the steps be broken down so that I can understand other problems that may be similiar in the future. 5 and 3/4-2 and 2/51 solutions Answer 119888 by ankor@dixie-net.com(15660)   on 2008-10-17 12:43:14 (Show Source): You can put this solution on YOUR website!5 - 2 : Convert both fractions to improper fractions. Multiply the whole number times the denominator and add the numerator - : They need to have a common denominator, 20 is a multiple of both denominators 20/4 = 5 and 20/5 = 4, so we have 5* - 4* which is - = : Convert this to a mixed number, divide 20 into 67, the remainder is the fraction 3
 Linear-equations/162649: hi, Can u solve this system of linear equation? The question is: x-y 4 ___ = _ x+y 5 Its x-y divided by x+y which is equal to 4 divided by 5 I need the answer today. Thank u1 solutions Answer 119876 by ankor@dixie-net.com(15660)   on 2008-10-17 11:09:26 (Show Source): You can put this solution on YOUR website!Assume the problems is: = : From this we can say: x - y = 4 x + y = 5 ---------------adding eliminates y, find x 2x = 9 x = x = 4.5 : Find y using x + y = 5 4.5 + y = 5 y = 5 - 4.5 y = .5 : Check solution in original equation: = =
 Complex_Numbers/162611: (2+3i)^2 could you please explain step by step please help soon!1 solutions Answer 119826 by ankor@dixie-net.com(15660)   on 2008-10-16 21:41:51 (Show Source): You can put this solution on YOUR website!(2+3i)^2 could you please explain step by step : Assume you want to FOIL (2+3i)(2+3i) Step by step F: mult first two term 2 * 2 = 4 0: mult outer terms: 2 * 3i = 6i I: mult inner terms: 3i * 2 = 6i L: mult last terms: 3i * 3i = 9i^2 : So we have: 4 + 6i + 6i + 9i^2 : Add like terms 4 + 12i + 9i^2 ; Remember that i^2 = -1 so you have: 4 + 12i + 9(-1) 4 + 12i - 9 : 4 - 9 + 12i : which is: -5 + 12i
 Polynomials-and-rational-expressions/162590: one moreee the biggest problem i have is word problems i hate them and i get frustrated heres one i'm really struggling with. a board is cut into two pieces. one piece is to be three times as long as the other. if the board is 4.2m long, what will the length of the longer piece be? i have to have a let statement i tried putting.. let x represent 1 piece let x+3 reprsent the other piece so i put the equation as.. 2x+3=4.2 but the number is so small i find it hard to believe it correct! can you show me what im doing wrong?1 solutions Answer 119825 by ankor@dixie-net.com(15660)   on 2008-10-16 21:03:31 (Show Source): You can put this solution on YOUR website!a board is cut into two pieces. one piece is to be three times as long as the other. if the board is 4.2m long, what will the length of the longer piece be? : Let's do it this way: : Let x = the smaller piece It said,"one piece is to be three times as long as the other." therefore: 3x = the long piece : small piece + longer piece = 4.2 meters x + 3x = 4.2 : 4x = 4.2 : Divide both sides by 4 x = x = 1.05 m is the smaller piece : They ask for the length of the longer piece: 3 * 1.05 = 3.15 m is the longer piece : : Check to see if this is true, add the two pieces 1.05 + 3.15 = 4.2 : Did this help?
 Linear-systems/162558: a basketball team sells tickets that cost \$10 \$20 or VIP seats, \$30. The team has sold 492 tickets over all. It has sold 177 more \$20 tickets than \$10 tickets. The total sales are \$8580. How Many tickets of each kind have been sold?1 solutions Answer 119824 by ankor@dixie-net.com(15660)   on 2008-10-16 20:07:49 (Show Source): You can put this solution on YOUR website!A basketball team sells tickets that cost \$10 \$20 or VIP seats, \$30. The no. of three types of tickets = x, y, z ; The team has sold 492 tickets over all. x + y + z = 492 : It has sold 177 more \$20 tickets than \$10 tickets. y = x + 177 : The total sales are \$8580. 10x + 20y + 30z = 8580 : How Many tickets of each kind have been sold? : Replace (x+177) for y in the 1st and 3rd equations x + (177+x) + z = 492 2x + z = 492 - 177 2x + z = 315 and 10x + 20(x+177) + 30z = 8580 10x + 20x + 3540 + 30z = 8580 30x + 30z = 8580 - 3540 30x + 30z = 5040 Simplify, divide equation by 30 x + z = 168 : Using these two equations for elimination 2x + z = 315 x + z = 168 ---------------subtracting eliminates z x = 147 ea \$10 tickets sold : y = 147 + 177 y = 324 ea \$20 tickets sold ; Find z using the 1st equation 147 + 324 + z = 492 471 + z = 492 z = 492 - 471 z = 21 ea \$30 tickets sold : Check solution in the \$\$ equation 10(147) + 20(324) + 30(21) = 1470 + 6480 + 630 = 8580; confirms our solutions
 Graphs/162486: write thev equation of a line in the form Ax+By=C throgh the point (-5,-3)and perpendicular to the line y= - 2over3x+61 solutions Answer 119802 by ankor@dixie-net.com(15660)   on 2008-10-16 19:01:40 (Show Source): You can put this solution on YOUR website!write the equation of a line in the form Ax+By=C through the point (-5,-3)and perpendicular to the line y= -(2/3)x+6 : Determine the slope m2, the relationship of perpendicular lines: m1*m2=-1 Let m1 = *m2 = -1 m2 = -1* m2 = : Use the point/slope formula y - (-3) = (x - (-5) y + 3 = (x +5) y + 3 = x + y = x + - 3 y = x + - y = x + Get rid of the denominators multiply equation by 2 2y = 3x + 9 arrange in the required format -3x + 2y = 9
 Linear-equations/162443: A hotdog stand can purchase hotdogs for \$.35 each and buns for \$.20 each. It has fixed costs of \$50. Each hotdog is sold for \$1. write a linear equation for both cost and revenue. Graph both cost and revenue. Estimate the break-even point. 1 solutions Answer 119796 by ankor@dixie-net.com(15660)   on 2008-10-16 18:18:23 (Show Source): You can put this solution on YOUR website!A hot-dog stand can purchase hot-dogs for \$.35 each and buns for \$.20 each. It has fixed costs of \$50. Each hot-dog is sold for \$1. : write a linear equation for both cost and revenue. Let x = no. sold; each cost .35+ .20 = .55 Cost = .55x + 50 Rev = 1x : Graph both cost and revenue. Cost: green Rev: purple : Estimate the break-even point. How about 110 hot dogs sold at \$110
 Surface-area/162480: How many gallons of water are in a well that is 36 inches in diameter and 20 feet deep? 1 solutions Answer 119760 by ankor@dixie-net.com(15660)   on 2008-10-16 15:50:22 (Show Source): You can put this solution on YOUR website!How many gallons of water are in a well that is 36 inches in diameter and 20 feet deep? : Change 36" diameter to 3 feet, radius will = 1.5 ft : Find the volume of a cylinder V = where: r=1.5, h= 20 V = V = 141.37 cu/ft : 1 cu/ft = 7.481 gallons : 141.37 * 7.481 = 1057.6 gallons
 Polynomials-and-rational-expressions/162414: Please help to solve Simplify and evaluate: (2^x^5y^-3z^4/4^0x^-2y^-8z^5)^3 I don't think I am coming up with the correct answer. 12x^3 z^9/y^111 solutions Answer 119758 by ankor@dixie-net.com(15660)   on 2008-10-16 15:41:45 (Show Source): You can put this solution on YOUR website!I assume you mean not 4^0 = 1 so we can ignore that Combine the exponents of like terms in a way to make them positive = Multiply all the exponents by 3 =
 Geometry_Word_Problems/162431: A and B working together can do a job in 20/3 hours. A became ill after 3 hours of working with B and B finished the job, continuing the work alone in 33/4 more hours. How long would it take each working alone to do the job????1 solutions Answer 119750 by ankor@dixie-net.com(15660)   on 2008-10-16 14:53:33 (Show Source): You can put this solution on YOUR website!A and B working together can do a job in 20/3 hours. A becames ill after 3 hours of working with B and B finished the job, continuing the work alone in 33/4 more hours. How long would it take each working alone to do the job???? : Let a = A's time working alone Let b = B's time working alone Let the completed job = 1 : Equation 1, for the statement,"A and B working together can do a job in 20/3 hours" + = 1 Which is: + = 1; (we invert the dividing fraction and multiply) : Equation 2 when A gets sick: B works 3 hr + 33/4 hr = 45/4; hrs total for B : + = 1 Multiply the 1st fraction by 3/3 to have same denominator as the 1st equation + = 1 ; Try to use elimination here with these two equations: + = 1 + = 1 : Multiply the 1st equation by 20, and the 2nd equation by 9, results: + = 20 + = 9 ---------------------------------------subtraction eliminates a, leaving: - = 11 - = 11; reduced the fractions = 11 b = b = 15 hrs by himself : Find a using eq: + = 1; + = 1; + = 1; + = 1; reduced the fraction = 1 - = Cross multiply 5(3a) = 20*9 15a = 180 a = a = 12 hrs by himself : : Check solution using eq; + = 1 + = 1 + = 1; confirms the solutions to this horrible problem!
 Mixture_Word_Problems/162391: A container is partly filled with 12 liters of whole milk containing 4% butterfat. How much 1% milk must be added to get a mixture that is 2% butterfat?1 solutions Answer 119686 by ankor@dixie-net.com(15660)   on 2008-10-15 21:49:13 (Show Source): You can put this solution on YOUR website!A container is partly filled with 12 liters of whole milk containing 4% butterfat. How much 1% milk must be added to get a mixture that is 2% butterfat? : Let x = amt of 1% milk then (x+12) = resulting amt : Write an "amt of butterfat" equation ; .01x + .04(12) = .02(x+12) : .01x + .48 = .02x + .24 : .48 - .24 = .02x - .01x : .24 = .01x x = x = 24 liters of 1% milk required : : Check solution in the original equation: .01(24) + .04(12) = .02(24+12) .24 + .48 = .02(36 .72 = .72; confirms our solution
 Human-and-algebraic-language/162366: dianne has six steel balls of equal mass. if she puts five of them in one pan of a beam balance and one ball and a 100 g mass in the other pan, the pans balance each other. what is the mass of each steel ball?1 solutions Answer 119685 by ankor@dixie-net.com(15660)   on 2008-10-15 21:37:25 (Show Source): You can put this solution on YOUR website!Dianne has six steel balls of equal mass. If she puts five of them in one pan of a beam balance and one ball and a 100 g mass in the other pan, the pans balance each other. What is the mass of each steel ball? : Let x = mass of 1 steel ball : 5x = x + 100 : 5x - x = 100 : 4x = 100 x = x = 25 gr : : Check solution in original equation 5(25) = 25 + 100
 Reduction-of-unit-multipliers/162390: 1qt/min = (?)gal/week1 solutions Answer 119682 by ankor@dixie-net.com(15660)   on 2008-10-15 21:32:09 (Show Source): You can put this solution on YOUR website!1qt/min = (?)gal/week : We find the no. of min in 1 week, then change quarts to gallons 2520 gal/week
 Linear-systems/162404: I would love it if you would tell me I'm doing this right, however, if I am not please help me to see what I am doing wrong. Solve the linear equation by graphing 2x-y=5 3x+y=5 y=-2x+5 y=3x-5 my answer: 2,11 solutions Answer 119681 by ankor@dixie-net.com(15660)   on 2008-10-15 21:27:45 (Show Source): You can put this solution on YOUR website!Solve the linear equation by graphing 2x-y=5 3x+y=5 y=-2x+5 y=3x-5 : the 1st equation: 2x - y = 5 -y = -2x + 5 we must have the coefficient of y to be positive 1, multiply the equation by -1 y = 2x - 5 : : The 2nd equation 3x + y = 5 y = -3x + 5 : you must change the signs when you move a term from one side to the other. : Graphing these: You can see the solution is: 2,-1
 Money_Word_Problems/162396: In the period of a year, an investor lost twice as much as he gained. if he originally had \$10,000 and now has \$8,000. What amount did he gain and what did he lose?1 solutions Answer 119680 by ankor@dixie-net.com(15660)   on 2008-10-15 21:16:58 (Show Source): You can put this solution on YOUR website!In the period of a year, an investor lost twice as much as he gained. If he originally had \$10,000 and now has \$8,000. What amount did he gain and what did he lose? : Let x = amt he gained then 2x = amt he lost : \$10000 + gained - lost = \$8000 ; 10000 + x - 2x = 8000 : 10000 - x = 8000 : -x = 8000 - 10000 : -x = -2000 : x = 2000 he gained and 2x = 4000 he lost
 Travel_Word_Problems/162351: Mr. Turner has a motorboat that can travel 14 mph in still water. He wishes to take a trip on a river whose current flows at the rate of 2 mph. If he has 7 hours at his disposal, how many hours should he spend on the first part of his trip going downstream before returning upstream to his starting point?1 solutions Answer 119662 by ankor@dixie-net.com(15660)   on 2008-10-15 18:51:41 (Show Source): You can put this solution on YOUR website!Mr. Turner has a motorboat that can travel 14 mph in still water. He wishes to take a trip on a river whose current flows at the rate of 2 mph. If he has 7 hours at his disposal, how many hours should he spend on the first part of his trip going downstream before returning upstream to his starting point? : Let t = time going down-stream then (7-t) = time going up-stream : 14 + 2 = 16 mph; boat speed down-stream 14 - 2 - 12 mph; boat speed up-stream : Distance both ways are the same, write a dist equation: dist = speed * time : Dist down = dist up 16t = 12(7-t) : 16t = 84 - 12t : 16t + 12t = 84 : 28t = 84 t = t = 3 hrs he can travel down-stream, before he has 4 hrs to return : : confirm solution by finding the distances down and back: 16*3 = 48 mi 12*4 = 48 mi
 Polynomials-and-rational-expressions/162053: CAN SOMEONE HELP ME WITH THIS PROBLEM In the formula A = I^ekt, A is the amount of radioactive material remaining from an initial amount I at a given time t and k is a negative constant determined by the nature of the material. An artifact is discovered at a certain site. If it has 53% of the carbon-14 it originally contained, what is the approximate age of the artifact? (carbon-14 decays at the rate of 0.0125% annually.) (Round to the nearest year.)1 solutions Answer 119651 by ankor@dixie-net.com(15660)   on 2008-10-15 17:55:20 (Show Source): You can put this solution on YOUR website!In the formula A = I^ekt, A is the amount of radioactive material remaining from an initial amount I at a given time t and k is a negative constant determined by the nature of the material. An artifact is discovered at a certain site. If it has 53% of the carbon-14 it originally contained, what is the approximate age of the artifact? (carbon-14 decays at the rate of 0.0125% annually.) (Round to the nearest year.) : I think the formula should be A = I*e^(-kt) In this problem: Assume I = 1 A = .53 Decimal value for .0125% = .000125 : e^(-.000125t) = .53 ; -.000125t*ln(e) = ln(.53) ; -.000125t = -.6834878; (the ln of e is 1) t = t = 5,079 years
 Travel_Word_Problems/162019: ROSE DROVE HER CAR FROM HER HOME TO THE PROVINCE AND BACK,A TOTAL DISTANCE OF 120KM.HER AVERAGE SPEED RETURNING WAS 3KPH SLOWER THAN HER AVERAGE SPEED GOING TO THE PROVINCE.IF HER TOTAL DRIVING TIME WAS 9 HOURS ,WHAT WAS HER AVERAGE SPEED IN GOING TO THE PROVINCE?1 solutions Answer 119635 by ankor@dixie-net.com(15660)   on 2008-10-15 16:43:08 (Show Source): You can put this solution on YOUR website!ROSE DROVE HER CAR FROM HER HOME TO THE PROVINCE AND BACK, A TOTAL DISTANCE OF 120KM. HER AVERAGE SPEED RETURNING, WAS 3KPH SLOWER THAN HER AVERAGE SPEED GOING, TO THE PROVINCE. IF HER TOTAL DRIVING TIME WAS 9 HOURS, WHAT WAS HER AVERAGE SPEED IN GOING TO THE PROVINCE? : From the given information we can assume that one way; 120/2 = 60 km : Let s = her speed going and (s-3) = her speed returning : Write a time equation: Time = Go time + return time = 9 hrs + = 9 : Eliminate the denominators, multiply equation by s(s-3), results: 60(s-3) + 60s = 9(s(s-3)) ; 60s - 180 + 60s = 9(s^2 - 3s) : 120s - 180 = 9s^2 - 27s : 0 = 9s^2 - 27s - 120s + 180 A quadratic equation: 9s^2 - 147s + 180 = 0 This can be factored to (3s - 45)(3s - 4) = 0 Two solutions 3s = 4 s = and 3s = 45 s = 15 km/h this seems to be the most reasonable : Speed going: 15 km/h; and speed returning 12 km/h : Check in original equation 60/15 + 60/12 = 4 + 5 = 9 hrs