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 Polynomials-and-rational-expressions/542858: please help me to multiply and put in simplest form: b+4/b-2 * b^2-4/b^2-16 (my final answer : b^2-4b+4b^2-16/b^3-16b-2b^2+32 is obviously incorrect)1 solutions Answer 354729 by ankor@dixie-net.com(15656)   on 2011-12-06 20:58:41 (Show Source): You can put this solution on YOUR website! * perhaps you overlooked that the 2nd fraction contains difference of square & can be factored to: * Cancel (b+4) and (b-2) and you left with
 Age_Word_Problems/542689: twelve years ago, a man was three times as old as his daughter. nine years from now, the man will be twice as old as his son. four years from now, the sum of the ages of the son and daughter will equal the age of the man. how old is each now?1 solutions Answer 354716 by ankor@dixie-net.com(15656)   on 2011-12-06 20:06:47 (Show Source): You can put this solution on YOUR website!Let m = man's present age Let d = daughter's Let s = son's : Write an equation for each statement, simplify: : twelve years ago, a man was three times as old as his daughter. m - 12 = 3(d - 12) m - 12 = 3d - 36 m = 3d - 36 + 12 m = 3d - 24 : " nine years from now, the man will be twice as old as his son." m + 9 = 2(s + 9) m + 9 = 2s + 18 m = 2s + 18 - 9 m = 2s + 9 : "four years from now, the sum of the ages of the son and daughter will equal the age of the man." m + 4 = s+4 + d+4 m + 4 = s + d + 8 m = s + d + 8 - 4 m = s + d + 4 replace m with (3d-24) 3d - 24 = s + d + 4 3d - d - s = 4 + 24 2d - s = 28 then in the same equation m = s + d + 4 replace m with (2s + 9) 2s + 9 = s + d + 4 2s = s + d + 4 - 9 -d + 2s - s = - 5 -d + s = -5 : Use elimination on these two equations 2d - s = 28 -d + s = -5 ---------------addition eliminates s, find d d = 23 is the daughters age : Find s using the equation -d + s = -5 -23 + s = -5 s = -5 + 23 s = 18 is the son's age : Use m = 3d - 24 to find the man's m = 3(23) - 24 m = 69 - 24 m = 45 is the man's age : Check this in the equation: m = s + d + 4 45 = 18 + 23 + 4 45 = 45 : : how old is each now? man is 45, daughter is 23, son is 18
 Proportions/542800: If a car travels at 55mph covert this speed to meters per second1 solutions Answer 354695 by ankor@dixie-net.com(15656)   on 2011-12-06 19:04:19 (Show Source): You can put this solution on YOUR website!If a car travels at 55 mph convert this speed to meters per second. : Convert miles to km, (*1.609), times 1000 to get meters, divide by 3600 sec : = 24.58 m/sec
 Travel_Word_Problems/542646: Please help me with this word problem, "a cargo ship travels for five hours with a current of 22 mph and then returns that same distance against the current in 8 hours. what is the ship's speed in calm water? how far did the boat travel one way?" I did a rate times time equals distance table, but only know the times for both there are back, would 22 mph be the speed for the boat on the way there? Thank you so much1 solutions Answer 354675 by ankor@dixie-net.com(15656)   on 2011-12-06 18:13:48 (Show Source): You can put this solution on YOUR website!"a cargo ship travels for five hours with a current of 22 mph and then returns that same distance against the current in 8 hours. what is the ship's speed in calm water? how far did the boat travel one way?" : This is a poorly worded problem, they must mean that the boats effective speed with the current was 22 mph A 22 mph current, although not unheard of, is pretty extreme. : Let s = ship's speed in calm water Let c = rate of the current then s + c = 22 mph or c = (22-s); we can use this for substitution : Find the distance, dist = speed * time 22 * 5 = 110 miles one way : The distance equation for the trip against the current: 8(s-c) = 110 Replace c with (22-s) 8(s - (22-s)) = 110 8(s - 22 + s) = 110 8(2s-22) = 110 16s - 176 = 110 16s = 110 + 176 16s = 286 s = 286/16 s = 17.875 mph, which is a reasonable speed for a cargo ship
 Mixture_Word_Problems/542684: Cashews cost \$4 per pound and peanuts cost \$1 per pound. How many pounds of peanuts should be used with the cashews to get a mixture of 24 pounds that will cost \$2 per pound?1 solutions Answer 354654 by ankor@dixie-net.com(15656)   on 2011-12-06 15:58:51 (Show Source): You can put this solution on YOUR website!Cashews cost \$4 per pound and peanuts cost \$1 per pound. How many pounds of peanuts should be used with the cashews to get a mixture of 24 pounds that will cost \$2 per pound? : Let x = no. of lbs of peanuts It states the total weight will be 24 lb, therefore (24-x) = no. of lbs of cashews : A typical mixture equation 1x + 4(24-x) = 2(24) x + 96 - 4x = 48 x - 4x = 48 - 96 -3x = -48 x = 48/3 x = 16 lb of peanuts required : Check solution (8 lb of cashews required) 1(16) + 4(8) = 2(24)
 test/542584: a 290-inch board is cut into two pieces. one side if four times the length of the other find the length of the two pieces. 1 solutions Answer 354651 by ankor@dixie-net.com(15656)   on 2011-12-06 15:52:11 (Show Source): You can put this solution on YOUR website!a 290-inch board is cut into two pieces. one side if four times the length of the other find the length of the two pieces. : Let x = one side then 4x = the other side : x + 4x = 290 5x = 290 x = 290/5 x = 58 is the smaller side you can find the longer side, see if they add up 290
 Quadratic_Equations/542384: Two numbers differ by 7,the different of their squares is 91,find the numbers.1 solutions Answer 354649 by ankor@dixie-net.com(15656)   on 2011-12-06 15:48:47 (Show Source): You can put this solution on YOUR website!Two numbers differ by 7,the different of their squares is 91,find the numbers. Two numbers: a, b a - b = 7 a = (b+7) : a^2 - b^2 = 91 : Replace a with (b+7) (b+7)^2 - b^2 = 91 : FOIL (b+7)(b+7) b^2 + 14b + 49 - b^2 = 91 b^2 - b^2 + 14b = 91 - 49 14b = 42 b = 42/14 b = 3 : Find a a = 3 + 7 a = 10 : : Check: 10^2 - 3^2 = 91
 Proportions/542482: Sweets were placed in 3 containers, A, B, and C. The ratio of sweets in A and B was 7:4 and the ratio in B and C was 3:2. After 36 sweets were from A, the number of sweets in C was 2/3 the number of sweets in A. What was the total number of sweets left in the three containers?1 solutions Answer 354646 by ankor@dixie-net.com(15656)   on 2011-12-06 15:38:30 (Show Source): You can put this solution on YOUR website!Sweets were placed in 3 containers, A, B, and C. The ratio of sweets in A and B was 7:4 and the ratio in B and C was 3:2. After 36 sweets were from A, the number of sweets in C was 2/3 the number of sweets in A. What was the total number of sweets left in the three containers? : Write some equation : "he ratio of sweets in A and B was 7:4 " = cross multiply 4A = 7B B = A : "the ratio in B and C was 3:2." = 2B = 3C : "After 36 sweets were from A, the number of sweets in C was 2/3 the number of sweets in A. C = (A-36) 3C = 2(A-36); multiplied both sides by 3 3C = 2A - 72 Replace 3C with 2B 2B = 2A - 72 Simplify, divide by 2 B = A - 36 Replace B with A A = A - 36 4A = 7(A - 36); multiplied both sides by 7 4A = 7A - 252 4A - 7A = - 252 -3A = -252 A = A = +84 sweets in A : Find B B = *84 B = 48 in B : Find C 3C = 2B 3C = 2(48) 3C = 96 C = C = 32 in C : Total in all 3 containers 84 + 48 + 32 = 164 sweets : : You can confirm this by checking these values in all the equations
 absolute-value/542471: Please help me answer this question: A wire is 224cm long, it has been cut in 3 pieces, the 1st piece is twice as long as the 2nd piece, the 3rd piece is 1/2 as long as the 2nd piece. How long is the second piece. I need the equation for this word problem and am unable to attain it. Thank you for your help. 1 solutions Answer 354586 by ankor@dixie-net.com(15656)   on 2011-12-06 08:54:38 (Show Source): You can put this solution on YOUR website!A wire is 224cm long, it has been cut in 3 pieces, the 1st piece is twice as long as the 2nd piece, the 3rd piece is 1/2 as long as the 2nd piece. How long is the second piece. : Let the three pieces be a, b, c : Write an equation for each statement: : "A wire is 224cm long, it has been cut in 3 pieces," a + b + c = 224 : "the 1st piece is twice as long as the 2nd piece," a = 2b : "the 3rd piece is 1/2 as long as the 2nd piece. " c = .5b : In the 1st equation, replace a with 2b, replace c with .5b 2b + b + .5b = 224 3.5b = 224 b = b = 64 cm is the 2nd piece : Use the 2nd and 3rd equations to find a and c, check that your solutions add up to 224
 Travel_Word_Problems/542250: Two cyclists are competing in a 12-mile race on a quarter mile circular track. They began at the same time. One biker’s average speed is 24 miles per hour. The other’s average speed is 30 miles per hour. How many complete laps will the slower cyclist have left to complete after the faster cyclist finishes? 1 solutions Answer 354516 by ankor@dixie-net.com(15656)   on 2011-12-05 22:01:16 (Show Source): You can put this solution on YOUR website!Two cyclists are competing in a 12-mile race on a quarter mile circular track. They began at the same time. One biker’s average speed is 24 miles per hour. The other’s average speed is 30 miles per hour. How many complete laps will the slower cyclist have left to complete after the faster cyclist finishes? : 4 * 12 = 48 laps required to go 12 mi : The faster cyclist requires = .4 hrs to complete 48 laps. : Find how far the slower cyclist goes in .4 hrs .4 * 24 = 9.6 mi, which is 9.6 * 4 = 38.4 laps completed 48 - 38.4 = 9.6 laps to go, when the faster cyclist finishes
 Rectangles/542271: Two rectangles are similar. One is 5 cm by 12 cm. The longer side of the second rectangle is 8 cm greater than twice it's shorter side. Find it's length and width1 solutions Answer 354511 by ankor@dixie-net.com(15656)   on 2011-12-05 21:40:21 (Show Source): You can put this solution on YOUR website!Two rectangles are similar. One is 5 cm by 12 cm. The longer side of the second rectangle is 8 cm greater than twice it's shorter side. Find it's length and width. : Since the rectangles are similar, the relationships between the length and width are the same, so we can write it : let x = the shorter side = Cross multiply 5(2x+8) = 12x 10x + 40 = 12x 40 = 12x - 10x 40 = 2x x = 40/2 x = 20 cm is the shorter side then 2(20)+8 = 48 cm is the length : The 2nd rectangle: 48 by 20
 Linear_Equations_And_Systems_Word_Problems/542183: A river has two bridges spanning it that are exactly one mile from each other. While practicing for a boat race, a competitor went upstream. He rowed at a constant rate, and, in doing so, passed under the two bridges. Just underneath the second bridge his cap fell into the water. A further tem minutes passed before he realized that he had lost it. He then turned around and began rowing, still at the same constant rate, in the direction from which he had come. He finally caught up with the cap under the first bridge. How fast does the river flow? 1 solutions Answer 354500 by ankor@dixie-net.com(15656)   on 2011-12-05 21:03:06 (Show Source): You can put this solution on YOUR website!A river has two bridges spanning it that are exactly one mile from each other. While practicing for a boat race, a competitor went upstream. He rowed at a constant rate, and, in doing so, passed under the two bridges. Just underneath the second bridge his cap fell into the water. A further ten minutes passed before he realized that he had lost it. He then turned around and began rowing, still at the same constant rate, in the direction from which he had come. He finally caught up with the cap under the first bridge. How fast does the river flow? : The boat and the hat are in the same frame of reference, unaffected by the current. If the boat traveled 10 min away from the hat, it would require 10 min to return. During this 20 min time the current carried the hat from the 2nd bridge, back to the 1st bridge, a distance of 1 mile Another words the hat traveled 1 mi in 20 min. Therefore we can say: the current = 3 mph
 Age_Word_Problems/542134: Can someone please help me break down these problems please Thank you. 1) "I dont understand how to show the work of this word problem" LUC IS THREE YEARS MORE THAN TWICE KATE'S AGE. FOUR YEARS AGO TH SUM OF THEIR AGES WAS 25. HOW OLD IS LUC NOW? 2) 16:0 3) 3/5N - 5 = 5N + 39 1 solutions Answer 354465 by ankor@dixie-net.com(15656)   on 2011-12-05 19:07:46 (Show Source): You can put this solution on YOUR website!Let L = Luc's present age Let K = Kate's present age : Write an equation for each statement: : "LUC IS THREE YEARS MORE THAN TWICE KATE'S AGE. L = 2K + 3 : "FOUR YEARS AGO TH SUM OF THEIR AGES WAS 25." L-4 + K-4 = 25 L + K - 8 = 25 L + K = 25 + 8 L + K = 33 From the 1st statement, replace L with (2K+3) 2K + 3 + K = 33 3K = 33 - 3 3K = 30 K = 30/3 K = 10 yrs is Kate's present age : Find L L = 2(10) + 3 L = 23 is Luc's present age : : You can check these solutions in the statement: "FOUR YEARS AGO TH SUM OF THEIR AGES WAS 25." : : : 2. ?? : 3) N - 5 = 5N + 39 add 5 to both sides N = 5N + 39 + 5 N = 5N + 44 Multiply both sides by 5 to get rid of the denominator 3N = 5(5N + 44) 3N = 25N + 220 3N - 25N = 220 -22N = 220 Divide both sides by -22 N = 220/-22 N = -10 : You can check this solution in the original equation
 Age_Word_Problems/542059: Andy and Ben had a total of \$60. If Andy gave been \$8.they would have an equal amount.of money. How much money did Ben have in the beginning? 1 solutions Answer 354453 by ankor@dixie-net.com(15656)   on 2011-12-05 18:45:59 (Show Source): You can put this solution on YOUR website!Andy and Ben had a total of \$60. If Andy gave been \$8. they would have an equal amount.of money. How much money did Ben have in the beginning? : write an equation for the original amts a + b = 60 : "If Andy gave Ben \$8, they would have an equal amount.of money." a - 8 = b + 8 a - b = 8 + 8 a - b = 16 : We can use elimination here a + b = 60 a - b = 16 -------------adding eliminates b, find a 2a = 76 a = 76/2 a = \$38, Andy's original amt then 60 - 38 = \$22, Ben's original amt ; : You can check these solutions in the statement: "If Andy gave Ben \$8, they would have an equal amount of money. "
 Money_Word_Problems/541729: I am kinda slow when working on there problems and have already work them out I am just making sure that I did them right. Your company would like to know how sales levels affect profits. If too few items are sold, then there is a loss. Even if too many items are sold, however, the company can lose money (likely because of low pricing). It is good to know how many items can be sold for there to be profit. Functions are very useful in many areas, such as in business to find the profit an organization is making. For example, the following function expresses profit in terms of the number of phones sold by a particular company: P(x) = –x2 + 110x – 1,000 This function can be used to compute the profit (in thousands of dollars) from producing and selling a certain number, x, of thousands of smartphones. Compute the following: P(5), P(50), and P(120). an Graph1 solutions Answer 354351 by ankor@dixie-net.com(15656)   on 2011-12-05 14:27:33 (Show Source): You can put this solution on YOUR website!the following function expresses profit in terms of the number of phones sold by a particular company: P(x) = –x^2 + 110x – 1000 This function can be used to compute the profit (in thousands of dollars) from producing and selling a certain number, x, of thousands of smartphones. Compute the following: P(5), P(50), and P(120). an Graph : P(5) = –x^2 + 110x – 1000 Substitute 5 for x: P(5) = -5^2 + 110(5) – 1000 P(5) = -25 + 550 - 1000 P(5) = -475, a loss : P(50) = –x^2 + 110x – 1000 Substitute 50 for x: P(50) = –50^2 + 110(50) – 1000 P(50) = -2500 + 5500 - 1000 P(50) = 2000, a profit : P(120), you can do this one, you can see on the graph, it will be a loss : Graph equation: y = -x^2 + 110x - 1000:
 Radicals/541672: √10a + 2√40a^3 I can't find the instructions in my reading! I think I have to factor something, but I have no idea.1 solutions Answer 354294 by ankor@dixie-net.com(15656)   on 2011-12-05 09:44:24 (Show Source): You can put this solution on YOUR website! + : Factor the 2nd term inside the radical to reveal some perfect squares + : Extract the square root of those perfect squares + + : Factor out the square root of 10a (4a + 1)
 Expressions-with-variables/541710: There are 630 dishes that need to be rinsed. John can rinse them in 70 min by himself it will take his friend Bob 105 min to rinse these dishes. How long will it take them if they rinse these 630 dishes together?1 solutions Answer 354293 by ankor@dixie-net.com(15656)   on 2011-12-05 09:33:00 (Show Source): You can put this solution on YOUR website!There are 630 dishes that need to be rinsed. John can rinse them in 70 min by himself it will take his friend Bob 105 min to rinse these dishes. How long will it take them if they rinse these 630 dishes together? : Do it as a "shared work" equation : Let t = time required when they work together Let the completed job = 1 (the rinsing of 630 dishes) : Each will do a fraction of the job, the two fractions add up to 1 : + = 1 multiply by the LCM of 70 & 105 which is 210 210* + 210* = 210 Cancel the denominators and you hav 3t + 2t = 210 5t = 210 t = 42 min together : : Check this + = 1 .6 + .4 = 1
 Miscellaneous_Word_Problems/541752: Hi there! Just wondering if you could help me with a question :) "A 120-page book has p lines to a page. If the number of lines were reduced by three on each page, the number of pages would need to be increased by 20 to give the same amount of writing space. How many lines were there on the page originally? Thanks! 1 solutions Answer 354288 by ankor@dixie-net.com(15656)   on 2011-12-05 08:59:13 (Show Source): You can put this solution on YOUR website!"A 120-page book has p lines to a page. If the number of lines were reduced by three on each page, the number of pages would need to be increased by 20 to give the same amount of writing space. How many lines were there on the page originally? : Let p = no. of pages originally : 120p = no. of lines originally then 140(p-3) = when page lines are reduced by 3, and pages increased by 20 : Total no. of lines remain the same, therefore the equation is: 140(p-3) = 120p 140p - 420 = 120p 140p - 120p = 420 20p = 420 p = p = 21 lines per page originally : : Prove this by seeing the total number of lines remain the same. 120*21 = 2520 lines 140*18 = 2520
 Rate-of-work-word-problems/540853: A truck drove from City A to City B, and the car drove from City B to City A on the same road leaving at the same time. When they met, the truck drove 108 km more than the car. The truck took another 9 hours to arrive at city B, and the car took another 16 hours to get to City A. What is the distance between the two cities?1 solutions Answer 354225 by ankor@dixie-net.com(15656)   on 2011-12-04 21:34:00 (Show Source): You can put this solution on YOUR website!A truck drove from City A to City B, and the car drove from City B to City A on the same road leaving at the same time. When they met, the truck drove 108 km more than the car. The truck took another 9 hours to arrive at city B, and the car took another 16 hours to get to City A. What is the distance between the two cities? : See what we can get from the limited information we have. : Let m = distance to meeting point driven by the car then (m+108) = distance to the meeting point driven by the truck Then Distance from A to B = m + m+108 or 2m + 108 = the distance from A to B : Let t = travel time of both the truck and the car to the meeting point Then = speed of the car = speed of the truck : Speed should be the same on both parts of the trip, therefore Car speed: = Cross multiply t(m+108) = 16m t = : Truck speed: = cross multiply mt = 9(m+108) mt = 9m + 972 t = : From the car speed, replace t with = Cross multiply (m+108)(9m+972) = 16m^2 Foil 9m^2 + 972m + 972m + 104976 = 16m^2 -16m^2 + 9m^2 + 1944m + 104976 = 0 -7m^2 + 1944m + 104976 = 0 : Solve this quadratic equation with the quadratic formula: the positive solution is what we want m = 324 km : Then dist of A to B 2m+108, therefore: 2(324) + 108 = 756 km : : We can confirm this solution by finding the speed of the car of the truck then finding the time truck: 324/9 = 36 mph Car (324+108)/16 = 27 mph Find the total travel time of each 756/27 = 28 hrs 756/36 = 21 hrs ---------------- time dif: 7 hrs as given (16-9) : A lot of steps here, hopefully you follow the steps and it will make sense to you. Let me know please. C
 Miscellaneous_Word_Problems/541453: If someone runs the 1st half of a race at 5mph and the 2nd half at 10mph then what's the average speed? 1 solutions Answer 354213 by ankor@dixie-net.com(15656)   on 2011-12-04 20:00:56 (Show Source): You can put this solution on YOUR website!If someone runs the 1st half of a race at 5mph and the 2nd half at 10mph then what's the average speed? : let d = the halfway distance of the race let a = average speed for the whole race : Write a time equation, time = dist/speed : time at 5mph + time at 10mph = total time + = multiply by 10a, results 2ad + ad = 10(2d) 3ad = 20d divide both sides by d 3a = 20 a = 20/3 a = 6 mph
 Percentage-and-ratio-word-problems/541562: carlos got an 84% on his math test with 25 problems . Write a fraction to show how many questions he got right.1 solutions Answer 354209 by ankor@dixie-net.com(15656)   on 2011-12-04 19:50:25 (Show Source): You can put this solution on YOUR website!.84 * 25 = 21 right : 21/25 is the fraction
 Age_Word_Problems/541467: For my math problem I need to answer this: Three cousins, Heather, Gena, and Jessie, were sitting around watching football on TV.  The game was really boring, and so they started talking about how old they were.  Heather (the oldest) noticed that they were all between 11 and 30.  Jessie noticed that the sum of their ages was 70.  Gena (the youngest) burst out, “Gee, if you write the square of each of our ages, all of the digits from 1 to 9 will appear exactly once in the digits of the three squares.”  How old is each person?  Clearly show and explain your thinking and the process you used to find their ages. I was wondering if there's some kind of equation to solve for their ages or something like that? If you could help me out that would be great! Thanks so much in advance.1 solutions Answer 354208 by ankor@dixie-net.com(15656)   on 2011-12-04 19:46:45 (Show Source): You can put this solution on YOUR website! Heather (the oldest) noticed that they were all between 11 and 30. Jessie noticed that the sum of their ages was 70. Gena (the youngest) burst out, “Gee, if you write the square of each of our ages, all of the digits from 1 to 9 will appear exactly once in the digits of the three squares.” How old is each person? : I don't think there is an equation that will solve this (except the sum of the ages) Try to eliminate as much as you can, with logic : Throw out, 11, 12, 15, 20, 21, 22, 26, 30; squares have two digits the same : From the table below: Choose a value, try another value, if that looks OK, subtract their sum from 70 and see. : 13, 169 14, 196 ------- 16, 256 17, 289 ------- 18, 324 19, 361 ------- 23, 529 24, 576 ------- 25, 625 ------- 27, 729 28, 784 ------- 29, 841 : After several failures, I chose: 19 (361); then 23 (529); then 28,(784)
 logarithm/541358: 6^(3x-1)=7^(x+1) I have tried logging both sides and then moving the exponents in front I think I'm supposed to distribute, but I can't quite remember how. so this is where I am at: 3x-1 log 6 = x+1 log 71 solutions Answer 354187 by ankor@dixie-net.com(15656)   on 2011-12-04 16:51:02 (Show Source): You can put this solution on YOUR website!3x-1 log 6 = x+1 log 7 Find the log of 6 and the log of 7, and you have .778(3x-1) = .845(x+1) 2.334x - .778 = .845x + .845 2.334x - .845x = .845 + .778 let you do the math here : Check your solution in the original equation
 Age_Word_Problems/541339: in three years. michael's uncle will be six times as old as michael was last year. when michael's present age is added to his uncle's present age, the total is 68. how old is each one now?1 solutions Answer 354184 by ankor@dixie-net.com(15656)   on 2011-12-04 16:36:52 (Show Source): You can put this solution on YOUR website!in three years. michael's uncle will be six times as old as michael was last year. when michael's present age is added to his uncle's present age, the total is 68. how old is each one now? : Let m = Michael's age Let u = Uncle's age : Write an equation for each statement: : "in three years. michael's uncle will be six times as old as michael was last year. u + 3 = 6(m - 1) u + 3 = 6m - 6 u = 6m - 6 - 3 u = 6m - 9 : "when michael's present age is added to his uncle's present age, the total is 68. m + u = 68 Replace u with (6m-9) m + 6m - 9 = 68 7m = 68 + 9 7m = 77 m = 77/7 m = 11 yrs is M's present age then 68 - 11 = 57 yrs is Uncle's present age : : Check our solutions in the statement: in three years. michael's uncle will be six times as old as michael was last year. 57 + 3 = 6(11-1) 60 = 6(10); confirms our solutions
 Miscellaneous_Word_Problems/541307: A certain kind of bacteria triples every 2 hours.At 8:00 P.M.,there was 153,090 bacteria counted in the petri dish.How many were there at 6:00 A.M.?1 solutions Answer 354182 by ankor@dixie-net.com(15656)   on 2011-12-04 16:18:41 (Show Source): You can put this solution on YOUR website!A certain kind of bacteria triples every 2 hours. At 8:00 P.M., there was 153,090 bacteria counted in the petri dish. How many were there at 6:00 A.M.? : 153,090 after 14 hrs : Let Ao = initial amt at 6 AM : = 153090 that's 14/2 so we have = 153090 Ao*2187 = 153090 Ao = Ao = 70 bacteria at 6 AM
 Travel_Word_Problems/541106: A car drove from one city to another and returned by different route. The outward journey was 48 km and the return journey was 8 km shorter. The speed of the car on the return journey increased by 4 km/h. The return journey took one hour less time. Find the speed of the car on the outward journey.1 solutions Answer 354058 by ankor@dixie-net.com(15656)   on 2011-12-03 21:23:32 (Show Source): You can put this solution on YOUR website!A car drove from one city to another and returned by different route. The outward journey was 48 km and the return journey was 8 km shorter. The speed of the car on the return journey increased by 4 km/h. The return journey took one hour less time. Find the speed of the car on the outward journey. : let t = time of the outward journey (48 km) then (t-1) = time of the return journey (40km) : Write speed equation, speed = dist/time : return speed - outbound speed = 4 km/hr - = 4 km : multiply by t(t-1), results: 40t - 48(t-1) = 4t(t-1) 40t - 48t + 48 = 4t^2 - 4t -8t + 48 = 4t^2 - 4t 0 = 4t^2 - 4t + 8t - 48 : A quadratic equation 4t^2 + 4t - 48 = 0 : Simplify, divide by 4 t^2 + t - 12 = 0 : factors to: (t+4)(t-3) = 0 : The positive solution t = 3 hrs travel time of the outbound journey Find the speed = 16 km/hr speed on the outbound journey : : Confirm this solution by finding the speed on the return journey = 20 km/hr, a 4 km/hr difference
 Percentage-and-ratio-word-problems/540822: A tank measuring 20 cm by 12 cm by 15 cm was filled with some water. The ratio of the volume of water in the tank to the volume of water in a tub was 5:2. When 1/10 of the water in the tank was poured into the tub, the volume of water in the tub increased by 12 cm^3. What fraction of the tank was not filled with water in the beginning?1 solutions Answer 354040 by ankor@dixie-net.com(15656)   on 2011-12-03 20:06:29 (Show Source): You can put this solution on YOUR website!A tank measuring 20 cm by 12 cm by 15 cm was filled with some water. The ratio of the volume of water in the tank to the volume of water in a tub was 5:2. When 1/10 of the water in the tank was poured into the tub, the volume of water in the tub increased by 12 cm^3. What fraction of the tank was not filled with water in the beginning? : Find the vol of the tank: 20*12*15 = 3600 cu/cm : Let x = amt of water in the tank originally : "When 1/10 of the water in the tank was poured into the tub, the volume of water in the tub increased by 12 cm^3." .1x = 12 cu/cm x = 120 cu/cm in the tank originally : I don't think it matters how much was in the tub, we just want to know it increased by 12 cu/cm, which represented 1/10 of the amt in the tank. : "What fraction of the tank was not filled with water in the beginning?" = was not filled with water
 Travel_Word_Problems/541064: I need help with this word problem: A plane is traveling from Los Angeles to New York for a total of 2650 miles. It will take 5.4 hours to complete the trip after traveling 475 miles. How many hours will it take to complet the whole trip?1 solutions Answer 354028 by ankor@dixie-net.com(15656)   on 2011-12-03 19:28:19 (Show Source): You can put this solution on YOUR website!A plane is traveling from Los Angeles to New York for a total of 2650 miles. It will take 5.4 hours to complete the trip after traveling 475 miles. How many hours will it take to complete the whole trip? : Find the speed of the plane s = s = 402.778 mph : Find the time of the whole trip t = t = 6.58 hrs ; : Check this by finding the time of the 1st 475 mi = 1.18 hrs Add to the time of the rest of the trip 5.4 + 1.18 = 6.58 hrs
 Rate-of-work-word-problems/540708: To finish one task, Cathy need 2 more days than Mike.Cathy worked on it for 3 days, then Mike worked on it another 4 days. They only finish 80% of the task. How many days does Cathy need to finish the task alone.1 solutions Answer 354025 by ankor@dixie-net.com(15656)   on 2011-12-03 19:08:15 (Show Source): You can put this solution on YOUR website!To finish one task, Cathy need 2 more days than Mike. Cathy worked on it for 3 days, then Mike worked on it another 4 days. They only finish 80% of the task. How many days does Cathy need to finish the task alone. : Let t = no. of days required by Cathy working alone then (t-2) - no. of days required by Mike : Let the completed job = 1 then .8 = 80% of the job : The equation for the statement: "Cathy worked on it for 3 days, then Mike worked on it another 4 days. They only finish 80% of the task." + = .8 : multiply by t(t-2), results 3(t-2) + 4t = .8t(t-2) 3t - 6 + 4t = .8t^2 - 1.6t 7t - 6 = .8t^2 - 1.6t 0 = .8t^2 - 1.6t - 7t + 6 : A quadratic equation .8t^2 - 8.6x + 6 : Get rid of those decimals, mult by 10 8t^2 - 86t + 60 = 0 ; Simplify, divide by 2 4t^2 - 43t + 30 = 0 : Factors to: (4t - 3)(t - 10) = 0 Two solutions 4t = 3 t = 3/4 t = .75 and t = 10 hrs is the reasonable answer for Cathy's time alone : : Check solution (Mike's time is 8 hrs + = .3 + .5 = .8
 Quadratic_Equations/540859: a parabola passes through the points (0,8),(2,-1) and (4,-1). find the equation of the parabola. thanks 1 solutions Answer 354018 by ankor@dixie-net.com(15656)   on 2011-12-03 18:42:19 (Show Source): You can put this solution on YOUR website!a parabola passes through the points (0,8),(2,-1) and (4,-1). find the equation of the parabola. : Using the form ax^2 + bx + c = y The first point, 0,8, indicates that c = 8 : Write equations for the other two points x=2, y=-1 4a + 2b + 8 = -1 4a + 2b = -1 -8 4a + 2b = -9 : x=4, y=-1 16a + 4b + 8 = -1 16a + 4b = -9 : multiply the 1st equation by -2, add to the 2nd equation -8a - 4b = +18 16a + 4b = -9 ---------------adding eliminates b, find a 8a = 9 a = a = 1.125 : Find b 4a + 2b = -9 4(1.125) + 2b = -9 4.5 + 2b = -9 2b = -9 - 4.5 2b = -13.5 b = -6.75 : The equation: y = 1.125x^2 - 6.75x + 8 : You can confirm this by substituting for x and finding y for each point
 Equations/540745: This is the last one that I am struggling with. 2r-2/ r^2+3r-28 + 4/r+7 = r/r-4 This should read 2r-2 over r squared plus 3r minus 28 plus 4 over r+7 equals 1 over r-4.1 solutions Answer 353845 by ankor@dixie-net.com(15656)   on 2011-12-02 21:38:41 (Show Source): You can put this solution on YOUR website! I am assuming the last fraction is 1/(r-4) as you said in the text : + = Factor the 1st denominator and this will all make sense + = Multiply by (r+7)(r-4), cancels the denominators and you have 2r - 2 + 4(r-4) = r + 7 2r - 2 + 4r - 16 = r + 7 6r - 18 = r + 7 6r - r = 7 + 18 5r = 25 r = 25/5 r = 5 You can check this solution in the original equation