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 Money_Word_Problems/447073: Upon his death Mr. Money Bags left 1/2 of his eastate to his wife, 1/8 to each of his two children, 1/10 to each of his two grandchildren and \$10,000 to his favorite charity. What was the value of his eastate?1 solutions Answer 307869 by ankor@dixie-net.com(15645)   on 2011-05-09 17:23:01 (Show Source): You can put this solution on YOUR website!Upon his death Mr. Money Bags left 1/2 of his eastate to his wife, 1/8 to each of his two children, 1/10 to each of his two grandchildren and \$10,000 to his favorite charity. What was the value of his estate? : Let x = the value of his estate : x - x - x - x = 10000 Reduce fractions x - x - x - x = 10000 multiply by 20 to get rid of those annoying fractions 20x - 10x - 5x - 4x = 20(10000) 20x - 19x = 200000 x = \$200,000
 Triangles/446980: 1) The legs in an isosceles right triangle measure 5 units more than twice the measure of the third side. Find the measure of each side of the triangle if the perimeter is 30.1 solutions Answer 307867 by ankor@dixie-net.com(15645)   on 2011-05-09 17:13:20 (Show Source): You can put this solution on YOUR website!The legs in an isosceles right triangle measure 5 units more than twice the measure of the third side. Find the measure of each side of the triangle if the perimeter is 30. : I don't think this can be a "right triangle" : Let x = the third side then it say,"legs in an isosceles triangle measure 5 units more than twice the measure of the third side" 2x + 5 = legs of the isosceles triangle : The three sides = 30 2(2x+5) + x = 30 4x + 10 + x = 30 4x + x = 30 - 10 5x = 20 x = x = 4 units is the 3rd side then 2(4) + 5 = 13 units are the other two sides : : Check: 13+13+4 = 30
 Systems-of-equations/447133: During the 1998-1999 Little League season, the Tigers played 52 games. They won 12 more games than they lost. How many games did they win that season? I figured if you divided 52 by 2 and you get 26 then add 12 then you get the answer of 38 but not sure how to put it into an equation . Or am I even close ? 1 solutions Answer 307863 by ankor@dixie-net.com(15645)   on 2011-05-09 17:03:50 (Show Source): You can put this solution on YOUR website!During the 1998-1999 Little League season, the Tigers played 52 games. They won 12 more games than they lost. How many games did they win that season? : Here's how they probably want you to do this: : Let x = no. of games won then since the total no. of game is 52, we know: (52-x) = no. of games lost : Write an equation for: "They won 12 more games than they lost." or Games won = Games lost + 12 games x = (52-x) + 12 Add x to both sides x + x = 52 + 12 2x = 64 divide both sides by 2 x = x = 32 games won
 Pythagorean-theorem/446910: I tried using the solver for this problem but I still can't get it right. Can someone help me? I have read about legs but I'm not sure which leg is which, so I'll have to descibe the problem as height, width, and diagonal. The problems says: Use a Pythagorean theorem to find the value of x. The height of the triangle is x-10 and the diagonal is x+10, the width is x. When I used the solver it gave me the answer of 0, which was wrong. Thanks x 1 solutions Answer 307857 by ankor@dixie-net.com(15645)   on 2011-05-09 16:55:53 (Show Source): You can put this solution on YOUR website!Use a Pythagorean theorem to find the value of x. The height of the triangle is x-10 and the diagonal is x+10, the width is x. : You don't need a solver for something as simple as this: a^2 + b^2 = c^2 is all you need to know where a and b are the legs, which is which does not matter c = the hypotenuse (or diagonal) and is always the longest dimension : In your problem x^2 + (x-10)^2 = (x+10)^2 FOIL x^2 + (x^2 - 20x + 100) = x^2 + 20x + 100 Combine like terms on the left x^2 + x^2 - x^2 - 20x - 20x + 100 - 100 = 0 which is x^2 - 40x = 0 Factor out x x(x - 40) = 0 Two solutions x = 0 and x = 40; the solution we want : : see if this works a = 40 b = (40-10) = 30 c = (40+10) = 50 40^2 + 30^2 = 50^2 1600 + 900 = 2500; confirms our solution of x=40
 Geometry_Word_Problems/446911: Suppose there are two cubes, with the first cube having a side of h, and the second cube having a side of 5h. What is the relation of the volume of the first cube to the volume of the second?1 solutions Answer 307854 by ankor@dixie-net.com(15645)   on 2011-05-09 16:39:08 (Show Source): You can put this solution on YOUR website!Suppose there are two cubes, with the first cube having a side of h, and the second cube having a side of 5h. What is the relation of the volume of the first cube to the volume of the second? : Since all three dimensions multiplied by 5, the volume relationship is 5^3 or 125 times the original : Illustrate that original: 1*1*1 = 1 cu unit Second: 5*5*5 = 125 cu units
 Quadratic_Equations/447037: Write a quadratic equation that has as solutions the given pair of numbers: -7/2 and 1/4. Please help, I don't have the slightest idea where to begin.1 solutions Answer 307805 by ankor@dixie-net.com(15645)   on 2011-05-09 14:27:16 (Show Source): You can put this solution on YOUR website!Write a quadratic equation that has as solutions the given pair of numbers: -7/2 and 1/4. : x = and x = Which come from the factors (2x + 7) = 0 and (4x - 1) = 0 : FOIL: (2x+7)*(4x-1) y = 8x^2 - 2x + 28x - 7 y = 8x^2 + 26x - 7; is the quadratic equation for these two solutions : Did that make some sense to you?
 Travel_Word_Problems/446986: PLEASE HELP! A cyclist traveled 60 miles at a constant before reducing the speed by 2 mph. Another 40 miles was traveled at the reduced speed. The total time for the 100-mile trip was 9 hours. Find the rate during the first 60 miles.1 solutions Answer 307790 by ankor@dixie-net.com(15645)   on 2011-05-09 13:27:42 (Show Source): You can put this solution on YOUR website!A cyclist traveled 60 miles at a constant before reducing the speed by 2 mph. Another 40 miles was traveled at the reduced speed. The total time for the 100-mile trip was 9 hours. Find the rate during the first 60 miles. : Let s = rate during the 1st 60 mi then (s-2) = reduced rate for the last 40 mi : Write a time equation; time = dist/speed : Normal rate time + reduced rate time = 9 hrs + = 9 multiply by s(s-2), results 60(s-2) + 40s = 9s(s-2) 60s - 120 + 40s = 9s^2 - 18s 100s - 120 = 9s^2 - 18s Arrange as a quadratic equation on the right 0 = 9s^2 - 18s - 100s + 120 9s^2 - 118s + 120 = 0 You can solve for s using the quadratic formula, but this will factor to (9s-10)(s-12) = 0 Two solutions, but only one is reasonable 9s = 10 and s = 12 mph, is the speed on the 1st 60 mi : : Confirm this by finding the times 60/12 + 40/10 = 5 + 4 = 9 hrs
 Triangles/446954: Two cars leave an intersection. One car travels north;the other east. When the car traveling north had gone 6 mi, the distance between the cars was 2 mi more than the distance traveled by the car heading east. How far had the eastbound car traveled?1 solutions Answer 307779 by ankor@dixie-net.com(15645)   on 2011-05-09 12:00:15 (Show Source): You can put this solution on YOUR website!Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 6 mi, the distance between the cars was 2 mi more than the distance traveled by the car heading east. How far had the eastbound car traveled? : let a = distance traveled by the eastbound car : Solve this as a right triangle: a^2 + b^2 = c^2 Where a = east dist b = 6 mi c = (a+2) : a^2 + 6^2 = (a+2)^2 FOIL the right side a^2 + 36 = a^2 + 4a + 4 Combine like terms on the right 0 = a^2 - a^2 + 4a + 4 - 36 4a - 32 = 0 4a = 32 a = a = 8 mi east dist : : See if that is right 8^2 + 6^2 = 10^2
 Exponential-and-logarithmic-functions/446793: I need help solving this problem: 1n (x+2) - 1n (x-1)=11 solutions Answer 307740 by ankor@dixie-net.com(15645)   on 2011-05-09 08:22:35 (Show Source): You can put this solution on YOUR website!1n (x+2) - 1n (x-1) = 1 When logs are subtracted we can divide the terms = 1 exponent equiv = which is = 2.71828 x + 2 = 2.71828(x-1) : x + 2 = 2.71828x - 2.71828 : 2 + 2.71828 = 2.71828x - x : 4.71828 = 1.71828x : x = x = 2.746 : : Check this on a calc: enter ln(4.746) - ln(1.746), results .99997 ~ 1
 Travel_Word_Problems/446733: Ben has to go to soccer practice. He and his brother leave their house and drive to the school averaging 50 miles per hour. On the way home they averaged only 30 miles per hour due to traffic. What was the average speed of the trip? The answer is NOT 40 miles per hour.1 solutions Answer 307652 by ankor@dixie-net.com(15645)   on 2011-05-08 21:53:08 (Show Source): You can put this solution on YOUR website!He and his brother leave their house and drive to the school averaging 50 miles per hour. On the way home they averaged only 30 miles per hour due to traffic. What was the average speed of the trip? : Let a = average speed for the round trip : Let d = one-way distance to school ; Write time equation: time = dist/speed : To time + return time = total time + = Multiply by 150a to clear the denominators 150a* + 150a* = 150a* cancel the denominators 3a(d) + 5a(d) = 150(2d) Divide thru by d, we don't need that 3a + 5a = 150(2) 8a = 300 a = a = 37.5 mph is the average speed for the round trip : : You can confirm this. Use a one-way dist of 150 mi 150/50 + 150/30 = 300/37.5
 Money_Word_Problems/446471: A cow costs seven times as much as a goat,for 84000,I can buy 18 more goats than cows.How much does a goat cost?1 solutions Answer 307644 by ankor@dixie-net.com(15645)   on 2011-05-08 21:29:24 (Show Source): You can put this solution on YOUR website!A cow costs seven times as much as a goat,for 84000, I can buy 18 more goats than cows. How much does a goat cost? : Let x = cost of a goat (g) then 7x = cost of a cow (c) : g = no. of goats c = no. or cows "I can buy 18 more goats than cows" g - c = 18 g = (c+18) : Cost equation xg + 7xc = 84000 Replace g with (c+18) x(c+18) + 7xc = 84000 xc + 18x + 7xc = 84000 18x + 8xc = 84000 x(18 + 8c) 84000 x = From this equation we can see that there are many solutions, for example: Using integer values, let c = 24 cows, find the cost of one goat (x) x = x = x = x = \$400 for one goat : Check this: 24 + 18 = 42 goats, and 7(400) = \$2800 for one cow 42(400) + 24(2800) = 16800 + 67200 = \$84000 : another integer solution: 3 cows, yield a cost of \$2000 for one goat You can confirm this solution yourself
 logarithm/446445: Solve the logarithmic equation for x. (Round your answer to four decimal places.) ln(x − 6) + ln(x + 7) = 1 1 solutions Answer 307575 by ankor@dixie-net.com(15645)   on 2011-05-08 16:56:37 (Show Source): You can put this solution on YOUR website!Solve the logarithmic equation for x. (Round your answer to four decimal places.) ln(x - 6) + ln(x + 7) = 1 : Adding logs is multiply ln((x-6)*(x+7)) = 1 : FOIL ln(x^2 + 7x - 6x - 42) = 1 ln(x^2 + x - 42) = 1) exponent equiv x^2 + x - 42 = e^1 which is x^2 + x - 42 = 2.71828 x^2 + x - 42 - 2.71828 = 0 x^2 + x - 44.71828 = 0 use the quadratic formula is find x x = -7.2058 x = 6.2058; only the positive solution can be used here
 Square-cubic-other-roots/446603: solve if possible could you include steps on how you reached the answer1 solutions Answer 307572 by ankor@dixie-net.com(15645)   on 2011-05-08 16:21:14 (Show Source): You can put this solution on YOUR website!solve = x + 1 if possible could you include steps on how you reached the answer : Square both sides: FOIL the right side x + 3 = x^2 + 2x + 1 Combine like terms on the right 0 = x^2 + 2x - x + 1 - 3 A quadratic equation x^2 + x - 2 = 0 Factors to (x+2)(x-1) = 0 Two solutions x = -2 and x = +1 : : You must check both solutions in the original equation x = -2 = -2 + 1 = -1 1 does not = -1, not a valid solition try x=1 = 1 + 1 = 2; a good solution
 Triangles/446459: Jessica, Mary and Alice share a tin of beans in the ratio 4:5:6 and a portion of peas in the ratio 5:3:4. Alice's helping of beans is three times as big as her helping of peas. 1) Show clearly that the ratio of the size of the tin of beans to the size of the portion of peas is 5:2 2)What is the ratio of the sizes of Mary's helpings of beans and peas?1 solutions Answer 307557 by ankor@dixie-net.com(15645)   on 2011-05-08 15:25:19 (Show Source): You can put this solution on YOUR website!Jessica, Mary and Alice share a tin of beans in the ratio 4:5:6 and a portion of peas in the ratio 5:3:4. Alice's helping of beans is three times as big as her helping of peas. ; Let x Bean multiplier Let y Peas multiplier then J, M, A Beans: 4x, 5x, 6x J, M, A Peas: 5y, 3y, 4y : "Alice's helping of beans is three times as big as her helping of peas." 6x = 3(4y) 6x = 12y x = 2y : 1) Show clearly that the ratio of the size of the tin of beans to the size of the portion of peas is 5:2 Beans: 4x + 5x + 6x = 16x is the amt of beans Replace x with 2y, find amt of beans in terms of y: then: 8y + 10y + 12y = 30y is the amt of beans : Peas: 5y + 3y + 4y = 12y is the amt of peas : Ratio of Beans to Peas: 30:12 which is 5:2 : ; 2)What is the ratio of the sizes of Mary's helpings of beans and peas? Mary's beans: 5x, Mary's peas: 3y replace x with 2y 10y:3y, 10:3 is Mary's helpings of beans and peas
 Travel_Word_Problems/446506: A car starts from town A towards town B. Another car starts from town B towards town A at the same time. The pass each other 64km from town B. Both cars continued on their journey after passing each other. When they reach the respective towns, they turn around, back to where they came from. This time, they pass each other 52km from town A. What is the distance between town A & B?1 solutions Answer 307538 by ankor@dixie-net.com(15645)   on 2011-05-08 14:21:44 (Show Source): You can put this solution on YOUR website!A car starts from town A towards town B. Another car starts from town B towards town A at the same time. The pass each other 64km from town B. Both cars continued on their journey after passing each other. When they reach the respective towns, they turn around, back to where they came from. This time, they pass each other 52km from town A. What is the distance between town A & B? : A rough diagram of this (first meeting): : Let d = distance from a to b : A --------------------d-----------------------B car a>--------(d-64)------*-----64------< car b : First time they meet: car a travels (d-64) km car b travels 64 km : 2nd meeting car b>----52-------*--------(d-52)------< car a : car a travels 64 + (d-52) = (d+12) car b travels (d-64) + 52 = (d-12) : The ratio a:b of the distances traveled by the two cars remain the same; therefore: 1st meeting = 2nd meeting = ; Cross multiply (d-64)(d-12) = 64(d+12) d^2 - 12d - 64d + 768 = 64d + 768 ; Subtract 768 from both sides, arrange as a quadratic equation d^2 - 76d - 64d = 0 d^2 - 140d = 0 ; Factor d(d - 140) = 0 ; Two solutions d = 0 and d = 140 km distance between the towns : : Find a way to check this: First meeting: a travels (140-64) = 76 mi b travels 64 mi Second meeting a travels 64 + (140-52) = 152 mi b travels (140-64) + 52 = 128 mi ; Check the ratios 76/64 = 1.1875 152/128 = 1.1875; confirms our distance of 140 km
 Mixture_Word_Problems/446543: How much water must be added to 6 ounces of a 20% acid solution to obtain a 15% acid solution? 1 solutions Answer 307527 by ankor@dixie-net.com(15645)   on 2011-05-08 12:32:35 (Show Source): You can put this solution on YOUR website!How much water must be added to 6 ounces of a 20% acid solution to obtain a 15% acid solution? : Let x = amt of water : Write an amt of acid equation, (the amt of acid remains the same only the percent changes) .20(6) = .15(x+6) 1.2 = .15x + .9 1.2 - .9 = .15x .3 = .15 x = x = 2 oz of pure water required : : Prove this by finding the amt of acid in each mixture .2(6) = 1.2 .15(2+6) = 1.2
 Travel_Word_Problems/446486: Two town A and B are 300 km apart. C is exacly halfway between A and B. A cyclist departs from B to C at x km/h at 9h00 and one hour later a second cyclist depatrs form A to C, 5 km/h faster than the first cyclist. They reach C simultaneously. 1.1) Calculate, in terms of x, the time each cyclist requires to reach C. 1.2) Calculate at what time they will reach C.1 solutions Answer 307508 by ankor@dixie-net.com(15645)   on 2011-05-08 11:23:51 (Show Source): You can put this solution on YOUR website!Two town A and B are 300 km apart. C is exacly halfway between A and B. A cyclist departs from B to C at x km/h at 9h00 and one hour later a second cyclist departs form A to C, 5 km/h faster than the first cyclist. They reach C simultaneously. : 1.1) Calculate, in terms of x, the time each cyclist requires to reach C. Time = dist/speed A cyclist: t(x) = hrs B cyclist: t(x) = hrs : Find x B's time + 1 hr = A's time + 1 = : Multiply by x(x+5), results: 150x + x(x+5) = 150(x+5) 150x + x^2 + 5x = 150x + 750 x^2 + 5x + 150x - 150x - 750 = 0 x^2 + 5x - 750 = 0 : Factors to (x+30)(x-25) = 0 : the positive solution x = 25 km/h is A's speed then 25 + 5 = 30 km/h is B's speed : find the travel times A: 150/25 = 6 hrs B: 150/30 = 5 hrs : : 1.2) Calculate at what time they will reach C. 9:00 + 6 = 3 PM; A will reach C and 10:00 + 5 = 3 PM; B will reach C also
 Travel_Word_Problems/446304: A projectile is fired upward from a tower 300 feet high with an intial velocity of 320 feet per second. Its height above ground(h feet)is given at any time(t seconds) by the equation: h=-16t^2+320t+300. How many seconds will it take the projectile to reach its maximum height? What is that maximum height? 1 solutions Answer 307377 by ankor@dixie-net.com(15645)   on 2011-05-07 20:05:18 (Show Source): You can put this solution on YOUR website!A projectile is fired upward from a tower 300 feet high with an initial velocity of 320 feet per second. Its height above ground(h feet)is given at any time(t seconds) by the equation: h=-16t^2+320t+300. How many seconds will it take the projectile to reach its maximum height? : Use the axis of symmetry formula to find the time for max height: x=-b/(2a) t = t = t = +10 seconds it will be at max height : What is that maximum height? Replace t with 10 in the original equation h = -16(10^2) + 320(10) + 300 h = -1600 + 3200 + 300 h = 1900 ft is the max height
 Human-and-algebraic-language/446314: six times the reciprocal of a number equals three times the reciprocal of six. Find the number1 solutions Answer 307345 by ankor@dixie-net.com(15645)   on 2011-05-07 16:46:04 (Show Source): You can put this solution on YOUR website!six times the reciprocal of a number equals three times the reciprocal of six. Find the number : = Cross multiply so find the number
 Travel_Word_Problems/446306: Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 40 miles per hour and Train B is traveling at 50 miles per hour. Train A passes a station at 11:25AM. If Train B passes the same station at 11:37AM, at what time will Train B catch up to Train A? When will Train B catch up with Train A?1 solutions Answer 307344 by ankor@dixie-net.com(15645)   on 2011-05-07 16:43:42 (Show Source): You can put this solution on YOUR website!Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 40 miles per hour and Train B is traveling at 50 miles per hour. Train A passes a station at 11:25AM. If Train B passes the same station at 11:37AM, at what time will Train B catch up to Train A? When will Train B catch up with Train A? : From the given information, we know that Train B is 12 min behind A at at 11:25 am therefore Train B is: * 50 = 10 miles behind Train A at that time. : Let t = time required for Train B to catch Train A : Write a distance equation; dist = speed * time : Train B dist = Train A dist + 10 mi 50t = 40t + 10 50t - 40t = 10 10t = 10 t = 1 hr for B to catch A : Find the time from 11:25 am: 11:25 + 1:00 = 12:25 pm, Train B catches Train A : : Check this by finding the actual distance each train travels B travels: 50*1 = 50 mi while A travels: 40*1 = 40 mi
 Linear-equations/446122: If an object is tossed into the air the path of this object is represented by the equation atē+bt+c=h where h is the height after t seconds, a is the acceleration due to gravity, b is the initial velocity, and c is the initial height. a.A rocket is thrust vertically upward from the top of a tower 80 feet tall, with an initial velocity of 64 ft/s, (the acceleration due to gravity is -16ft/sec). Write the quadratic equation representing this scenario when h is 0. b.Find the roots (solutions) for this quadratic equation, solving by factoring. c.How high will the rocket be after 3 seconds? d.How long will it take for the rocket to hit the ground? How long will it take for the rocket to hit the ground? Given the graph of the equation, identify and appropriately label, the vertex, solutions or roots, all intercepts, and axis of symmetry. Given the graph of the equation, identify and appropriately label, the vertex, solutions or roots, all intercepts, and axis of symmetry. 1 solutions Answer 307336 by ankor@dixie-net.com(15645)   on 2011-05-07 16:21:13 (Show Source): You can put this solution on YOUR website!If an object is tossed into the air the path of this object is represented by the equation atē+bt+c=h where h is the height after t seconds, a is the acceleration due to gravity, b is the initial velocity, and c is the initial height. : a.A rocket is thrust vertically upward from the top of a tower 80 feet tall, with an initial velocity of 64 ft/s, (the acceleration due to gravity is -16ft/sec). Write the quadratic equation representing this scenario when h is 0. -16t^2 + 64t + 80 = 0 : b.Find the roots (solutions) for this quadratic equation, solving by factoring. -16t^2 + 64t + 80 = 0 Simplify, divide by -16, (makes it easier to factor), results: t^2 - 4t - 5 = 0 factors to (t-5)(t+1) = 0 Roots t=+5 t=-1 : c.How high will the rocket be after 3 seconds? Replace t with 3 in the original equation h = -16(3^2) + 64(3) + 80 h = -16(9) + 192 + 80 h = -144 + 192 + 80 h = 128 ft after 3 sec : d.How long will it take for the rocket to hit the ground? the positive root: t=5 sec, then h=0, which is the ground : Given the graph of the equation, identify and appropriately label, the vertex, solutions or roots, all intercepts, and axis of symmetry. You can see on the graph, the x intercepts, -1 and +5, y intercept y=80 Vertex: x=2, y=144 Axis of symmetry: x=2
 Age_Word_Problems/445977: Today Justin reached 1/11 the age his mother was when he was born. Today, Justin's mother is ____ times as old as Justin. 1 solutions Answer 307265 by ankor@dixie-net.com(15645)   on 2011-05-07 08:08:43 (Show Source): You can put this solution on YOUR website!Today Justin reached 1/11 the age his mother was when he was born. : Let x = mother's present age Let y = Justin's present age then (x-y) = Mother's age when J was born : y = (x - y) multiply both sides by 11 11y = x - y 11y + y = x 12y = x therefore "Today, Justin's mother is _12_ times as old as Justin. : : Let's see if that will work with real numbers Let J be 4 yrs old, then Mom is 12*4 which is 48 4 yrs ago Mom was 44 which is 11 times J's present age
 Geometry_Word_Problems/446009: A landscaper has an empty 1,000-gallon fish pond to fill. His hose delivers one quart of water every thirty seconds. He turns on the hose at 7:00 A.M. and leaves. When he returns at the same time the next day, the pond is: A. approximately one half full. B. about three quarters full. C. almost full. D. overflowing. How do I solve this problem?1 solutions Answer 307162 by ankor@dixie-net.com(15645)   on 2011-05-06 16:47:23 (Show Source): You can put this solution on YOUR website!A landscaper has an empty 1,000-gallon fish pond to fill. His hose delivers one quart of water every thirty seconds. He turns on the hose at 7:00 A.M. and leaves. When he returns at the same time the next day, the pond is: : that would be 1/2 gal/min : 24 hrs * 60 min * half gallon = , about three-quarters full
 Travel_Word_Problems/445754: During the first part of a trip, a canoeist travels 50 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 3hrs. What was the speed on each part of the trip?1 solutions Answer 307161 by ankor@dixie-net.com(15645)   on 2011-05-06 16:28:42 (Show Source): You can put this solution on YOUR website!During the first part of a trip, a canoeist travels 50 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 3hrs. What was the speed on each part of the trip? : Let s = speed on the 1st part of the trip then (s-5) = speed on the 2nd part : Write a time equation, Time = dist/speed : 1st part time + 2nd part time = 3 + = 3 Multiply by s(s-5); results: 50(s-5) + 2s = 3s(s-5) 50s - 250 + 2s = 3s^2 - 15s 52s - 250 = 3s^2 - 15s A quadratic equation 3s^2 - 15s - 52s + 250 = 0 3s^2 - 67s + 250 = 0 Solve this using the quadratic formula In this problem x=s; a=3; b=-67; c=250 : : Two solutions. only this one is reasonable s = s = 17.598 mph for the 1st 50 miles then 17.598 - 5 = 12.598 mph for the last 2 mi ; : Check this by finding the actual times 50/17.598 = 2.84 hrs 2/12.598 = .16 hrs --------------------- total time: 3 hrs
 Polynomials-and-rational-expressions/445795: how do you simplify 6b2 + 42b ---------- b3 1 solutions Answer 306996 by ankor@dixie-net.com(15645)   on 2011-05-05 21:37:59 (Show Source): You can put this solution on YOUR website!simplify Factor out 6b cancel b
 Mixture_Word_Problems/445611: the cooling system in ann's car contains 19 liters of 30% antifreeze. how much coolant must be drained out and replaced with 80% antifreeze so that the system will contain 50% antifreeze. how much of the original coolant will be left in the car?1 solutions Answer 306993 by ankor@dixie-net.com(15645)   on 2011-05-05 21:06:06 (Show Source): You can put this solution on YOUR website!the cooling system in ann's car contains 19 liters of 30% antifreeze. how much coolant must be drained out and replaced with 80% antifreeze so that the system will contain 50% antifreeze? : Let x = amt of 80% antifreeze added, this is also the amt of 30% antifreeze removed : .30(19-x) + .80x = .50(19) : 5.7 - .3x + .8x = 9.5 : -.3x + .8x = 9.5 - 5.7 : .5x = 3.8 x = x = 7.6 liters of 80% antifreeze added, the same amt of 30% removed : how much of the original coolant will be left in the car? 19 - 7.6 = 11.4 liters of 30% antifreeze remain : : Check solution .3(11.4) + .8(7.6) = 9.5
 logarithm/445173: Use properties of logarithms to expand the loarithmic expressions as much as possile. log2 (4x)1 solutions Answer 306822 by ankor@dixie-net.com(15645)   on 2011-05-05 09:13:45 (Show Source): You can put this solution on YOUR website!Use properties of logarithms to expand the logarithmic expressions as much as possible. log2 (4x) : log2(4) + log2(x) but we know log2(4) = 2 (2^2) write it log2(x) + 2
 Probability-and-statistics/445309: In the Fibonnaci sequence, what number follows 89?1 solutions Answer 306817 by ankor@dixie-net.com(15645)   on 2011-05-05 08:57:31 (Show Source): You can put this solution on YOUR website!: In the Fibonacci sequence, what number follows 89? the next number is the sum of the previous two numbers in the Fibonacci sequence For a low number like 89, the easiest way is just to write the sequence starting with 0 : 0 1 1 2 3 5 8 13 21 34 55 89 144, so 144 is the next number
 Quadratic_Equations/445089: Fireworks are shot upward with an intial velocity of 125 feet per second from a paltform 3 feet abouve the ground. use the model h= -16t squared + vt + s to find how long it will take the rocket to hit the ground?1 solutions Answer 306775 by ankor@dixie-net.com(15645)   on 2011-05-04 21:34:27 (Show Source): You can put this solution on YOUR website!Fireworks are shot upward with an intial velocity of 125 feet per second from a platform 3 feet abouve the ground. Use the model h = -16t squared + vt + s to find how long it will take the rocket to hit the ground? : In this problem: v = 125, s = 3, h = 0, (h = 0 when it hits the ground) : -16t^2 + 125t + 3 = 0 Use the quadratic formula to solve this: In this equation: x=t; a=-16, b=125, c=3 : : : Two solutions t = -.023926 and t = +7.8364 sec, the reasonable solution, for the rocket to hit the ground