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 Linear_Equations_And_Systems_Word_Problems/198713: Mr. Greene has 8.5 in by 11 in cardboard sheets. As a class project, Mr. Greene asked each of his students to amke an open-top box under these conditions: I. Each box must be made by cutting small squares from each corner of a cardboard sheet. II. The box must have a volume of 48 in^3 III. The amount of cardboard waste must be minimized. What is the appropriate side length for the small squares that would be cut from the cardboard sheet?1 solutions Answer 149271 by ankor@dixie-net.com(15746)   on 2009-06-02 21:43:44 (Show Source): You can put this solution on YOUR website!Mr. Greene has 8.5 in by 11 in cardboard sheets. As a class project, Mr. Greene asked each of his students to make an open-top box under these conditions: : I. Each box must be made by cutting small squares from each corner of a cardboard sheet. Let the side of the small square = x then the dimension of the box: (8.5-2x) by (11-2x) by x FOIL x(93.5 - 17x - 22x +4x^2) A volume equation V = 4x^3 - 39x^2 + 93.5x : ; II. The box must have a volume of 48 in^3 4x^3 - 39x^2 + 93.5x = 48 4x^3 - 39x^2 + 93.5x - 48 = 0 : : III. The amount of cardboard waste must be minimized. Graph the above equation to find the values of x: What is the appropriate side length for the small squares that would be cut from the cardboard sheet? : The smaller solution: x ~.7"; would give us the smallest removed squares ; ; : Check our solution: 2x = 1.4 (8.5-1.4) * (11-1.4) * .7 = 7.1 * 9.6 * .7 = 47.4 ~ 48
 Functions/198727: Please HELP!! A pelican flying in the air over water drops a crab from a height of 30 feet. The distance the crab is from the water as it falls can be represented by the function h(t)= -16t^2 + 30, where t is time in seconds. To catch the crab as it falls, a gull flies along a path represented by the function g(t)= -8t + 15. Can the gull catch the crab before the crab hits the water? Thanks!1 solutions Answer 149231 by ankor@dixie-net.com(15746)   on 2009-06-02 18:53:07 (Show Source): You can put this solution on YOUR website!A pelican flying in the air over water drops a crab from a height of 30 feet. The distance the crab is from the water as it falls can be represented by the function h(t)= -16t^2 + 30, where t is time in seconds. To catch the crab as it falls, a gull flies along a path represented by the function g(t)= -8t + 15. Can the gull catch the crab before the crab hits the water? : When the gull catches the crab, they will be at the same height, so we can say: Gull ht = crab ht -8t + 15 = -16t^2 + 30 16t^2 - 8t + 15 - 30 = 0 16t^2 - 8t - 15 = 0 Factors to (4t - 5)(4t + 3) = 0 Positive solution 4t = 5 t = 1.25 sec they will be at the same height (5 ft) : A graph would would show this
 absolute-value/198697: if one-half a number is subtracted from five-sixth of the number, the difference is 6. what is this number1 solutions Answer 149223 by ankor@dixie-net.com(15746)   on 2009-06-02 17:55:06 (Show Source): You can put this solution on YOUR website!if one-half a number is subtracted from five-sixth of the number, the difference is 6. what is this number : x - x = 6 The common denominator x - x = 6 x = 6 x = 6 Multiply both sides by 3 x = 3(6) x = 18
 Quadratic_Equations/198591: Solving Problems with Quadratic Equations 17. Sherri sells photos of athletes to baseball, basketball, and hockey fans after their games. Her regular price is \$10 per photograph, and she usually sells about 30 photographs. Sherri finds that, for each reduction in price of \$0.50, she can sell an additional two photographs. a) Total sales revenue is the product of the number of units sold and the price. Make an algebraic model to represent Sherri's total sales revenue. b) At what price will Sherri's revenue be \$150? c) At what price will her maximum revenue occur? d) At what price will her revenue be \$0? e) Graph the relationship between revenue and the number of price reductions. Which features on the graph represent the solutions to parts b), c), and d)? Thanksssssss1 solutions Answer 149216 by ankor@dixie-net.com(15746)   on 2009-06-02 17:09:15 (Show Source): You can put this solution on YOUR website!regular price is \$10 per photograph, and she usually sells about 30 photographs. Sherri finds that, for each reduction in price of \$0.50, she can sell an additional two photographs. : Let x = ea 50 cent reduction & also = ea photograph increase : a) Total sales revenue is the product of the number of units sold and the price. Make an algebraic model to represent Sherri's total sales revenue. Revenue = price * pictures sold Rev = (10-.5x)*(30+2x) FOIL f(x) = 300 + 20x - 15x - x^2 f(x) = -x^2 + 5x + 300 : ; b) At what price will Sherri's revenue be \$150? -x^2 + 5x + 300 = 150 -x^2 + 5x + 300 - 150 = 0 -x^2 + 5x + 150 = 0 Multiply equation by -1 (easier to factor) x^2 - 5x - 150 = 0 Factors to: (x-15)(x+10) = 0 Positive solution; x = 15 Price: 10 - .5(15) = \$2.50 for \$150 revenue ; Revenue Check: 2.50(30+2(15)) = \$150 : : c) At what price will her maximum revenue occur? Find the axis of symmetry of the equation: y = -x^2 + 5x + 300 x = x = x = 2.5 price(10-.5(2.5)) = 8.75 : : d) At what price will her revenue be \$0? -x^2 + 5x + 300 = 0 x^2 - 5x - 300 = 0 (x-20)(x+15) = 0 x = 20 Price: 10 - .5(20) = \$0 ; : e) Graph the relationship between revenue and the number of price reductions. Which features on the graph represent the solutions to parts b), c), and d)? b: x=15 price reductions; about \$150 c: you can see max rev occurs when x = 2.5 d: x=20, rev = 0
 Exponents/198692: x to the power of 2/3 divided by x to the power of 1/3 is equal to 4 what is x?1 solutions Answer 149203 by ankor@dixie-net.com(15746)   on 2009-06-02 15:45:05 (Show Source): You can put this solution on YOUR website!x to the power of 2/3 divided by x to the power of 1/3 is equal to 4 what is x? : = 4 Subtract exponents when you divide like terms : = 4 : = 4 ; Cube both sides: x = 64 : : Check solution on calc; enter: (64^(2/3))/(64^(1/3)) = 4
 Exponential-and-logarithmic-functions/198661: I need help solving: log(3x-2)^4=121 solutions Answer 149202 by ankor@dixie-net.com(15746)   on 2009-06-02 15:33:52 (Show Source): You can put this solution on YOUR website!I need help solving: log equiv of exponents Divide both sides by 4 which is 3x - 2 = 1000 3x = 1000 + 2 3x = 1002 x = x = 334 : : Check solution on a calc; enter: log((3(334)-2)^4) = 12
 Linear_Algebra/198623: x+2y-z=3 2x-y+z=3 3x-4y+2z=-11 solutions Answer 149197 by ankor@dixie-net.com(15746)   on 2009-06-02 15:10:30 (Show Source): You can put this solution on YOUR website! x + 2y - z = 3 2x - y + z = 3 3x -4y + 2z = -1 : Multiply the 1st equation by 2, add to the 3rd equation 2x + 4y - 2z = 6 3x - 4y + 2z = -1 --------------------Addition eliminates y and z, find x: 5x = 5 x = 1 : Replace x with 1 in the first two equations 1 + 2y - z = 3 2(1) - y + z = 3 : 2y - z = 3 - 1 -y + z = 3 - 2 : 2y - z = 2 -y + z = 1 --------------addition eliminates z, find y y = 3 : Use the 3rd equation to find z: 3x -4y + 2z = -1 3(1) - 4(3) + 2z = -1 3 - 12 + 2z = -1 -9 + 2z = -1 2z = -1 + 9 2z = 8 z = 4 : : Check solutions in the 2nd equation; x = 1; y = 3; z = 4 2x - y + z = 3 2(1) - 3 + 4 = 3 2 - 3 + 4 = 3
 Quadratic_Equations/198658: factorise: 1) 5m2-45n2 2)10m2n2-7mn-12 3) 9a2-(3a-2b)2 4)12x2+35xy+18y2 1 solutions Answer 149173 by ankor@dixie-net.com(15746)   on 2009-06-02 10:58:05 (Show Source): You can put this solution on YOUR website!1) 5m^2-45n^2 Factor out 5 5(m^2 - 9n^2) Factor difference of squares 5(m - 3n)(m + 3n) : 2)10m^2n^2 - 7mn - 12 mn(10mn - 7) - 12 : 3) 9a^2-(3a-2b)^2 9a^2 - (9a^2 - 12ab + 4b^2);square 3a-2b 9a^2 - 9a^2 + 12ab - 4b^2;removing brackets changes the signs 12ab - 4b^2 4b(3a- b) : 4)12x^2 + 35xy + 18y^2 This can be factored (4x + 9y)(3x + 2y)
 Mixture_Word_Problems/198580: Find the cost of liter of solution when you have 70L of cranberry juice that costs \$1.20 and 130L of apple juice that costs \$0.80.1 solutions Answer 149144 by ankor@dixie-net.com(15746)   on 2009-06-01 21:41:18 (Show Source): You can put this solution on YOUR website!Find the cost of liter of solution when you have 70L of cranberry juice that costs \$1.20 and 130L of apple juice that costs \$0.80. : Let x = the cost of the mixture : Resulting total: 70 + 130 = 200L : 200x = 1.20(70) + .80(130) : 200x = 84 + 104 x = x = \$.94 cost per liter
 Numbers_Word_Problems/198557: The sum of a number and its reciprocal is 34/15. Find the number.1 solutions Answer 149075 by ankor@dixie-net.com(15746)   on 2009-06-01 12:35:20 (Show Source): You can put this solution on YOUR website!The sum of a number and its reciprocal is 34/15. Find the number. : x + = Multiply equation by 15x, results 15x(x) + 15(1) = 34x : Arrange as a quadratic equation 15x^2 - 34x + 15 = 0 Factors to: (5x - 3)(3x - 5) = 0 Two solutions 5x = 3 x = and 3x = 5 x = ; ; Check solution using the 1st solution + = + =
 Age_Word_Problems/198528: A man being asked his age replied: "If you take one year from my present age, the result will be three times my son's now, and three years ago, my age was twice what his will be in 5 years." Find the present age of the man.1 solutions Answer 149070 by ankor@dixie-net.com(15746)   on 2009-06-01 10:56:18 (Show Source): You can put this solution on YOUR website!"If you take one year from my present age, the result will be three times my son's now, and three years ago, my age was twice what his will be in 5 years." Find the present age of the man. : Let m = present age of the man let s = present age of the son : Write an equation for each statement : "If you take one year from my present age, the result will be three times my son's now," m - 1 = 3s m = 3s + 1 : :"three years ago, my age was twice what his will be in 5 years." m - 3 = 2(s + 5) m - 3 = 2s + 10 m = 2s + 10 + 3 m = 2s + 13 : From the 1st statement: substitute (3s+1) for m 3s + 1 = 2s + 13 3s - 2s = 13 - 1 s = 12 yrs is son's present age then m = 3(12) + 1 m = 37 yrs is man's present age : : Check solution in the statement: :"three years ago, my age was twice what his will be in 5 years." 37-3 = 2(12+5)
 Age_Word_Problems/198526: Five years from now, A will be 4/5 as old as B; five years ago, he was 2/3 as old then. Find their present ages.1 solutions Answer 149058 by ankor@dixie-net.com(15746)   on 2009-06-01 08:02:41 (Show Source): You can put this solution on YOUR website!Five years from now, A will be 4/5 as old as B; five years ago, he was 2/3 as old then. Find their present ages. : Write an equation for each statement: : (A+5) = (B+5) Multiply by 5, to get rid of the denominator, simplify 4(A+5) = 5(B+5) 4A + 20 = 5B + 25 4A - 5B = -20 + 25 4A - 5B = 5 : (A-5) = (B-5) Multiply by 3 2(A-5) = 3(B-5) 2A - 10 = 3b - 15 2A - 3B = -15 + 10 2A - 3B = -5 : Multiply the above equation by -2, add to the 1st equation -4A + 6B = +10 +4A - 5B = 5 --------------- B = 15 yrs is B's age now then Use 4A - 5B = 5 to find A 4A - 5(15) - 5 4A - 75 = 5 4A = 5 + 75 4A = 80 A = A = 20 yrs is A's age now : : Check solutions in the statement Five years from now, A will be 4/5 as old as B; (20+5) = (15+5) : You can check solutions in the 2nd statement
 Rational-functions/198506: Can you please help me solve this equation? I forget the process for this type and there are no examples in my textbook. Thank you. (((21x^+14x=0)))1 solutions Answer 149034 by ankor@dixie-net.com(15746)   on 2009-05-31 21:51:40 (Show Source): You can put this solution on YOUR website!Can you please help me solve this equation? I forget the process for this type and there are no examples in my textbook. Thank you. : 21x^2 + 14x = 0 : Factor out 7x 7x(3x + 2) = 0 Two solutions 7x = 0 x = 0 and 3x = -2 x = : : Check solution using x = 21()^2 + 14() = 0 21() + 14() = 0 ) + () = 0 ) + () = 0
 Percentage-and-ratio-word-problems/198509: Al mows lawns at a rate of 30 square feet per minute, Bo mows 40 square feet per minute, and Cy mows 60 square feet per minute. They accept a job that requires that they mow 6060 square feet of lawn. Al begins mowing at 7:00 A.M., but Bo does not begin for another 15 minutes. Cy begins mowing at 7:45, and they finish together. How long did Bo work?1 solutions Answer 149032 by ankor@dixie-net.com(15746)   on 2009-05-31 21:23:09 (Show Source): You can put this solution on YOUR website!Al mows lawns at a rate of 30 square feet per minute, Bo mows 40 square feet per minute, and Cy mows 60 square feet per minute. They accept a job that requires that they mow 6060 square feet of lawn. Al begins mowing at 7:00 A.M., but Bo does not begin for another 15 minutes. Cy begins mowing at 7:45, and they finish together. How long did Bo work? : : Let t = Al's mowing time (minutes) then (t-15) = Bo's mowing time and (t-45) = Cy's mowing time : 30t + 40(t-15) + 60(t-45) = 6060 : 30t + 40t - 600 + 60t - 2700 = 6060 : 130t - 3300 = 6060 : 130t = 6060 + 3300 : 130t = 9360 t = t = 72 minutes is Al's mowing time then 72 - 15 = 57 minutes is Bo's mowing time : : Check solution 30(72) + 40(57) + 60(27) = 2160 + 2280 + 1620 = 6060
 test/198394: A triangle has sides 2y, 4y and ()y. Is the triangle a right triangle? Explain.1 solutions Answer 149011 by ankor@dixie-net.com(15746)   on 2009-05-31 16:49:36 (Show Source): You can put this solution on YOUR website!A triangle has sides 2y, 4y and ( root( 4, 5 ) )y. Is the triangle a right triangle? Explain. : A right triangle, the hypotenuse would be: h = h = h = which is h = Extract the perfect squares h = 0r
 Mixture_Word_Problems/198449: How many pounds of refined sugar costing \$1.35 a pound must be added to 120 pounds of another sugar brand of refined sugar costing \$1.75 per pound to make a misture costing \$1.50 a pound?1 solutions Answer 148969 by ankor@dixie-net.com(15746)   on 2009-05-31 14:24:15 (Show Source): You can put this solution on YOUR website!How many pounds of refined sugar costing \$1.35 a pound must be added to 120 pounds of another sugar brand of refined sugar costing \$1.75 per pound to make a mixture costing \$1.50 a pound? ; Let x = amt of \$1.35 sugar required : 1.35x + 1.75(120) = 1.50(x + 120) : 1.35x + 210 = 1.5x + 180 : 210 - 180 = 1.5x - 1.35x : 30 = .15x x = x = 200 lb of \$1.35 sugar ; : Check solution 1.35(200) + 1.75(120) = 1.5(200+120) 270 + 210 = 480
 Travel_Word_Problems/198446: A man traveling 40 miles finds that by traveling one more mile per hour he would make a journey in 2 hours less time. How many miles per hour did he actually travel?1 solutions Answer 148962 by ankor@dixie-net.com(15746)   on 2009-05-31 13:54:31 (Show Source): You can put this solution on YOUR website!A man traveling 40 miles finds that by traveling one more mile per hour he would make a journey in 2 hours less time. How many miles per hour did he actually travel? : Let s = mph he actually traveled : Write a time equation: Time = : Actual time - faster time = 2 hrs - = 2 Multiply each term by s(s+1); results: 40(s+1) - 40s = 2s(s+1) : 40s + 40 - 40s = 2s^2 + 2s Arrange as a quadratic equation, (40s's cancel) 2s^2 + 2s - 40 = 0 Simplify, divide by 2 s^2 + s - 20 = 0 Factors to (s-4)(s+5) = 0 The positive solution s = 4 mph, actual speed then 5 mph is the faster speed ; Check solution find the times 40/4 = 10 hrs 40/5 = 8 hrs
 Miscellaneous_Word_Problems/198445: The units digit of a 2-digit number exceeds the tens digit by 3. If the number, increased by 2, is divided by the sum of the digits decreased by 3, the quotient is 6. Find the number.1 solutions Answer 148954 by ankor@dixie-net.com(15746)   on 2009-05-31 13:24:00 (Show Source): You can put this solution on YOUR website!The units digit of a 2-digit number exceeds the tens digit by 3. If the number, increased by 2, is divided by the sum of the digits decreased by 3, the quotient is 6. Find the number. : two digits: x, y; the number: 10x + y : write an equation for each statement: ; "The units digit of a 2-digit number exceeds the tens digit by 3." y = x + 3 : " If the number, increased by 2, is divided by the sum of the digits decreased by 3, the quotient is 6." = 6 Replace y with (x+3) = 6 Do the math = 6 : Multiply both sides by 2x 11x + 5 = 2x(6) 5 = 12x - 11x x = 5 and y = 5 + 3 y = 8 : The number: 58 : ; Check solution in the statement: "If the number, increased by 2, is divided by the sum of the digits decreased by 3, the quotient is 6." = 6
 Miscellaneous_Word_Problems/198448: The sum of the digits of a three-digit number is 13. If the tens and hundreds digits are interchanged, the new number is 90 less than the original, and if the units and hundreds digit are interchanged, the resulting number is 99 less than the original. Find the original number.1 solutions Answer 148951 by ankor@dixie-net.com(15746)   on 2009-05-31 12:49:20 (Show Source): You can put this solution on YOUR website!The sum of the digits of a three-digit number is 13. If the tens and hundreds digits are interchanged, the new number is 90 less than the original, and if the units and hundreds digit are interchanged, the resulting number is 99 less than the original. Find the original number. : The three digits, x, y, z The original number: 100x + 10y + z : Write an equation for each statement: : "The sum of the digits of a three-digit number is 13." x + y + z = 13 : "If the tens and hundreds digits are interchanged, the new number is 90 less than the original," 100y + 10x + z = 100x + 10y + z - 90 : 100y - 10y + z - z = 100x - 10x - 90 : 90y = 90x - 90 Simplify,divide by 90 y = x - 1 : : "if the units and hundreds digit are interchanged, the resulting number is 99 less than the original." 100z + 10y + x = 100x + 10y + z - 99 : 100z - z + 10y - 10y = 100x - x - 99 : 99z = 99x - 99 Simplify, divide by 99 z = x - 1 : : Using the digit sum equation, substitute (x-1) for y and (x-1) for z x + y + z = 13 x + (x-1) + (x-1) = 13 3y - 2 = 13 3x = 13 + 2 x = x = 5 then y = 4 and z = 4 : The original number: 544 : : Check solution in the statement: "If the tens and hundreds digits are interchanged, the new number is 90 less than the original," 454 = 544 - 90 and "if the units and hundreds digit are interchanged, the resulting number is 99 less than the original." 445 = 544 - 99
 Quadratic_Equations/198392: Quadratic Equations 13. The three sides of a right triangle are consecutive even integers. What is the length of each side? Thanks!!!@@@1 solutions Answer 148910 by ankor@dixie-net.com(15746)   on 2009-05-30 21:31:45 (Show Source): You can put this solution on YOUR website!Quadratic Equations 13. The three sides of a right triangle are consecutive even integers. What is the length of each side? : Let side 1 = x, Let side 2 = (x+2) Hypotenuse = (x+4) : x^2 + (x+2)^2 = (x+4)^2 FOIL x^2 + x^2 + 4x + 4 = x^2 + 8x + 16 Combine on the left x^2 + x^2 - x^2 + 4x - 8x + 4 - 16 = 0 A quadratic equation x^2 - 4x - 12 = 0 Factors to: (x-6)(x+2) = 0 The positive solution x = 6 is side 1 6 + 2 = 8 is side 2 6 + 4 = 10 is the hypotenuse : 6, 8, 10 consecutive even integers ; ; Check solution 6^2 + 8^2 = 10^2
 Geometry_Word_Problems/198388: A landscape architect used the entire length of an 80ft rope to lay out a flower bed in the shape of a square. In another area, he used the entire length of the same rope to lay out a second flower bed in the shape of a circle. Perimeter of square = 80 feet Circumference of circle = 80 feet How many square feet greater is the area of one of the flower beds than the other? (use 3.14 for pi) This looks to be from a textbook, but no reference are made on the paper. Thank you!1 solutions Answer 148909 by ankor@dixie-net.com(15746)   on 2009-05-30 19:55:28 (Show Source): You can put this solution on YOUR website!A landscape architect used the entire length of an 80ft rope to lay out a flower bed in the shape of a square. In another area, he used the entire length of the same rope to lay out a second flower bed in the shape of a circle. Perimeter of square = 80 feet Circumference of circle = 80 feet How many square feet greater is the area of one of the flower beds than the other? (use 3.14 for pi) : Area of the square: 20 * 20 = 400 sq/ft : Find the radius of the circle using the circumference: 2*3.14*r = 80 r = r = 12.74 ft : Find the area of the circle using 13.03 as the radius A = 3.14*12.74^2 A = 509.6 sq/ft ; : 509.6 - 400 = 109.6 sq/ft more in the circle
 Rate-of-work-word-problems/198387: If John can paint a house in 6 hours. Mary can paint one in 4 hours and Sue can paint one in 2 hours, how long would it take them to paint a house if they worked together?1 solutions Answer 148906 by ankor@dixie-net.com(15746)   on 2009-05-30 19:19:40 (Show Source): You can put this solution on YOUR website!If John can paint a house in 6 hours. Mary can paint one in 4 hours and Sue can paint one in 2 hours, how long would it take them to paint a house if they worked together? : Let t = time required if they all work together : Let the completed job = 1 : Each will paint a fraction of the house. All three fractions add up to 1 + + = 1 Multiply by 12: 12* + 12* + 12* = 12(1) Cancel out the denominators; results: 2t + 3t + 6t = 12 : 11t = 12 t = t = 1.09 hrs or 1 hr + .09(60) = 5.45 min
 Rational-functions/198225: alyssa has determined that the function r(x)=3x(cubed)-2x(squared)+x+25 is good predictor of her income tax refund, where X is the number of years since 2000. use synthetic substitution to estimate alyssa's 2007 tax refund. 1 solutions Answer 148861 by ankor@dixie-net.com(15746)   on 2009-05-30 14:18:52 (Show Source): You can put this solution on YOUR website!r(x)= is good predictor of her income tax refund, where X is the number of years since 2000. use synthetic substitution to estimate alyssa's 2007 tax refund. Not sure what synthetic substitution is; but using substitution: : x = 7 : r(x)= : r(x)= : r(x)= 1029 - 98 + 32 : r(x) = \$963
 Polynomials-and-rational-expressions/198218: This question is from textbook Algebra ! I am having problems solving this problem : two Y over Y squared minus 25 plus y +5 over y-5 can you please help me and send me the step by step1 solutions Answer 148858 by ankor@dixie-net.com(15746)   on 2009-05-30 14:08:11 (Show Source): You can put this solution on YOUR website!two Y over Y squared minus 25 plus y +5 over y-5 You can't solve it, just simplify it. Assume the problem is: + Factor the 1st denominator (the difference of squares) + The common denominator:(y-5)(y+5), so we have FOIL and combine like terms = ; that's about all you can do with it.
 Exponential-and-logarithmic-functions/198119: please graph this logarithemic function.. thanks big time:) [] means the number in it is the base.. y=log[4](x+1)1 solutions Answer 148831 by ankor@dixie-net.com(15746)   on 2009-05-30 12:04:00 (Show Source): You can put this solution on YOUR website!y=log[4](x+1) : Write the exponent equiv of logs Choose values for x that will give you multiples of 4 x = 0 that would be : x = 15 : x = 63 : x = 255 : A table to plot a graph: x | y ------- 0 | 0 15 | 2 63 | 3 256| 4 etc
 Quadratic_Equations/198348: A fast train takes three hours less than the slow train for a journey of 600 km.If the speed of slow train is 10km/hr less than that of fast train.Find the speed of the two trains.1 solutions Answer 148820 by ankor@dixie-net.com(15746)   on 2009-05-30 09:54:46 (Show Source): You can put this solution on YOUR website!A fast train takes three hours less than the slow train for a journey of 600 km. If the speed of slow train is 10km/hr less than that of fast train. Find the speed of the two trains. : Let s = slow train speed then (s+10) = fast train : Write a time equation: Time ; Slow train time - Fast train speed = 3 hrs - = 3 Multiply each term by s(s+10); results 600(s+10) - 600s = 3s(s+10) : 600s + 6000 - 600s = 3s^2 + 30s : Arrange as a quadratic equation, (600s's cancel) 3s^2 + 30s - 6000 = 0 Simplify, divide by 3 s^2 + 10s - 2000 = 0 Factors to (s = 50)(s - 40) = 0 positive solution s = 40 km/hr speed of the slow train then 50 km/hr speed of the fast train : : Check solution by finding the time difference 600/40 = 15 hrs 600/50 = 12 hrs -------------- difference 3 hrs
 Quadratic_Equations/198328: Quadratic equation 4. The product of two consecutive numbers is 3306. What are the numbers? Thanks!!!1 solutions Answer 148791 by ankor@dixie-net.com(15746)   on 2009-05-29 21:20:57 (Show Source): You can put this solution on YOUR website!The product of two consecutive numbers is 3306. What are the numbers? : Two consecutive numbers, x, (x+1) : The product: x * (x+1) = 3306 : x^2 + x = 3306 : A quadratic equation x^2 + x - 3306 = 0 : Find the square root of 3306 = 57.497.. we know the x value will be close to that (x + 58)(x - 57) = 0 Two solutions x = 57, 58 are the two numbers and x = -58, -57 are also be a solution
 Miscellaneous_Word_Problems/198226: The Parkhursts used 160 yd of fencing to enclose a rectangular corral and to divide it into two parts by a fence parallel to one of the shorter sides. Find the dimensions of the corral if its area is 1000 yd^2.1 solutions Answer 148789 by ankor@dixie-net.com(15746)   on 2009-05-29 21:01:26 (Show Source): You can put this solution on YOUR website!The Parkhursts used 160 yd of fencing to enclose a rectangular corral and to divide it into two parts by a fence parallel to one of the shorter sides. Find the dimensions of the corral if its area is 1000 yd^2. : Let x = the width, the shorter side Let L = the length : Perimeter for this configuration 2L + 3x = 160 L in terms of x 2L = 160 - 3x divide both sides by 2 L = 80 - 1.5x : Area: L * x = 1000 substitute (80-1.5x) for L (80-1.5x) * x = 1000 A quadratic equation: -1.5x^2 + 80x - 1000 = 0 Multiply by -2, change the signs, get rid of the decimal 3x^2 - 160x + 2000 = 0 Factors to: (3x - 100)(x - 20) = 0 Two solutions 3x = 100 x = 33 and x = 20 yd wide is the reasonable solution : Find the length L = 80 - 1.5(20) L = 80 - 30 L = 50 yds long : : Check solution 2(50) + 3(20) = 160 and 50 * 20 = 1000 sq/yds
 Money_Word_Problems/198299: This question is from textbook Intermediate Algebra An Applied Approach A merchant mixed 10 lb of cinnamon tea with 5 lb of spice tea. The 15 pd mixture cost \$40. A second mixture included 12 lb of the cinnamon tea and 8 lb of the spice tea. The 20 pd mixture cost \$54. Find the cost per pound of the cinnamon tea and of the spice tea.1 solutions Answer 148764 by ankor@dixie-net.com(15746)   on 2009-05-29 16:25:19 (Show Source): You can put this solution on YOUR website!A merchant mixed 10 lb of cinnamon tea with 5 lb of spice tea. The 15 pd mixture cost \$40. : A second mixture included 12 lb of the cinnamon tea and 8 lb of the spice tea. : The 20 pd mixture cost \$54. Find the cost per pound of the cinnamon tea and of the spice tea. : Let c = cost/lb for cinnamon tea Let s = cost/lb for spice tea : Two equations 10c + 5s = 40 12c + 8s = 54 : Multiply 1st equation by 8, the 2nd equation by 5, results: 80c + 40s = 320 60c + 40s = 270 -------------------subtraction eliminates s, find c 20c = 50 c = c = \$2.50 a lb for cinnamon tea : Find s, substitute 2.5 for c in the 1st equation 25 + 5s = 40 5s = 40 - 25 s = s = \$3 for spice tea ; ; Check solution 2nd equation 12(2.5) + 8(3) = 30 + 24 = 54