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 Travel_Word_Problems/328832: At the beginning of a walk, Roberto and Juanita are 7.7 miles apart. If they leave at the same time and walk in the same directions. Roberto over take jaunita in 11 hours. If they walk towards each other they meet in one hour. What are their speeds?1 solutions Answer 235587 by ankor@dixie-net.com(15660)   on 2010-08-04 14:11:19 (Show Source): You can put this solution on YOUR website!At the beginning of a walk, Roberto and Juanita are 7.7 miles apart. If they leave at the same time and walk in the same directions. Roberto over take jaunita in 11 hours. If they walk towards each other they meet in one hour. What are their speeds? : let r = R's speed let j = J's speed : Write two distance equations, d = time * speed : Walking the same direction 11(r-j) = 7.7 divide both sides by 11 r - j = .7 : Walking toward each other 1(r+j) = 7.7 r + j = 7.7 : Add the two equations r - j = .7 r + j = 7.7 ---------------additional eliminates j, find r 2r = 8.4 r = r = 4.2 mph is R's walking speed : Find J's speed using eq: r + j = 7.7 4.2 + j = 7.7 j = 7.7 - 4.2 j = 3.5 mph is J's walking speed : : Check solutions in the "toward" equation 1 * (3.5 + 4.2) = 7.7
 Quadratic_Equations/328753: During the first part of a trip, a canoeist travels 87 miles at a certain speed. The canoeist travels 9 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 5 hours. What was the speed on the FIRST part of the trip? What was the speed on the SECOND part of the trip? (type an integer or a decimal. Round to the nearest hundredth)1 solutions Answer 235583 by ankor@dixie-net.com(15660)   on 2010-08-04 13:52:25 (Show Source): You can put this solution on YOUR website!During the first part of a trip, a canoeist travels 87 miles at a certain speed. The canoeist travels 9 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 5 hours. What was the speed on the FIRST part of the trip? What was the speed on the SECOND part of the trip? (type an integer or a decimal. Round to the nearest hundredth) : Let s = "a certain speed on the first part of the speed" then (s-5) = "speed on the second part of the trip" : : Write a time equation: Time = dist/speed : 1st part time + 2nd part time = 5 hrs + = 5 : Multiply equation by s(s-5), results: 87(s-5) + 9s = 5s(s-5) : 87s - 435 + 9s = 5s^2 - 25s : 96s - 435 = 5s^2 - 25s Arrange as a quadratic equation 5s^2 - 25s - 96s + 435 = 0 : 5s^2 - 121s + 435 = 0 Use the quadratic formula to find s: in this problem: x=s; a=5; b=-121; c= 435 : : Two solutions, but this is the one that makes sense s = s = 19.81 mph on the first part of the trip then 19.81 - 5 = 14.81 mph on the 2nd part : : Check solution + = 4.39 + .61 = 5 hrs, confirms our solutions
 Equations/328296: The chief of police for smalltown USA notice that, not including himself, 3/5 of his police force carries firearms. If he include himself, 5/8 of his force carries fairearms. How many people on his force do not carry firearms? a) 5 b) 6 c) 11 d) 16 e) 24 1 solutions Answer 235368 by ankor@dixie-net.com(15660)   on 2010-08-03 18:24:53 (Show Source): You can put this solution on YOUR website!The chief of police for small town USA notice that, not including himself, 3/5 of his police force carries firearms. If he include himself, 5/8 of his force carries firearms. How many people on his force do not carry firearms? : Originally then, 2/5 did not carry guns Later then, 3/8 did not carry guns : Let x = total on the police force not counting the chief : No. not carrying guns remains unchanged, so we have: x = (x+1) Multiply both sides by 40, results 8(2)x = 5(3(x+1)) 16x = 15x + 15 16x - 15x = 15 x = 15 total on the police force then *15 = 6 did not carry guns : Confirm solution *(15+1) = 6 also
 Miscellaneous_Word_Problems/328265: I need help please. I am unable to solve. Please show work. Thanks! The population of a certain geographic region is approximately 135 million and grows continuously at a relative growth rate of 1.87%. What will the population be in 6 years? Compute the answer to three significant digits. 1 solutions Answer 235357 by ankor@dixie-net.com(15660)   on 2010-08-03 17:46:11 (Show Source): You can put this solution on YOUR website!The population of a certain geographic region is approximately 135 million and grows continuously at a relative growth rate of 1.87%. What will the population be in 6 years? Compute the answer to three significant digits : Change the growth rate to a decimal; 1 + .0187 = 1.0187 Let P = population (in millions) in 6 yrs P = 135*1.0187^6 Using a calc P = 150.873 million in 6 yrs
 test/328415: chad drove 3 times as fast as katy pedaled. I fact, chad drove 90 miles in 2 hrs less than it took katy to pedal 40 miles. How fast did each of them travel. How long did they travel?1 solutions Answer 235350 by ankor@dixie-net.com(15660)   on 2010-08-03 16:47:15 (Show Source): You can put this solution on YOUR website!chad drove 3 times as fast as katy pedaled. In fact, chad drove 90 miles in 2 hrs less than it took katy to pedal 40 miles. How fast did each of them travel. How long did they travel? : Let s = K's speed then 3s = C's speed : Write a time equation: Time = dist/speed : K's time - C's time = 2 hrs - = 2 Reduce fraction - = 2 = 2 Multiply both sides by 2 10 = 2s s = s = 5 mph is K's speed then 2(5) = 15 mph is C's speed : Find the travel times 90/15 = 6 hrs 40/5 = 8 hrs -------------- diff: 2 hrs, confirms our solutions
 Geometry_Word_Problems/328356: Box Construction. An open box is to be made from a 10-ft by 20-ft rectangular piece of cardboard by cutting a square from each corner. The area of the bottom of the box is to be 96ft^2. What is the length of the sides of the squares that are cut from the corners?1 solutions Answer 235346 by ankor@dixie-net.com(15660)   on 2010-08-03 16:32:58 (Show Source): You can put this solution on YOUR website!An open box is to be made from a 10-ft by 20-ft rectangular piece of cardboard by cutting a square from each corner. The area of the bottom of the box is to be 96ft^2. What is the length of the sides of the squares that are cut from the corners? : let x = length of the sides of the removed squares : Then the dimensions of the box will be: (10-2x) by (20-2x) by x : The area of the bottom is given as 96 sq/ft therefore: (10-2x)*(20-2x) = 96 FOIL 200 - 20x - 40x + 4x^2 = 96 Arrange as a quadratic equation 4x^2 - 60x + 200 - 96 = 0 4x^2 - 60x + 104 = 0 Simplify, divide by 4 x^2 - 15x + 26 = 0 Factors to (x-13)(x-2) = 0 Two solutions x = 13 ft, does not make sense and x = 2 ft, is the length of the side of the removed squares : : Check solution by finding the area: [10 - 2(2)] * [20 - 2(2)] = 6 * 16 = 96
 Polynomials-and-rational-expressions/328472: Can you please break this down for me & show step by step? I am a visual learner and the book is not helping me on this. Thanks Find the product or quotient. 35a + 280 divide a^2 - 64 __________ __________ 7a - 35 divide a^2-a-20 1 solutions Answer 235273 by ankor@dixie-net.com(15660)   on 2010-08-03 14:07:28 (Show Source): You can put this solution on YOUR website!Find the product or quotient: : ----------------- : each expression can be factored here ----------------- : we can cancel some of this immediately, cancel (a+8) and (a-5) ----------------- : Invert the dividing fraction and multiply * : Cancel 7 into 35 * (a+4) = or
 Quadratic_Equations/328470: Find the quadratic in standard form that goes through (-4,27), (1,2) (3,34) 1 solutions Answer 235269 by ankor@dixie-net.com(15660)   on 2010-08-03 13:36:36 (Show Source): You can put this solution on YOUR website!Find the quadratic in standard form that goes through (-4,27), (1,2) (3,34) : Using the form, ax^2 + bx + c = y, write an equation for each pair : x=-4, y=27 a(-4^2) + b(-4) + c = 27 16a - 4b + c = 27 Do the same with the other two pairs x=1, y=2 a + b + c = 1 : x=3, y=34 9a + 3b + c = 34 : Subtract the 2nd equation from the 1st equation 16a - 4b + c = 27 a + b + c = 2 --------------------eliminates c 15a - 5b = 25 simplify divide by 5 3a - b = 5 : Subtract the 2nd equation from the 3rd equation 9a + 3b + c = 34 a + b + c = 2 --------------------Eliminates c 8a + 2b = 32 simplify, divide by 2 4a + b = 16 : Two equation which we can handle easily with elimination again 3a - b = 5 4a + b = 16 ---------------adding eliminates b, find a 7a = 21 a = 21/7 a = 3 : Find b using the equation 4a + b = 16, 4(3) + b = 16 12 + b = 16 b = 16 - 12 b = 4 : Find c using the equation a + b + c = 2 3 + 4 + c = 2 c = 2 - 7 c = -5 : The equation: y = 3x^2 + 4x - 5 : You can prove this to yourself by substituting for x and finding y for each pair
 Polynomials-and-rational-expressions/328430: Subtract and simplify if possible d/s+d - d/s-d Would the answer be 0? Can you please show me how to d this step by step? Thank you1 solutions Answer 235262 by ankor@dixie-net.com(15660)   on 2010-08-03 13:16:57 (Show Source): You can put this solution on YOUR website!Subtract and simplify if possible : The common denominator; (s+d)(s-d), therefore we have : Multiply what's inside the brackets : Combining like terms we have : FOIL the denominator (the difference of squares) Or
 Miscellaneous_Word_Problems/328191: If an object is propelled upward from a height of 96ft at an initial velocity of 80ft per second, then its height after t seconds is given by the equation h = -16t^2 + 80t + 96 where h is in feet. After how many seconds will the object reach a height of 196ft? I am not so good at word problems and am really confused! You have great tutors that I appreciate so very much. I hope that someone will lend me a hand this one has me stumped. Thank you in advance. 1 solutions Answer 235072 by ankor@dixie-net.com(15660)   on 2010-08-02 19:22:51 (Show Source): You can put this solution on YOUR website!an object is propelled upward from a height of 96ft at an initial velocity of 80ft per second, its height after t seconds is given by the equation h = -16t^2 + 80t + 96 where h is in feet. After how many seconds will the object reach a height of 196ft? : -16t^2 + 80t + 96 = h Replace h with 196 -16t^2 + 80t + 96 = 196 -16t^2 + 80t + 96 - 196 = 0 -16t^2 + 80t - 100 = 0 Simplify & change the signs, divide by -4, (easier to factor) 4t^2 - 20x + 25 = 0 Factors to (2t-5)(2t-5) = 0 2t = 5 t = t = 2.5 seconds it will be 196 ft (this is also the max height) : Graphically; t on the x axis, h on the y axis
 Triangles/327986: what would be the area of triangle with a base of 20 meters long and the perpendicular distance from the end of base to the opposite side is 27 meters long.1 solutions Answer 235055 by ankor@dixie-net.com(15660)   on 2010-08-02 16:55:41 (Show Source): You can put this solution on YOUR website!what would be the area of triangle with a base of 20 meters long and the perpendicular distance from the end of base to the opposite side is 27 meters long. : Wouldn't this just be a right triangle, then A = .5*20*27 = 270 sq/m
 Rectangles/328081: A rectangular garden is enclosed by a brick border. The total length of bricks used to enclose the garden is 42 meters. If the length of the garden is twice the width, what is the area of the garden?1 solutions Answer 235040 by ankor@dixie-net.com(15660)   on 2010-08-02 16:41:09 (Show Source): You can put this solution on YOUR website!A rectangular garden is enclosed by a brick border. The total length of bricks used to enclose the garden is 42 meters. If the length of the garden is twice the width, what is the area of the garden? : This is just a perimeter problem 2L + 2W = 42 Simplify, divide by 2 L + W = 21 : Then it says,"length of the garden is twice the width,"; therefore L = 2W : Replace L with 2W 2W + W = 21 3W = 21 W = 7 meters is the width : I'll let you find the length, multiply that by the width to find the area
 Linear_Algebra/328160: Solve the following system of nonlinear equations y=x^4-x^2+2x-1 y=x^4+3x^2+2x-21 solutions Answer 235034 by ankor@dixie-net.com(15660)   on 2010-08-02 16:28:28 (Show Source): You can put this solution on YOUR website!Solve the following system of nonlinear equations y = x^4 - x^2 + 2x - 1 y = x^4 +3x^2 + 2x - 2 Therefore x^4 +3x^2 + 2x - 2 = x^4 - x^2 + 2x - 1 Combine like terms x^4 - x^4 + 3x^2 + x^2 + 2x - 2x = -1 + 2 : 4x^2 = 1 x^2 = x = +/- x = +/-, or +/-.5 : Find y using the 1st equation, x=+.5 y = .5^4 - .5^2 + 2(.5) - 1 y = .0625 - .25 + 1 - 1 y = -.1875 One solution: x=.5, y=-.1875 : Find y using the 1st equation, x=-.5 y = -.5^4 - (-.5^2) + 2(-.5) - 1 y = .0625 - .25 - 1 - 1 y = -2.1875 A 2nd solution: x=-.5, y = -2.1875 : I'll let you check the solutions in the 2nd equation
 Geometry_Word_Problems/328113: A small rectangular playground that is 10ft by 14ft is going to have a grass border of a uniform width on all sides. If the area of the grass border is 145 sqare feet, how wide is the border? I have tried to think of the correct formula but have come up blank! please can someone help me with this one! 1 solutions Answer 235022 by ankor@dixie-net.com(15660)   on 2010-08-02 16:03:24 (Show Source): You can put this solution on YOUR website!A small rectangular playground that is 10ft by 14ft is going to have a grass border of a uniform width on all sides. If the area of the grass border is 145 square feet, how wide is the border? : Find the area of the playground: 10 * 14 = 140 sq/ft : Let x = the width of the border : Then the overall dimensions including the border will be: (2x+10) by (2x+14) Find the overall area (A) A = (2x+10)*(2x+14) FOIL A = 4x^2 + 28x + 20x + 140 A = 4x^2 + 48x + 140 : Overall area - playground area = border area, therefore: 4x^2 + 48x + 140 - 140 = 145 Arrange as a quadratic equation 4x^2 + 48x - 145 = 0 You can use the quadratic formula here, but this will factor (2x-5)(2x+29) = 0 The positive solution is what we want here 2x = 5 x = 5/2 x = 2.5 ft is the width of the grass border : : Check our solution by finding the overall area and subtracting the playground area (5+10)*(5+14) = 285 sq/ft 285 - 140 = 145 sq/ft; confirms our solution of x=2.5
 Equations/328038: I have three questions that deal with area, diameter, and perimeter. I could not find a better classification to put them in so I chose this one. Thank you in advance for taking the time to help me. It is greatly appreciated. The sooner I get an answer the better. #1) Diameter of a circle. If the diameter of a circle is 1.3 X 10-12(that should read 10 to the negative 12th) meters, then what is its radius? #2)Area of a parallelogram. Find a trinomial A(x) that represents the area of a parallelogram whose base is 3x + 2 meters and whose height is 2x+ 3 meters. Find A(3). #3) Perimeter of a rectangle. The perimeter of a rectangular backyard is 6x+ 6 yards. If the width is x yards, find a binomial that represents the length 1 solutions Answer 234980 by ankor@dixie-net.com(15660)   on 2010-08-02 14:02:55 (Show Source): You can put this solution on YOUR website!#1) Diameter of a circle. If the diameter of a circle is 1.3 X 10-12 (that should read 10 to the negative 12th) meters, then what is its radius? d = r = = ; divided 1.3 by 2 Write in scientific notation r = : : #2)Area of a parallelogram. Find a trinomial A(x) that represents the area of a parallelogram whose base is 3x + 2 meters and whose height is 2x+ 3 meters. A = b*h A = (3x+2)*(2x+3) FOIL A(x) = 6x^2 + 9x + 4x + 6 A(x) = 6x^2 + 13x + 6, is your trinomial Find A(3). A(3) = 6(3^2) + 13(3) + 6 A(3) = 6(9) + 39 + 6 A(3) = 54 + 39 + 6 A(3) = 99 : : #3) Perimeter of a rectangle. The perimeter of a rectangular backyard is 6x+ 6 yards. If the width is x yards, find a binomial that represents the length Perimeter equation: 2L + 2W = P In this problem: 2L + 2x = 6x+6 2L = 6x - 2x + 6 2L = 4x + 6 Divide both sides by 2 L = 2x + 3, is the length : : did this make sense to you?
 Average/328054: In a science test a class of 30 students had an average of 80. The 20 girls had an average of 85. Whats the average of the 10 remaining boys?1 solutions Answer 234949 by ankor@dixie-net.com(15660)   on 2010-08-02 12:45:01 (Show Source): You can put this solution on YOUR website!In a science test a class of 30 students had an average of 80. The 20 girls had an average of 85. What's the average of the 10 remaining boys? : Let x = av of the 10 boys : = 80 multiply both sides by 30, results 20(85) + 10x = 30(80) 1700 + 10x = 2400 10x = 2400 - 1700 10x = 700 x = x = 70 is the av of the 10 boys
 Quadratic_Equations/328056: Hello. I was hoping you could please help me with this problem. I have to factor completely, and if prime, say so. a. 40x^3 - 64x^2y b. 13-14y + y^2 c. 9x^2- 30 + 25 I was hoping you could please show me how to factor these, because I don't know how to. Thank you so much. 1 solutions Answer 234946 by ankor@dixie-net.com(15660)   on 2010-08-02 12:38:31 (Show Source): You can put this solution on YOUR website! factor completely, and if prime, say so. a. 40x^3 - 64x^2y Factor out 8x^2 8x^2(5x - 8y) ; b. 13-14y + y^2 Factor out - y 13 - y(14 - y) : c. 9x^2- 30 + 25 Factor out 3 3(x^2 - 10) + 25
 Miscellaneous_Word_Problems/327863: Dimensions of a box. Rosita’s Christmas present from Carlos is in a box that has a width that is 3 inches shorter than the height. The length of the base is 5 inches longer than the height. If the area of the base is 84 square inches, then what is the height of the package? 1 solutions Answer 234800 by ankor@dixie-net.com(15660)   on 2010-08-01 22:03:07 (Show Source): You can put this solution on YOUR website!a box that has a width that is 3 inches shorter than the height. w = h-3 : The length of the base is 5 inches longer than the height. L = h+5 : If the area of the base is 84 square inches L*W = 84 : what is the height of the package? Replace L and W (h-3)(h+5) = 84 FOIL h^2 + 5h - 3h - 15 = 84 h^2 + 2h - 15 - 84 = 0 h^2 + 2h - 99 = 0 Factor to (h+11)(h-9) = 0 The positive solution h = 9 inches is the height : : Check solution by finding the area 14 * 6 = 84
 Age_Word_Problems/327807: Kathy and Juanita had a light afternoon snack. Kathy enjoyed 3 chips and 2 pretzels, for a total of 77 calories. Juanita enjoyed 2 chips and 15 pretzels, for a total of 195 calories. How many calories are each pretzel? 1 solutions Answer 234784 by ankor@dixie-net.com(15660)   on 2010-08-01 20:42:07 (Show Source): You can put this solution on YOUR website!Kathy and Juanita had a light afternoon snack. Kathy enjoyed 3 chips and 2 pretzels, for a total of 77 calories. Juanita enjoyed 2 chips and 15 pretzels, for a total of 195 calories. How many calories are each pretzel? : let c = no. of calories in a chip let p = no. of calories in a pretzel : Write an equation for each girl : 3c + 2p = 77 2c + 15p = 195 : Multiply the 1st equation by 7.5, subtract the 2nd equation 22.5c + 15p = 577.5 2c + 15p = 195 ------------------subtraction eliminate p, find c 20.5c = 382.5 c = c = 18.7 calories : Find p 3(18.7) + 2p = 77 56 + 2p = 77 2p = 77-56 2p = 21 p = p = 10.5 calories : : Check solution in 2nd original equation, 2c + 15p = 195: 2(18.7) + 15(10.5) = 37.4 + 157.5 = 194.9 ~ 195
 Problems-with-consecutive-odd-even-integers/327831: The smaller of two consecutive integers is four more than half of the greater.1 solutions Answer 234779 by ankor@dixie-net.com(15660)   on 2010-08-01 20:21:43 (Show Source): You can put this solution on YOUR website!Two consecutive digits: x, (x+1) : Write an equation for the statement: 'The smaller of two consecutive integers is four more than half of the greater." x = 4 + .5(x+1) solve for x x = 4 + .5x + .5 x -.5x = 4 + .5 .5x = 4.5 Multiply both sides by 2 x = 9 : 9, 10 are the digits : : Check solution in original equation 9 = 4 +.5(10)
 Mixture_Word_Problems/327704: how many ounces of an alloy containing 30% gold on the world market must be mixed with an alloy containing 5% gold to obtain 25 ounces of an alloy containing 20% gold?1 solutions Answer 234777 by ankor@dixie-net.com(15660)   on 2010-08-01 20:12:37 (Show Source): You can put this solution on YOUR website!how many ounces of an alloy containing 30% gold on the world market must be mixed with an alloy containing 5% gold to obtain 25 ounces of an alloy containing 20% gold? : Let x = amt of 30% alloy The resulting total is to be 25 oz, therefore: (25-x) = amt of 5% alloy : A typical mixture equation: .30x + .05(25-x) = .20(25) .30x + 1.25 - .05x = 5 .30x - .05x = 5 - 1.25 .25x = 3.75 x = x = 15 oz of 30% alloy required then 25-15 = 10 oz of 5% alloy : : Check solution .30(15) + .05(10) = .20(25) 4.5 + .5 = 5
 Linear-equations/327814: Write an equation of the line containing the given point and parellel to the given line. Express your answer in the form y = mx + b (5,8); x + 2y = 5 the equation of the line is y= ?1 solutions Answer 234770 by ankor@dixie-net.com(15660)   on 2010-08-01 19:25:49 (Show Source): You can put this solution on YOUR website!Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y = mx + b (5,8); x + 2y = 5 Find the slope (parallel lines have the same slope) x + 2y = 5 2y = -x + 5 y = -.5x + 2.5 slope (m) = -.5 the equation of the line is y= ? : y - 8 = -.5(x - 5) y - 8 = -.5x + 2.5 y = -.5x + 2.5 + 8 y = -.5x + 10.5 is the equation of the line
 Expressions-with-variables/327804: John takes 3 hours longer than Andrew to peel 500 pounds (lb) of apples. If together they can peel 500 lb of apples in 8 hours, then how long would it take each one working alone1 solutions Answer 234767 by ankor@dixie-net.com(15660)   on 2010-08-01 18:48:48 (Show Source): You can put this solution on YOUR website!John takes 3 hours longer than Andrew to peel 500 pounds (lb) of apples. If together they can peel 500 lb of apples in 8 hours, then how long would it take each one working alone. : Let t = time required by Andrew then (t+3) = time required by John : Let the completed job = 1; (the peeling of 500 lb of potatoes) : Each person will do a fraction of job, the two fractions add up to 1 + = 1 Multiply by t(t+3), results: 8(t+3) + 8t = t(t+3) : 8t + 24 + 8t = t^2 + 3t : 16t + 24 = t^2 + 3t Arrange as quadratic equation t^2 + 3t - 16t - 24 = 0 : t^2 - 13t - 24 = 0 Use the quadratic formula to find t x=t, a=1, b=-13, c=-24 : : The positive solution is what we want here: t = t = 14.64 hrs, Andrew working alone then 14.64+3 = 17.64 hrs, John working alone : : Check solution + = .546 + .454 = 1
 Miscellaneous_Word_Problems/327777: Use the formula , where N is the number of items in terms of the initial population I, at time t, and k is the growth constant equal to the percent of growth per unit of time. An artifact is discovered at a certain site. If it has 65% of the carbon-14 it originally contained, what is the approximzte age of the artifact? (carbon-14 decays at the rate of 0.0125% annually.) possible answers(5200 years, 3446 years, 1497 years, 2800 years.)1 solutions Answer 234758 by ankor@dixie-net.com(15660)   on 2010-08-01 18:12:21 (Show Source): You can put this solution on YOUR website!Use the formula , where N is the number of items in terms of the initial population I, at time t, and k is the growth constant equal to the percent of growth per unit of time. : An artifact is discovered at a certain site. If it has 65% 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.) : where: N = .65 I = 1 k = -.000125, decay is negative Find t : Using nat logs Find ln -.000125t = -.43078 t = t = +3,446 yrs
 Expressions-with-variables/327717: I need help solving please. x-1/x+2 = 5/7 Thank you1 solutions Answer 234721 by ankor@dixie-net.com(15660)   on 2010-08-01 14:51:19 (Show Source): You can put this solution on YOUR website! we can cross multiply here 7(x-1) = 5(x+2) : 7x - 7 = 5x + 10 : 7x - 5x = 10 + 7 : 2x = 17 x = x = 8.5 : : Check solution in original problem; replace x with 8.5 calculate to decimals .714 = .714; confirms solution
 Radicals/327716: Would someone be so kind as to help me out with this problem: sqrt(3x)-1=sqrt(2x+1) Thank you in advance for any help. You all have been a great help in the past. 1 solutions Answer 234719 by ankor@dixie-net.com(15660)   on 2010-08-01 14:40:24 (Show Source): You can put this solution on YOUR website! : Square both sides, FOIL ()() : 3x - - + 1 = 2x + 1 : 3x - + 1 = 2x + 1 : 3x - 2x + 1 - 1 = : x = Square both sides x^2 = 4(3x) : x^2 = 12x Divide both sides by x x = 12 : : Check the solution in original equation; Replace x with 12 6 - 1 = 5; confirms our solution
 Linear-systems/327665: I am having problems finding the equation of a line. Problem is: write an equation for the line parallel to the line -4y=2 through the point (8, -4). I can't get the jist of the way to figure out this problem1 solutions Answer 234718 by ankor@dixie-net.com(15660)   on 2010-08-01 14:24:16 (Show Source): You can put this solution on YOUR website!write an equation for the line parallel to the line -4y = 2 through the point (8, -4). : -4y = 2 y = y = : This is a horizontal line passing thru y=-.5 the parallel line will also be horizontal and pass thru y=-4 and all values of x : looks like this (y=-4 is green)
 Average/327650: The average weight of 10 children is 88 pounds. Two more children join the group: one weighs 95 pounds and the other 93 pounds. What is the average weight for the twelve children? a. 89 pounds b. 90 pounds c. 91 pounds d. 92 pounds e. 93 pounds1 solutions Answer 234716 by ankor@dixie-net.com(15660)   on 2010-08-01 14:07:45 (Show Source): You can put this solution on YOUR website!The average weight of 10 children is 88 pounds. Two more children join the group: one weighs 95 pounds and the other 93 pounds. What is the average weight for the twelve children? : Now the number children is 12 : Av = : Av = : Av = : Av = 89 lb
 Linear-systems/327016: If you multiply the sale price per box times the number of boxes, that's your total price. But remember, these boxes are on sale. The regular price per box is the same as the number of boxes. Your total price will be 75 times the amount you are saving on each box. When you add the regular price for each box to my sale price for each box, the result is 7 time the amount you are saving on each box. How many boxes are there, and what sale price for each box? 1 solutions Answer 234604 by ankor@dixie-net.com(15660)   on 2010-07-31 20:18:02 (Show Source): You can put this solution on YOUR website!let n = no. boxes let s = sale price per box let r = reg price per box : If you multiply the sale price per box times the number of boxes, that's your total price. ns = total price : But remember, these boxes are on sale. The regular price per box is the same as the number of boxes. n = r : Your total price will be 75 times the amount you are saving on each box. ns = 75(r-s) replace n with r rs = 75r - 75s : When you add the regular price for each box to my sale price for each box, the result is 7 time the amount you are saving on each box. r + s = 7(r-s) r + s = 7r - 7s s + 7s = 7r - r 8s = 6r s = r s = .75r : In equation; rs = 75r - 75s, replace s with .75r .75r*r = 75r - 75(.75r) .75r^2 = 75r - 56.25r Divide thru by r .75r = 75 - 56.25 .75r = 18.75 r = r = 25 then \$25 = reg price and 25 is the no. of units Find the sale price s = .75r s = .75(25) s = \$18.75 is the sale price : Check solution in the statement: "Your total price will be 75 times the amount you are saving on each box." 25(18.75) = 75(25-18.75) 468.75 = 75*6.25 468.75 = 468.75, confirms our solution of reg price: \$25 no. units: 25 ea sale price: \$18,75
 Quadratic_Equations/327454: I saw this problem in my textbook: A rectangular pool is surrounded by a walk 4 meters wide. The pool is 6 meters longer than its width. If the total area is 576 square meters more than the area of the pool, find the dimensions of the pool. How do they get the answer? I've tried by making Total Area = x^2+6x+576, but have been unable to obtain the answer.1 solutions Answer 234596 by ankor@dixie-net.com(15660)   on 2010-07-31 19:37:44 (Show Source): You can put this solution on YOUR website!A rectangular pool is surrounded by a walk 4 meters wide. The pool is 6 meters longer than its width. If the total area is 576 square meters more than the area of the pool, find the dimensions of the pool. : Let x = the width of the pool then (x+6) = length of the pool : Find the area (a) of the pool a = x(x+6) a = x^2 + 6x; area of the pool only : The dimensions of the area including the 4' walkway (add 8 to each dimension) (x+8) = overall width (x+14) = overall length : Find the area (A) including the 4m walkway FOIL: (x+8)(x+14) A = x^2 + 22x + 112; the total area : "If the total area is 576 square meters more than the area of the pool," (x^2 + 22x + 112) - (x^2 + 6x) = 576 remove the brackets x^2 + 22x + 112 - x^2 - 6x = 576 results 22x - 6x = 576 - 112 : 16x = 464 x = x = 29 m is the width of the pool then 29 + 6 = 35 m is length : : Check solution using x=29 29(29+6) = 1015 pool area (29+8)(29+14) = 1591 overall area 1591 - 1015 = 576; confirms our solution
 Square-cubic-other-roots/327527: what do i get when i square both sides of this equation? √a +√b =√a+b Are these truly equal? 1 solutions Answer 234581 by ankor@dixie-net.com(15660)   on 2010-07-31 18:43:56 (Show Source): You can put this solution on YOUR website!what do i get when i square both sides of this equation? √a +√b =√a+b Assume the problem is: = You have to FOIL the left side a + + b = a + b obviously this can't be true