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 Polynomials-and-rational-expressions/160326: an open topped box is made from a rectangular piece of cardboard, with the dimensions 24 cm by 30 cm, by cutting congruent squares from each corner and folding up the sides. determine the dimensions of the squares to be cut to create a box with a volume of 1040cm^31 solutions Answer 118266 by ankor@dixie-net.com(15658)   on 2008-10-04 16:29:58 (Show Source): You can put this solution on YOUR website!An open topped box is made from a rectangular piece of cardboard, with the dimensions 24 cm by 30 cm, by cutting congruent squares from each corner and folding up the sides. determine the dimensions of the squares to be cut to create a box with a volume of 1040cm^3 : Let the side of the removed squares = x : The dimension of the box will be: (24-2x) by (30-2x) by x (height) : A volume equation, L * W * H (24-2x) * (30-2x) * x = 1040 FOIL (720 - 48x - 60x + 4x^2) * x = 1040 : Multiply by x; 720x - 108x^2 + 4x^3 = 1040 ; 4x^3 - 108x^2 + 720x - 1040 = 0 : Simplify; divide by 4: x^3 - 27x + 180x - 260 = 0 : Graphing this would be one way to solve this : ; x = 2 cm would work : L: 30-4 = 26 cm W: 24-4 = 20 cm H: 2 cm : Check the volume (26*20*2 = 1040 : You can see there is another solution on the graph: x ~ 7.4 The dimensions for that would be L: 30-14.8 = 15.2 W: 24-14.8 = 9.2 H: 7.4 cm : Check vol with this: 15.2*9.2*7.4 = 1035.8 (because not an integer)
 Complex_Numbers/160308: (10+i)^2 / 4-i thanks for the help!1 solutions Answer 118264 by ankor@dixie-net.com(15658)   on 2008-10-04 15:50:27 (Show Source): You can put this solution on YOUR website! ; Foil (10+i)(10+i) = = : Multiply by the conjugate of the denominator over itself * = = = : Minus a minus is a plus (denominator) = = +
 Functions/160322: How do you factor completely: 5x^2 - 10x? What's the answer?1 solutions Answer 118263 by ankor@dixie-net.com(15658)   on 2008-10-04 15:44:18 (Show Source): You can put this solution on YOUR website!How do you factor completely: 5x^2 - 10x? What's the answer? : you can factor out 5x 5x(x-2)
 Polynomials-and-rational-expressions/160302: This question is from textbook Algerbra and Trigonometry structure and method two ships leave port, one sailing east and the other south. Some time later they are 17 miles apart, with the eastbound ship 7 miles further from the port than the southbound ship. how far is each from port?1 solutions Answer 118254 by ankor@dixie-net.com(15658)   on 2008-10-04 14:09:44 (Show Source): You can put this solution on YOUR website!two ships leave port, one sailing east and the other south. Some time later they are 17 miles apart, with the eastbound ship 7 miles further from the port than the southbound ship. how far is each from port? : If you look at this, you can see that the hypotenuse of a right triangle is the distance between the ships. The two legs are the distance from the ships to port A rough diagram will make it easy to understand. : Let x = distance of the southbound ship from port then (x+7) = distance of the eastbound ship from port : Hypotenuse = 17 mi : x^2 + (x+7)^2 = 17^2 ; FOIL (x+7)(x+7) x^2 + (x^2 + 14x + 49) = 289 : Arrange as a quadratic equation which we can solve: x^2 + x^2 + 14x + 49 - 289 = 0 : 2x^2 + 14x - 240 = 0 : Simplify, divide by 2 x^2 + 7x - 120 = 0 : Factor (x - 8)(x + 15) = 0 : Positive solution x = 8 mi is southbound ship and 8 + 7 = 15 mi is the eastbound ship : : Check solution in pythag 8^2 + 15^2 = 17^2 64 + 225 = 298 : Did this make sense? Any questions? :
 Rate-of-work-word-problems/160276: One job. two power shovels excavate 20,000 cubic meters of earth, the larger shovel working for 40 hours and the smaller for 35 hours. On another job, they removed 40,000 cubic meters with the larger shovel working 70 hours and the smaller working 90 hours. How much earth can each move in 1 hour working alone? 1 solutions Answer 118248 by ankor@dixie-net.com(15658)   on 2008-10-04 13:13:50 (Show Source): You can put this solution on YOUR website!One job. two power shovels excavate 20,000 cubic meters of earth, the larger shovel working for 40 hours and the smaller for 35 hours. On another job, they removed 40,000 cubic meters with the larger shovel working 70 hours and the smaller working 90 hours. How much earth can each move in 1 hour working alone? : Let x = large shovel amt of earth moved in 1 hr Let y = small shovel amt in 1 hr ; Write an equation for each project: 40x + 35y = 20000 70x + 90y = 40000 : Simplify, divide the 1st equation by 5, and the 2nd equation by 10 8x + 7y = 4000 7x + 9y = 4000 : Multiply the 1st equation by 7 and the 2nd equation by 8 56x + 49y = 28000 56x + 72y = 32000 ----------------------subtraction eliminates x 0x - 23y = - 4000 y = y ~ 174 yds/hr, the small shovel : Find x using; 7x + 9y = 4000 7x + 9(174) = 4000 7x = 1566 = 4000 7x = 4000 - 1566 7x = 2434 x = x ~ 348 yds/hr, the large shovel : : Check solution in 1st original equation: 40x + 35y = 20000 40(348) + 35(174) = 13920 + 6090 = 200010 ~ 20000
 Sequences-and-series/160195: If Steven can mix 20 drinks in 5 min, Sue can mix 20 drinks in 10 min, and Jack can mix drinks in 15 min. How much time will it take all 3 of them working together to mix the 20 drinks? The answer is 2 min and 44 seconds, but I don't know how.1 solutions Answer 118121 by ankor@dixie-net.com(15658)   on 2008-10-03 13:57:49 (Show Source): You can put this solution on YOUR website!If Steven can mix 20 drinks in 5 min, Sue can mix 20 drinks in 10 min, and Jack can mix 20 drinks in 15 min. How much time will it take all 3 of them working together to mix the 20 drinks? : Let t = time required when they all work together : Let the completed job = 1 (the mixing of 20 drinks) : Each will do a fraction of the job, which added together, will = 1 : + + = 1 : Clear the denominators, multiply equation by 30, results: 6t + 3t + 2t = 30 : 11t = 30 t = t = 2.727 min or about 2 min 43.6 sec. all working together : : Check solution on calc: + + = .54 + .27 + .18 = .99 ~ 1
 Equations/160102: when young MacDonal was starting his farm a long time ago,cows cost \$10 each,pigs cost \$3 each and chickens cost \$0.50 each. He puechsed at least one of kind of animal. He paid \$100 for exatly 100 animals. HOW MANY CHICKENS DID HE BUY?1 solutions Answer 118117 by ankor@dixie-net.com(15658)   on 2008-10-03 13:30:10 (Show Source): You can put this solution on YOUR website!If cows cost \$10 each, pigs cost \$3 each and chickens cost \$0.50 each. He got at least one of kind of animal. He paid \$100 for exactly 100 animals. HOW MANY CHICKENS DID HE BUY? : x = no. cows y = no. pigs z = no. of chickens : Total animal equation x + y + z = 100 : Total cost equation 10x + 3y + .5z = 100 : Multiply the above equation by 2 and subtract the 1st equation (total animals) 20x + 6y + 1z = 200 x + y + 1z = 100 -----------------------subtraction eliminates z 19x + 5y = 100 Arrange equation in the general y= form 5y = 100 - 19x y = 20 - x; divided both sides by 5 : Study this equation and it's apparent the only value for x that will give a positive integer value for y, is x = 5 : y = 20 - *5 y = 20 - 19 y = 1 pig : We have 5 cows, 1 pig Find chickens: 100 - 5 - 1 = 94 chickens : Check: 10(5) + 3(1) + 94(.5) = 50 + 3 + 47 = 100
 Expressions-with-variables/159970: On one side of a scale there are 4 blocks, 2 weighing 2 grams each and 2 weighing x grams each. The scale is balanced if 8 blocks weighing x grams each are placed on the other side of the scale. How much does each of the unknown blocks weigh?1 solutions Answer 118115 by ankor@dixie-net.com(15658)   on 2008-10-03 12:55:51 (Show Source): You can put this solution on YOUR website!On one side of a scale there are 4 blocks, 2 weighing 2 grams each and 2 weighing x grams each. The scale is balanced if 8 blocks weighing x grams each are placed on the other side of the scale. How much does each of the unknown blocks weigh? : 2x + 4 = 8x : 4 = 8x - 2x : 4 = 6x x = x = grams : : Check solution in original equation: 2* + 4 = 8* + =
 Expressions-with-variables/159969: Lois rides her bike to visit a friend. She travels at 10 mi/h. While shes there, it starts to rain. Her friend drives her home in a car traveling at 25 mi/h. It takes lois 1.5h longer to to friends than it does to return home.How many hours did it take lois to ride to her friends house?1 solutions Answer 118065 by ankor@dixie-net.com(15658)   on 2008-10-02 21:55:48 (Show Source): You can put this solution on YOUR website!Lois rides her bike to visit a friend. She travels at 10 mi/h. While shes there, it starts to rain. Her friend drives her home in a car traveling at 25 mi/h. It takes Lois 1.5h longer to go to friend's house than it does to return home. How many hours did it take Lois to ride to her friends house? : Let t = time in hrs for reach friend's house then (t-1.5) = time for friend to drive her home : Both trips are the same distance, Write a distance equation from this fact: Dist = speed * time : Drive dist = Bike dist 25(t-1.5) = 10t : 25t - 37.5 = 10t : 25t - 10t = +37.5 : 15t = 37.5 t = t = 2.5 hrs to ride to her friends house : : Check solution by finding the distances, should be equal: 10*2.5 = 25 mi 25*(2.5-1.5) = 25 mi
 Travel_Word_Problems/160056: Mary is running to school. She leaves home at 7:00 am trotting at a speed of 12 mph. Her little lamb leaves home at 7:15 am running after her at a speed of 17 mph. What time of the day will the lamb catch Mary? Round your answer to the nearest minute.1 solutions Answer 118063 by ankor@dixie-net.com(15658)   on 2008-10-02 21:41:03 (Show Source): You can put this solution on YOUR website!Mary is running to school. She leaves home at 7:00 am trotting at a speed of 12 mph. Her little lamb leaves home at 7:15 am running after her at a speed of 17 mph. What time of the day will the lamb catch Mary? Round your answer to the nearest minute. : Let t = Mary's travel time in hrs when lamb catches her Convert 15 min to hrs 15/60 = .25 hrs (t-.25) = travel time of lamb : When lamb catches Mary, they will have traveled the same distance Write a distance equation using this fact; Dist = speed * time : lamb's dist = Mary's dist 17(t-.25) = 12t : 17t - 4.25 = 12t : 17t - 12t = +4.25 : 5t = 4.25 t = t = .85 hrs Convert this to minutes: .85 * 60 = 51 min : Lamb catches Mary at 7:51 am : : Check solution by ensuring they traveled the same dist: lambs time .85 - .25 = .6 hrs 17*.6 = 10.2 mi 12*.85 = 10.2 mi
 Polynomials-and-rational-expressions/160048: This question is from textbook Elementary and Intermediate Algebra The perimeter of a cross section of a "two-by-four" piece of lumber is 10 1/2 in. The length is twice the width. Find the actual dimension of the cross section of a two-by-four. I have tried 2n+n=10 1/2 and that formula didn't work. I have tried 2(2n+n)=10 1/2 and thats wrong. Please help me?1 solutions Answer 118050 by ankor@dixie-net.com(15658)   on 2008-10-02 20:21:53 (Show Source): You can put this solution on YOUR website!The perimeter of a cross section of a "two-by-four" piece of lumber is 10 1/2 in. The length is twice the width. Find the actual dimension of the cross section of a two-by-four. : You're right on the last equation 2(2n+n) = 10.5. Let n = the width "length is twice the width 2n = length : Perimeter is: 2L + 2W = 10.5 Replace L with 2n and W with n 2(2n) + 2(n) = 10.5 4n + 2n = 10.5 6n = 10.5 n = n = 1.75" is the width, and 2(1.75) = 3.5" is the length or 1 by 3 if you prefer
 Equations/159960: Cycle paths inc. makes bicycles, tricycles, and unicycles. Last week they made 88 more bicycles than unicycles, and 5 times as many tricycles as unicycles. If they made 40 more bicycles that tricycles, how many unicycles did they make?1 solutions Answer 118047 by ankor@dixie-net.com(15658)   on 2008-10-02 20:11:23 (Show Source): You can put this solution on YOUR website!Cycle paths inc. makes bicycles, tricycles, and unicycles. Last week they made 88 more bicycles than unicycles, and 5 times as many tricycles as unicycles. If they made 40 more bicycles that tricycles, how many unicycles did they make? : Write an equation for each statement: "they made 88 more bicycles than unicycles," b = u + 88 : "and 5 times as many tricycles as unicycles." t = 5u : " If they made 40 more bicycles that tricycles," b = t + 40 ; how many unicycles did they make? : In the last equation, replace b with (u+88), and replace t with 5u u + 88 = 5u + 40 88 - 40 = 5u - u 48 = 4u u = u = 12 unicyles : Check solution in the last equation; b = 12 + 88 = 100 t = 5(12) = 60 : 100 = 60 + 40
 Miscellaneous_Word_Problems/160049: 2 less than 3 times a number is the same as 3 more than 2 times the number. find the number. 1 solutions Answer 118045 by ankor@dixie-net.com(15658)   on 2008-10-02 19:58:31 (Show Source): You can put this solution on YOUR website!Let x = "the number" : Write exactly what it says: "2 less than 3 times a number is the same as 3 more than 2 times the number." 3x - 2 = 2x + 3 : find the number. 3x - 2x - 3 + 2 x = 5 : : Check: 3(5) - 2 = 2(5) + 3
 Equations/159816: An outboard engine uses a gasoline-oil fuel mixture in the ratio of 15 to 1. How much gasoline must be mixed with a gasoline-oil mixture, which is 75% gasoline, to make 8.0L of the mixture for the outboard engine?1 solutions Answer 118028 by ankor@dixie-net.com(15658)   on 2008-10-02 17:20:32 (Show Source): You can put this solution on YOUR website!An outboard engine uses a gasoline-oil fuel mixture in the ratio of 15 to 1. How much gasoline must be mixed with a gasoline-oil mixture, which is 75% gasoline, to make 8.0L of the mixture for the outboard engine? : Find the percent of gasoline in a 15:1 mixture % gasoline = * 100 = 93.75% gasoline : Let x = amt of gasoline to accomplish this Then (8-x) = amt of 75% mixtures used : .75(8-x) + 1.0x = .9375(8) : 6 - .75x + 1x = 7.5 : -.75x + 1x = 7.5 - 6 : .25x = 1.5 : x = x = 6 liters of gas required (plus 2 liters of the 75% mixture) ; : Check our solution : .75(8-6) + 6 = .9375(8) .75(2) + 6 = 7.5 1.5 + 6 = 7.5
 Rectangles/159892: Calculating the dimension of a rectangle with 28 inch length and surrounds a 48 square inch picture. How do I calculate the dimension of the rectangle given this information.1 solutions Answer 118020 by ankor@dixie-net.com(15658)   on 2008-10-02 16:39:52 (Show Source): You can put this solution on YOUR website!Calculating the dimension of a rectangle with 28 inch length and surrounds a 48 square inch picture. How do I calculate the dimension of the rectangle given this information. : Not enough information here. If we knew the width of the border surrounding the picture or one dimension of the picture, it would be easy : If I can make an assumption here, that the picture is 8 by 6 (48sq/in) then I can find the width of the border: Let x = the width of the border : Border + picture length = rectangle length 2x + 8 = 28 2x = 28 - 8 2x = 20 x = 10" is the width of the border : Then we can find the width of the rectangle, using the width of the picture w = 2(10) + 6 w = 20 + 6 w = 26 ; In this case an 8 by 6 inch picture is on a 28 by 26 inch rectangle and has a 10 inch border around the picture : Did this help?
 percentage/159891: As an investment Ms. Astoy purchased 2 paintings. She later sold the 2 paintings for \$24,000 each. On one painting she made a 20% profit, but on the other she experienced a 20% loss. Ms. Astoy los ____ on her investments in the 2 paintings.1 solutions Answer 118007 by ankor@dixie-net.com(15658)   on 2008-10-02 16:12:57 (Show Source): You can put this solution on YOUR website!As an investment Ms. Astoy purchased 2 paintings. She later sold the 2 paintings for \$24,000 each. On one painting she made a 20% profit, but on the other she experienced a 20% loss. Ms. Astoy lost ____ on her investments in the 2 paintings. : Find the value of the two painting before they were sold 1st painting original value = x: 1.2x = 24000 x = x = 20,000 original value : 2nd painting original value = y .8y = 24000 y = y = 30,000 original value : then \$50,000 is the original total value of the paintings : The total she got for the paintings = 48000 ; Therefore she lost \$2000 on her investments.
 Equations/159813: In testing the rate at which a polluted stream flows, a boat that travels at 5.5 km/h in still water took 5.0 h to go downstream between two points, and it took 8.0 h to go upstream between the same two points. What is the rate of flow of the stream ?1 solutions Answer 117999 by ankor@dixie-net.com(15658)   on 2008-10-02 15:57:59 (Show Source): You can put this solution on YOUR website!A boat that travels at 5.5 km/h in still water, took 5.0 h to go downstream between two points, and it took 8.0 h to go upstream between the same two points. What is the rate of flow of the stream ? : Let x = rate of the stream Then (5.5+x) = boat speed downstream and (5.5-x) = boat speed upstream : The distance for each trip is the same; write a dist equation; dist = time * speed : Dist down = dist up 5(5.5+x) = 8(5.5-x) ; 27.5 + 5x = 44 - 8x : 5x + 8x = 44 - 27.5 : 13x = 16.5 x = x = 1.27 km/hr is the rate of the stream : ; Confirm solution by finding the dist of each trip, should be equal Speed upstream: 5.5-1.27 = 4.23 Speed downstream: 5.5+1.27 = 6.77 5(6.77) = 33.85 km 8(4.23) = 33.84 km; close enough : : That wasn't so hard, was it? Any questions?
 Graphs/159848: A treasure hunting team of divers is placed in a computer controlled diving cage. The equation d= 40/3t - 2/9t squared describes the depth d ( in feet) that the cage will descend in t minutes. A) sketch the graph of the equation d = 40/3t - 2/9t squared. B) What part of the graph represents the physical aspects of the problem? C) What is the total time of the entire diving experiment?1 solutions Answer 117990 by ankor@dixie-net.com(15658)   on 2008-10-02 15:40:11 (Show Source): You can put this solution on YOUR website!A treasure hunting team of divers is placed in a computer controlled diving cage. The equation d = 40/3t - 2/9t squared describes the depth d (in feet) that the cage will descend in t minutes. : A) sketch the graph of the equation d = 40/3t - 2/9t squared. : d = y axis; t = x axis: graph equation: y = -(2/9)x^2 + (40/3)x : Plot the graph for x=0 to x = 60 (10 min intervals), should look like this: : B) What part of the graph represents the physical aspects of the problem? : Only the positive values for x & y : C) What is the total time of the entire diving experiment? 60 min as you can see on the graph
 Linear-equations/160021: solve the following for the variable Y CZ/Y=B1 solutions Answer 117986 by ankor@dixie-net.com(15658)   on 2008-10-02 15:25:54 (Show Source): You can put this solution on YOUR website!Solve the following for the variable Y = B Multiply both sides by Y, results: CZ = BY ; Divide both sides by B, results: = Y
 Rational-functions/160005: I thought I submitted this yesterday, but I did not get any answers on it. I need to see if I came up with the correct answers. The * sign is used as the mulitplication sign in this problem. Problem #1) x-6/x-3 = 2x/x-3 x-3/1 (x-6/x-3) = x-3/1 (2x/x-3) x(x-3/1) - x-3/1 * 6/x-3 = 2x x^2 - 3x-6 = 2x -2x -2x x^2 - 5x-6 = 0 (x+1)(x-6) = 0 x=-3 x=6 Problem #2 Word problem In a city of 25,000 homes, a survey was taken to determine the number with cable television. Of the 300 homes survey, 210 had cable television. Estimate the number of homes in the city that had cable television. 210/300 = x/25,000 25,000 * 210/300 = x/25,000 * 25,000 17,500 = x Thanks for you help 1 solutions Answer 117984 by ankor@dixie-net.com(15658)   on 2008-10-02 15:12:28 (Show Source): You can put this solution on YOUR website!Problem #1) x-6/x-3 = 2x/x-3 You don't have to do all that, multiply both sides by (x-3) and you have: x - 6 = 2x -6 = 2x-x x = -6 : : Problem #2 Word problem In a city of 25,000 homes, a survey was taken to determine the number with cable television. Of the 300 homes survey, 210 had cable television. Estimate the number of homes in the city that had cable television. 210/300 = x/25,000 25,000 * 210/300 = x/25,000 * 25,000 17,500 = x : This is right
 Functions/160018: Find the x-intercepts(if they exits) of the following quadratic functions. Graph the function and mark the intercepts. f(x)=x^2-6. I am completely confused on how to solve this problem and several others taht are similar. Please if you could show me step by step I'm sure I will be able to figure out the others.1 solutions Answer 117983 by ankor@dixie-net.com(15658)   on 2008-10-02 14:58:34 (Show Source): You can put this solution on YOUR website!Find the x-intercepts(if they exits) of the following quadratic functions. Graph the function and mark the intercepts. f(x) = x^2 - 6 : Understand that in the graphing world y = f(x), so we have: y = x^2 - 6 : Understand that the x intercept occurs when y = 0, substitute 0 for y: Solve: x^2 - 6 = 0 x^2 = +6; added 6 to both sides x = + and x = - : These are x intercepts, approx +2.4494897 and -2.4494897 : A graph of this would look like this : : You can see the x intercepts corresponds to the values we found : Did this make sense to you now?
 Percentage-and-ratio-word-problems/160016: If the basketball team makes 80% of their foul shot, and the ratio of foul shots to lay ups is 5 to 3 and the ratio of layups to 3 point is 2 to 1 what will the team's score be if they take 28 four shots1 solutions Answer 117982 by ankor@dixie-net.com(15658)   on 2008-10-02 14:46:04 (Show Source): You can put this solution on YOUR website!If the basketball team makes 80% of their foul shot, and the ratio of foul shots to lay ups is 5 to 3; and the ratio of layups to 3 point is 2 to 1. what will the team's score be if they take 28 four shots.(Assume you mean foul) : Find out how many foul shots are made: .8 * 28 = 22.4 points : Foul shots to lay-ups = 5L = 3(22.4) 5L = 67.2 L = L = 13.44 lay ups (26.88 points) : Lay-ups to 3 pointers = 2P = 13.44 P = P = 6.72 3-pointers (20.16 points) : Score: 22.4 + 26.88 + 20.16 = 69.44 ~ 69 points scored
 Miscellaneous_Word_Problems/159928: Terrell drove to the mountains at an average of 60 miles per hour. His return trip by the same roads averaged 40 miles per hour. His total driving time was 12 hours. How far did he drive one way? 60x = 720 x = 12 60(1/3) = 240 60(2/3) = 480 1 solutions Answer 117981 by ankor@dixie-net.com(15658)   on 2008-10-02 14:27:24 (Show Source): You can put this solution on YOUR website!Terrell drove to the mountains at an average of 60 miles per hour. His return trip by the same roads averaged 40 miles per hour. His total driving time was 12 hours. How far did he drive one way? : let d = distance one way : Write a time equation: Time = ; To time + return time = 12 hrs + = 12 Multiply equation by 120 to get rid of the denominators, results: 2d + 3d = 12(120) : 5d = 1440 d = d = 288 mi one way: : : Check solution by finding the total time 288/60 + 288/40 = 4.8 + 7.2 = 12
 Equations/159910: Pls help me to solve these 2 problems.Thanks in advance. 1. p=l + m/f Calculate m 2.- x-1/3 + 4x = 2/3 + 13x-2/3 Thanks again1 solutions Answer 117979 by ankor@dixie-net.com(15658)   on 2008-10-02 13:11:40 (Show Source): You can put this solution on YOUR website! 1. p = l + Calculate m : Subtract l from both sides p - l = : Multiply both sides by f f(p-l) = m : : 2. -x-1/3 + 4x = 2/3 + 13x-2/3 : This is very ambiguous. Assume you mean: - + 4x = + Multiply each term by 3, to get rid of the denominators, results -(x-1) + 3(4x) = 2 + 13x - 2 : -x + 1 + 12x = 13x; (removing the bracket changes the signs when it's neg) : 11x + 1 = 13x : 1 = 13x - 11x : 2x = 1 x = : If this is not what you mean, tell me what you do mean, use brackets.
 Graphs/159927: Find the slope and the y-intercept 2- 1/5y=5x The slope is ____ The y-intercept is (0,___)1 solutions Answer 117976 by ankor@dixie-net.com(15658)   on 2008-10-02 12:50:26 (Show Source): You can put this solution on YOUR website!Find the slope and the y-intercept 2 - y = 5x : We want the equation in the slope/intercept form : Subtract 2 from both sides and you have y = 5x - 2 Multiply both sides by 5 to get rid of the denominator 1y = 5(5x) - 5(2) : y = 25x - 10 : The slope is 25 The y-intercept is (0,-10)
 Exponents/159912: This question is from textbook Suppose you own a card shop. You buy one line of cards at a rate of 4 cards for \$5. You plan to sell the cards at a rate of 3 cards for \$5. How many cards must you sell in order to make a profit of \$100.1 solutions Answer 117958 by ankor@dixie-net.com(15658)   on 2008-10-02 09:51:06 (Show Source): You can put this solution on YOUR website!Suppose you own a card shop. You buy one line of cards at a rate of 4 cards for \$5. You plan to sell the cards at a rate of 3 cards for \$5. How many cards must you sell in order to make a profit of \$100. : Let x = no. of cards required to make \$100 profit : Cost = (5/4)x Revenue = (5/3)x : Revenue - cost = Profit (5/3)x - (5/4)x = 100 Multiply equation by 12 to get rid of the denominators; results: 4(5x) - 3(5x) = 12(100) 20x - 15x = 1200 : 5x = 1200 x = x = 240 cards need to be sold : : Check solution: (5/3)240 - (5/4)240 = 100
 Travel_Word_Problems/159939: This question is from textbook Algebra 2 Brandon goes on a ACaub Scout hike and hikes to a waterfall in 3 hours and hikes back along the same route to the compground in 2 hours. If the hiking rate is 1mph faster returning than going, how fast are the boys hiking each way?1 solutions Answer 117942 by ankor@dixie-net.com(15658)   on 2008-10-02 08:08:17 (Show Source): You can put this solution on YOUR website!Brandon goes on a a Cub Scout hike and hikes to a waterfall in 3 hours and hikes back along the same route to the campground in 2 hours. If the hiking rate is 1mph faster returning than going, how fast are the boys hiking each way? : Let s = hiking rate going then (s+1) = hiking rate returning : The distance of each trip is the same. Write a distance equation Dist = time * speed. : go dist = return dist 3s = 2(s+1) 3s = 2s + 2 3s - 2s = 2 s = 2 mph is the hiking rate going, : Obviously, 3 mph is the hiking rate returning ; : Check solution by confirming the distances are the same: 3*2 = 6 mi 2*3 = 6 mi
 Travel_Word_Problems/159809: A 6-passenger plane cruises at 180 mph in calm air. If the plane files 7 miles with the wind in the same smount of time as it flies 5 miles against the wind, then what is the wind speed?1 solutions Answer 117921 by ankor@dixie-net.com(15658)   on 2008-10-01 20:40:58 (Show Source): You can put this solution on YOUR website!A 6-passenger plane cruises at 180 mph in calm air. If the plane files 7 miles with the wind in the same amount of time as it flies 5 miles against the wind, then what is the wind speed? : Let x = wind speed then (180+x) = speed with the wind and (180-x) = speed against : Write a time equation; time = ; With time = against time = Cross multiply 5(180+x) = 7(180-x) : 900 + 5x = 1260 - 7x : 5x + 7x = 1260 - 900 : 12x = 360 x = x = 30 mph is speed of the wind : : Check solution, find the times at both speeds 210 mph and 150 mph: 7/210 = .033 hrs 5/150 = .033 hrs
 Equations/159800: After a sailboat has been on the water for 3h, a change in the wind direction reduced the average speed of the boat by 5mph. The entire distance sailed was 57mi. The total time spent sailing was 6h. How far did the sailboat travel the in the first 3 h?1 solutions Answer 117917 by ankor@dixie-net.com(15658)   on 2008-10-01 20:18:19 (Show Source): You can put this solution on YOUR website!After a sailboat has been on the water for 3h, a change in the wind direction reduced the average speed of the boat by 5mph. The entire distance sailed was 57mi. The total time spent sailing was 6h. How far did the sailboat travel the in the first 3 h? : Let s = speed of the boat the 1st three hrs then (s-5) = reduced speed during the last 3 hrs : Write a distance equation; Dist = time * speed : Initial dist + reduced speed dist = 57 mi 3s + 3(s-5) = 57 : 3s + 3s - 15 = 57 : 6s = 57 + 15 : 6s = 72 : s = s = 12 mph hr therefore 3 * 12 = 36 mi in the 1st 3 hrs : : Check solution by finding the total dist (reduced speed = 12 - 5 = 7 mph) 36 + 7(3) = 57 mi