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Quadratic_Equations/204078: Please help me solve this problem. Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle. 1 solutions Answer 154012 by ankor@dixie-net.com(15649)   on 2009-07-24 09:44:01 (Show Source): You can put this solution on YOUR website! Steve traveled 150 miles at a certain speed. Had he gone 20 mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle. : Let s = the speed of the car then (x+20) = the faster speed : Write a time equation: Time : = + 2 : Multiply this equation by s(s+20) and solve for s, and you have it

Numbers_Word_Problems/204036: The difference of two numbers is 16. Three-fourths of the larger number is 14 larger than one-half of the smaller number. Find the numbers. 1 solutions Answer 153981 by ankor@dixie-net.com(15649)   on 2009-07-23 20:55:29 (Show Source): You can put this solution on YOUR website! Two numbers, x & y ; The difference of two numbers is 16. x - y = 16 x = (y+16) : Three-fourths of the larger number is 14 larger than one-half of the smaller number. .75x = .5y + 14 : Replace x with (y+16) .75(y + 16) = .5y + 14 : .75y + 12 = .5y + 14 : .75y - .5y = 14 - 12 : .25y = 2 y = y = 8 then x = 8 + 16 x = 24

Geometry_Word_Problems/204031: The perimeter of a swimming pool is 96m. The width is 3m more than half the length of the pool. find the length and breadth of the pool. 1 solutions Answer 153971 by ankor@dixie-net.com(15649)   on 2009-07-23 16:40:25 (Show Source): You can put this solution on YOUR website! The perimeter of a swimming pool is 96 m. The width is 3m more than half the length of the pool. Find the length and breadth of the pool. : Let x = the length of the pool It says,"The width is 3m more than half the length of the pool.", therefore (.5x + 3) = the width ; Perimeter equation: 2L + 2W = 96, therefore: 2x + 2(.5x+3) = 96 2x + x + 6 = 96 3x = 96 - 6 3x = 90 x = x = 30 m is the length therefore .5(30) + 3 = 18 m is the width ; ; Check solution, find the perimeter 2(30) + 2(18) = 96

Miscellaneous_Word_Problems/203837: A diagonal of a square connects the points (-4,3) and (2,-3). Find the area and perimeter of the square. 1 solutions Answer 153963 by ankor@dixie-net.com(15649)   on 2009-07-23 15:08:48 (Show Source): You can put this solution on YOUR website! A diagonal of a square connects the points (-4,3) and (2,-3). Find the area and perimeter of the square. : If you draw this on graph paper you can see this is a square 6 by 6 You can do it in your head: 4*6 = 24 is the perimeter and 6^2 = 36 is the area

Equations/203958: Hi all, I was hoping someone could help me in answering the following 2 problems. They are two similiar problems bbut they are seperate problems and are not related to eachother. 1. Make t the subject of the equation y = sqrt(8t + 3) 2. Make x the subject of the equation y = 3e^(2x). Any help with steps would be most appreciated. Thanks, -Nick. 1 solutions Answer 153955 by ankor@dixie-net.com(15649)   on 2009-07-23 14:21:32 (Show Source): You can put this solution on YOUR website! 1. Make t the subject of the equation y = sqrt(8t + 3) y = Square both sides: y^2 = 8t + 3 Subtract 3 from both sides y^2 - 3 = 8t Divide both sides by 8 = t : : 2. Make x the subject of the equation y = 3e^(2x) y = Divide both sides by 3 = find the natural log of both sides = log equiv of exponents: = natural log of e is 1 = 2x divide both sides by 2 = x

Linear_Equations_And_Systems_Word_Problems/203995: Four times the sum of the digits of a two-digit number is equal to the number. It the digits are reversed, the resulting number is 27 greater than the original number. What is the number? 1 solutions Answer 153933 by ankor@dixie-net.com(15649)   on 2009-07-23 12:22:05 (Show Source): You can put this solution on YOUR website! Four times the sum of the digits of a two-digit number is equal to the number. It the digits are reversed, the resulting number is 27 greater than the original number. What is the number? : Let x = the 10's digit Let y = the units digit then 10x + y = "the number" : Write an equation for each statement: : "Four times the sum of the digits of a two-digit number is equal to the number." 4(x+y) = 10x + y 4x + 4y = 10x + y 4y - y = 10x - 4x 3y = 6x Simplify, divide by 3 y = 2x : "If the digits are reversed, the resulting number is 27 greater than the original number." 10y + x = 10x + y + 27 10y - y = 10x - x + 27 9y = 9x + 27 Simplify divide by 9 y = x + 3 : From the 1st statement equation, replace y with 2x 2x = x + 3 2x - x = 3 x = 3 then y = 2(3) y = 6 : 36 = " the number" : : Check solutions in the statement: "If the digits are reversed, the resulting number is 27 greater than the original number." 63 = 36 + 27

Miscellaneous_Word_Problems/203841: Jean goes to a movie theater where a ticket costs $7 and any snack item-candy,popcorn,or drink-sells for $1.50 each. Frank goes to a theater where the ticket costs $4 and candy, popcorn, or drinks sell for $2.50 each. How many snack items would jean and Frank need to buy, so that they each pay the same amount at the theater? 1 solutions Answer 153880 by ankor@dixie-net.com(15649)   on 2009-07-22 21:22:08 (Show Source): You can put this solution on YOUR website! Jean goes to a movie theater where a ticket costs $7 and any snack item-candy,popcorn,or drink-sells for $1.50 each. Frank goes to a theater where the ticket costs $4 and candy, popcorn, or drinks sell for $2.50 each. How many snack items would jean and Frank need to buy, so that they each pay the same amount at the theater? : Let n = number of snack items bought for equal amts : Franks$ = Jeans% 2.50n + 4 = 1.50n + 7 2.5n - 1.5n = 7 - 4 n = 3 snack items : : Check solution in original equation 2.5(3) + 4 = 1.5(3) + 7 7.50 + 4 = 4.50 + 7

Miscellaneous_Word_Problems/203843: When 6 students show up for the Swift River Cleanup Day, they can pick up all of the bottles and trash on their section of the riverfront in 2 1/2 hr. If 9 students show up, how long will the same cleanup take? 1 solutions Answer 153879 by ankor@dixie-net.com(15649)   on 2009-07-22 21:10:21 (Show Source): You can put this solution on YOUR website! When 6 students show up for the Swift River Cleanup Day, they can pick up all of the bottles and trash on their section of the riverfront in 2 1/2 hr. If 9 students show up, how long will the same cleanup take? : Let t = time required using 9 students ; You can solve this using man-hrs, given: 6 * 2.5 = 15 man-hrs required to do the job Then 9t = 15 t = t = 1 hrs if 9 students work :

Radicals/203886: This question is from textbook Intermediate Algebra 3(sqrt7t)((2(sqrt7t) + 3(sqrt3t^2)) I need help solving it. I guess distributing the equation. Honestly, I do not know. I really need help. Thank you. 1 solutions Answer 153839 by ankor@dixie-net.com(15649)   on 2009-07-22 15:23:01 (Show Source): You can put this solution on YOUR website! 3(sqrt7t)((2(sqrt7t) + 3(sqrt3t^2)) : * : Multiply both terms inside the brackets by ; results: 6(7t) + or 6(7t) + Extract the square root of t^2 42t + : Factor out 3t :

Functions/203846: Find the numbers C and D such that (-4,-7) is a solution of the following system: -4x + Cy =-3 Dx - 2y =24 1 solutions Answer 153837 by ankor@dixie-net.com(15649)   on 2009-07-22 14:49:33 (Show Source): You can put this solution on YOUR website! Find the numbers C and D such that (-4,-7) is a solution of the following system: -4x + Cy =-3 Dx - 2y = 24 : Substitute -4 for x and -7 for y -4(-4) + C(-7) = -3 D(-4) - 2(-7) = 24 : +16 - 7C = -3 -4D + 14 = 24 : -7C = -3 - 16 7C = 3 + 16 C = and -4D = 24 - 14 -4D = 10 D = D =

Miscellaneous_Word_Problems/203852: You are in line at a ticket window. There are two more people ahead of you in line than there are behind you. In the entire line, there are three times as many people as there are behind you. how many are in the line? 1 solutions Answer 153823 by ankor@dixie-net.com(15649)   on 2009-07-22 12:54:18 (Show Source): You can put this solution on YOUR website! You are in line at a ticket window. There are two more people ahead of you in line than there are behind you. In the entire line, there are three times as many people as there are behind you. how many are in the line? : Let x = no. behind you then (x=2) = no. ahead of you : Write an equation for the statement: "there are three times as many people as there are behind you." x + 1 + (x+2) = 3x 2x + 3 = 3x 3 = 3x - 2x x = 3 people behind you then 3 + 2 = 5 people ahead : Total: ahead + you + behind: 5 + 1 + 3 = 9 folks in line :

Volume/203829: A cylinder can of cleaner holds 1 liter of liquid. What is its height if the diameter of the base is 10cm. I am failing my geomerty class, I just do not get it, but trying. I did not get to give a reply of a "thank you" to a tutor(Stan) that answered 2 questions of mine a couple of weeks ago because it would not let me send it for some reason- So just in case-Thanks so much for your time in helping me. 1 solutions Answer 153814 by ankor@dixie-net.com(15649)   on 2009-07-22 11:24:34 (Show Source): You can put this solution on YOUR website! A cylinder can of cleaner holds 1 liter of liquid. What is its height if the diameter of the base is 10 cm. : Change 1 liter to cu/cm: 1 liter = 1000 cu/cm : Volume of a cylinder: V = Find the radius: a 10 cm diameter = 5 cm radius : = 1000 : = 1000 : h = h = 12.73 cm is the height : : Check solution on a calc: enter pi*5^2*12.73 = 999.8 ~ 1000, which is 1 liter

logarithm/203739: A certain strain on bacteria divides every three hours. If a colony is started with 30 bacteria, then the time(t, in hours) required for the colony to groww to N bacteria is given by the following formula. Find the time required for the colony to grow to a million bacteria.(Give your answer to the nearest tenth) t= 3(log(n/30))/log 2 1 solutions Answer 153756 by ankor@dixie-net.com(15649)   on 2009-07-21 16:17:12 (Show Source): You can put this solution on YOUR website! A certain strain on bacteria divides every three hours. If a colony is started with 30 bacteria, then the time(t, in hours) required for the colony to groww to N bacteria is given by the following formula. Find the time required for the colony to grow to a million bacteria. (Give your answer to the nearest tenth) ; t= : t= : t= : t= t = 45.1 hrs

Mixture_Word_Problems/203665: Angela needs 20 quarts of 50% antifreeze solution in her radiator. She plans to obtain this by mixing some pure antifreeze with an appropriate amount of a 40% antifreeze solution. How many quarts of each should she use? 1 solutions Answer 153669 by ankor@dixie-net.com(15649)   on 2009-07-20 19:51:58 (Show Source): You can put this solution on YOUR website! needs 20 quarts of 50% antifreeze solution in her radiator. plans to obtain this by mixing some pure antifreeze with an appropriate amount of a 40% antifreeze solution. How many quarts of antifreeze? : Let x = amt of pure antifreeze The resulting amt is to be 20 qts, therefore (20-x) = amt of 40% solution required : A typical mixture problem : x + .40(20-x) = .50(20) ; x + 8 - .4x = 10 : x - .4x = 10 - 8 : .6x = 2 x = x = 3 qts of pure anti-freeze and 20 - 3 = 16 qts of 40% mixture

Numeric_Fractions/203662: I am having a hard time with Algebra. Here's one I do not get. I do not get what the letters stand for. Please help..... Solve for w: 3w - 10 = 4w +5 1 solutions Answer 153668 by ankor@dixie-net.com(15649)   on 2009-07-20 19:41:14 (Show Source): You can put this solution on YOUR website! 3w - 10 = 4w + 5 You want to isolate the unknown (w) on one side, and numerical value on the other side : Subtract 5 from both sides 3w - 10 - 5 = 4w + 5 - 5 ; and you have 3w - 15 = 4w ; Subtract 3w from both sides: 3w - 3w - 15 = 4w - 3w ; and you have -15 = w : : Check your solution by substituting -15 for w in the original equation 3w - 10 = 4w + 5 3(-15) - 10 = 4(-15) + 5 -45 - 10 = -60 + 5 -55 = -55; equality reigns, confirms your solution of w = 15

Percentage-and-ratio-word-problems/203597: This question is from textbook mathematics for igcse if an employer reduce the working week from 40 hours to 35 hours with no loss of weekly pay,calculate the percentage increase in the hourly rate of pay 1 solutions Answer 153634 by ankor@dixie-net.com(15649)   on 2009-07-20 13:38:31 (Show Source): You can put this solution on YOUR website! an employer reduce the working week from 40 hours to 35 hours with no loss of weekly pay, calculate the percentage increase in the hourly rate of pay : Let the weekly pay = 400 : = $10 per/hr original hourly pay : = $11.43 increased hourly pay : Pay increase divided by original pay = Per cent increase : = 1.43/10 = .143 * 100 = 14.3% increase in pay

Volume/203576: Suppose you are designing a cardboard box that must have a volume of 34 cubic feet. The cost of the cardboard is $9 per square ft. How much will the material for each box cost? 1 solutions Answer 153586 by ankor@dixie-net.com(15649)   on 2009-07-19 21:10:32 (Show Source): You can put this solution on YOUR website! Suppose you are designing a cardboard box that must have a volume of 34 cubic feet. The cost of the cardboard is $9 per square ft. How much will the material for each box cost? : If it is a square box the dimension (s) will be: s = cube root(34) s ~ 3.24 ft : Find the cost using the Surface area: 6(3.24^2) * $9 = $566.87

Expressions-with-variables/203543: How do I simplify the following question 5x+x2 . 6x-15 ----- ------ 2x-5 x+2xy 1 solutions Answer 153584 by ankor@dixie-net.com(15649)   on 2009-07-19 19:57:05 (Show Source): You can put this solution on YOUR website! 5x+x2 . 6x-15 ----- ------ 2x-5 x+2xy : Assume it's: * Factor out like terms, cancel (2x-5) * = x(x+5) * Cancel x (x+5) * =

Quadratic_Equations/203510: Could someone help me with this one? I have trouble with word problems? You are greatly appreciated. An express train and a local train both leave Gray’s Lake at 12:00 noon and head for Chicago 60 miles away. The express travels twice as fast as the local and arrives 2 hours ahead of it. Find the speed of each train. 1 solutions Answer 153583 by ankor@dixie-net.com(15649)   on 2009-07-19 19:41:07 (Show Source): You can put this solution on YOUR website! An express train and a local train both leave Gray’s Lake at 12:00 noon and head for Chicago 60 miles away. The express travels twice as fast as the local and arrives 2 hours ahead of it. Find the speed of each train. : Let s = speed of the freight then 2s = speed of the express : Write a time equation: Time = Freight time = Express time + 2 hrs = + 2 Multiply equation by 2s, results: 2(60) = 60 + 2(2s) 120 = 60 + 4s 120 - 60 = 4s 60 = 4s s = s = 15 mph is the freight, then 2(15) = 30 mph is express ; : Check solution by finding the time of each train 60/15 = 4 hr 60/30 = 2 hr ------------ differ = 2 hrs

Quadratic_Equations/203530: A bridge is the shape of a parabola. It is 10 m wide and the highest point of the bridge is 6m above ground. A transport truck is 4.5 m tal and 3 m wide. The road is centered on the axis of symmetry and the transport truck must stay on its own side of the road. Will the trick fit under the bridge? Justify your decision. 1 solutions Answer 153577 by ankor@dixie-net.com(15649)   on 2009-07-19 19:02:09 (Show Source): You can put this solution on YOUR website! A bridge is the shape of a parabola. It is 10 m wide and the highest point of the bridge is 6m above ground. A transport truck is 4.5 m tal and 3 m wide. The road is centered on the axis of symmetry and the transport truck must stay on its own side of the road. Will the truck fit under the bridge? Justify your decision. : Find the parabola equation using the form ax^2 + bx = y x = 5; y = 6 25a + 5b = 6 and x = 10; y = 0 100a + 10b = 0 : Multiply the 1st equation by 2 and subtract from th above equation 100a + 10b = 0 50a + 10b = 12 ---------------- 50a = -12 a = a = -.24 ; Find b using 100a + 10b = 0 100(-.24) + 10b = 0 -24 + 10b = 0 10b = 24 b = 2.4 : The equation y = -.24x^2 + 2.4x which we can plot: Assuming the truck will be just at the right of the centerline, a 3 m wide truck will be at x = 8> Find the height of the parabola where x = 8 y = -.24(8^2) + 2.4(8) y = -15.36 + 19.2 y = +3.84, so 4.5 is too high

Rate-of-work-word-problems/203558: Five workers paint four houses in six days. Working at the same rate as these workers, how many workers are needed to paint 12 houses in three days? 1 solutions Answer 153571 by ankor@dixie-net.com(15649)   on 2009-07-19 18:26:11 (Show Source): You can put this solution on YOUR website! Five workers paint four houses in six days. Working at the same rate as these workers, how many workers are needed to paint 12 houses in three days? : Use Man-days (no.of men * no. of days) : Let x = the no. of man-days required to paint 1 house : x = x = x = 7.5 man-days per house : "how many workers are needed to paint 12 houses in three days?" Let w = no. of workers 3w = 12(7.5) 3w = 90 w = w = 30 workers to paint 12 house in 3 days.

Proportions/203409: The ratio of domestic stamps to foreign stamps in John’s stamp collection is 3:1. If John sold thirty of his domestic stamps, the ratio of domestic stamps to foreign stamps would be 1:2. How many foreign stamps does John have in his collection? 1 solutions Answer 153553 by ankor@dixie-net.com(15649)   on 2009-07-19 15:39:50 (Show Source): You can put this solution on YOUR website! The ratio of domestic stamps to foreign stamps in John’s stamp collection is 3:1. If John sold thirty of his domestic stamps, the ratio of domestic stamps to foreign stamps would be 1:2. How many foreign stamps does John have in his collection? : "The ratio of domestic stamps to foreign stamps in John’s stamp collection is 3:1." = d = 3f : "If John sold thirty of his domestic stamps, the ratio of domestic stamps to foreign stamps would be 1:2." : = f = 2(d-30) f = 2d - 60 replace d with 3f f = 2(3f) - 60 f = 6f - 60 60 = 6f - f 60 = 5f f = f = 12 foreign stamps ; : Check solution d = 3(12 d = 36 domestic stamps : Check in statement: " John sold thirty of his domestic stamps, the ratio of domestic stamps to foreign stamps would be 1:2." 36 - 30 = 6 stamps 6/12 = 1/2

Quadratic_Equations/203509: Could someone help me with this one? I have difficulty with word problems. You are greatly appreciated. Joe has a collection of nickels and dimes that is worth $6.05. If the number of dimes was doubled and the number of nickels was decreased by 10, the value of the coins would be $9.85. How many dimes does he have? 1 solutions Answer 153551 by ankor@dixie-net.com(15649)   on 2009-07-19 15:15:12 (Show Source): You can put this solution on YOUR website! Joe has a collection of nickels and dimes that is worth $6.05. If the number of dimes was doubled and the number of nickels was decreased by 10, the value of the coins would be $9.85. How many dimes does he have? : Let d = no. of dimes Let n = no. of nickels : Write an equation for each statement: : "a collection of nickels and dimes that is worth $6.05." .05n + .10d = 6.05 : "If the number of dimes was doubled and the number of nickels was decreased by 10, the value of the coins would be $9.85." .05(n-10) + .10(2d) = 9.85 : .05n - .50 + .20d = 9.85 : .05n + .20d = 9.85 + .50 : .05n + .20d = 9.35 : Subtract the 1st equation from the above equation: .05n + .20d = 9.35 .05n + .10d = 6.05 ---------------------Subtraction eliminate n, find d 0n + .10d = 3.30 d = d = 33 dimes : : Check solution Find n: .05n + .10d = 6.05 .05n + .10(33) = 6.05 .05n + 3.30 = 6.05 .05n = 6.05 - 3.30 .05n = 2.75 n = n = 55 nickels : .05(55) + .20(33) = 9.35 2.75 + 6.60 = 9.35

Polynomials-and-rational-expressions/203406: Five grams of sugar are added to a 45 gram serving of a breakfast cereal that is is 10% sugar. What is the percent concentration in the resulting mixture? 1 solutions Answer 153544 by ankor@dixie-net.com(15649)   on 2009-07-19 14:33:18 (Show Source): You can put this solution on YOUR website! Five grams of sugar are added to a 45 gram serving of a breakfast cereal that is is 10% sugar. What is the percent concentration in the resulting mixture? : Let x = the decimal equiv of percent of sugar of the resulting mixture .10(45) + 5 = x(45+5) : 4.5 + 5 = 50x : 9.5 = 50x x = x = .19 * 100 = 19% sugar concentration

Quadratic_Equations/203518: Can anyone help with this one? I cannot come up with a solution. I think I have it set up wrong. You are greatly appreciated. Translate the following into a quadratic equation, and solve it: The length of a rectangular garden is four times its width; if the area of the garden is 196 square meters, what are its dimensions? 1 solutions Answer 153543 by ankor@dixie-net.com(15649)   on 2009-07-19 13:24:08 (Show Source): You can put this solution on YOUR website! The length of a rectangular garden is four times its width; if the area of the garden is 196 square meters, what are its dimensions? ; Let x = the width then 4x = the length : Area; 4x * x = 196 4x^2 - 196 = 0 Simplify, divide by 4 x^2 - 49 = 0 difference of squares, factors to: (x-7)(x+7) = 0 positive solution x = 7 m is the width and 4(7) = 28 m is length ; ; Check solution 28 * 7 = 196

Systems-of-equations/203506: the units digit of a 3 digit number is 5. the sum of its digits is 11. if the units and 100s digits are reversed, the sum of the new number and the original number is 787. find the original number. 1 solutions Answer 153541 by ankor@dixie-net.com(15649)   on 2009-07-19 13:01:24 (Show Source): You can put this solution on YOUR website! the units digit of a 3 digit number is 5. the sum of its digits is 11. if the units and 100s digits are reversed, the sum of the new number and the original number is 787. find the original number. ; Let x = the 100's digit Let y = the 10's digit then 100x + 10y + 5 = original number : "the sum of its digits is 11." x + y + 5 = 11 x + y = 11 - 5 x + y = 6 y = (6-x) ; "if the units and 100s digits are reversed, the sum of the new number and the original number is 787." 500 + 10y + x + 100x + 10y + 5 = 787 Group like terms 10y + 10y + x + 100x + 505 = 787 : 101x + 20y = 787 - 505 : 101x + 20y = 282 Substitute (6-x) for y 101x + 20(6-x) = 282 : 101x + 120 - 20x = 282 : 101x - 20x = 282 - 120 : 81x = 162 x = x = 2 then y = 6 - 2 y = 4: : 245 = original number ; : Check solution in the statement: if the units and 100s digits are reversed, the sum of the new number and the original number is 787. 542 + 245 = 787

Surface-area/203465: having trouble setting this up can someone help please A rectangular box with no top (pictured above) is to contain 2250 cubic inches of volume. Find the dimensions of the box that will minimize the surface area. The length (l) of the base is three times the width (w). 1 solutions Answer 153540 by ankor@dixie-net.com(15649)   on 2009-07-19 12:22:48 (Show Source): You can put this solution on YOUR website! A rectangular box with no top (pictured above) is to contain 2250 cubic inches of volume. Find the dimensions of the box that will minimize the surface area. The length (l) of the base is three times the width (w). : But what about the height of the box? Is it the same as the width, or do we have to find it? (h), assuming this is the case: : l * w * h = 2250 cu/inches Let w = x, then we can write it: 3x * x * h = 2250 3x^2 * h = 2250 h = reduce fraction h = is the height of the box : Surface area for box without a top S.A. = (l*w) + 2(l*h) + 2(w*h) : Substitute 3x for l and x for w S.A. = 3x*x + 2(3x*h) + 2(x*h) S.A = 3x^2 + 6hx + 2hx S.A = 3x^2 + 8hx Substitute for h S.A = 3x^2 + 8(x*) S.A = 3x^2 + 8() : S.A = 3x^2 + : Graph this equation and find the min surface area: On a Ti-83, it says, min S.A. at x = 10, which is 900 sq/in, as indicated here. : find h: h = h = h = 7.5 Then l= 30, w=10, h=7.5; the dimensions of the box : Check volume: 30 * 10 * 7.5 = 2250 : Did this make sense?

Linear-systems/203481: I actually attempted the examples in my book but still do not grasp the concept if I can actually get someone to get to break this down for me i might be able to do the rest on my own: y= -3x+19 y= 2x-1 and x+3y=2 -x+y=1 thank you 1 solutions Answer 153509 by ankor@dixie-net.com(15649)   on 2009-07-18 22:00:02 (Show Source): You can put this solution on YOUR website! The first one lends itself to the substitution method : y= -3x+19 y= 2x - 1 Look at the 2nd equation, it should be apparent that we can substitute (2x-1) for y in the 1st equation, then find x 2x - 1 = -3x + 19 2x + 3x = 19 + 1 5x = 20 x = x = 4 Use the 2nd equation to find y. Substitute 4 for x y = 2(4) - 1 y = 8 - 1 y = 7 Check your solutions by substitution in the 1st equation y = - 3x + 19 7 = -3(4) + 19 7 = -12 + 19; confirms our solutions : : The 2nd equation lends itself to the elimination method x + 3y = 2 -x + y = 1 -------------adding these eliminates x, find y 0x + 4y = 3 y = : Find x using the 1st equation, substitute 3/4 of y x + 3(3/4) = 2 x + 9/4 = 2 x = 2 - 9/4 x = -1/4 : Check solution in the 2nd equation -x + y = 1 -(-1/4) + (3/4) = 1 +1/4 + 3/4 = 1

Travel_Word_Problems/203473: This question is from textbook Big plane. A six-passenger plane cruises at 180 mph in calm air. If the plane flies 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? 1 solutions Answer 153507 by ankor@dixie-net.com(15649)   on 2009-07-18 21:46:19 (Show Source): You can put this solution on YOUR website! A six-passenger plane cruises at 180 mph in calm air. If the plane flies 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 w = speed of the wind then (180+w) = plane speed with the wind and (180-w) = plane speed against the wind : The time of the two trips is equal, write a time equation Time = : 7 mi time = 5 mi time = Cross multiply 7(180-w) = 5(180+w) : 1260 - 7w = 900 + 5w : 1260 - 900 = 5w + 7w : 360 = 12w w = w = 30 mph is the speed of the wind : : Check solution by finding the times, are they equal(210 with, 150 against) 7/210 = .033 5/150 = .033

Miscellaneous_Word_Problems/203472: This question is from textbook Ride the peaks. Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one-half hour longer than Smith’s. How fast was each one traveling? I am not sure if i am suppose to use the D=r*t. I am confused on how to set it up. I know that smith's distance is 45 miles and Jones distance is 70 miles I am confused on how to write the part where Johes goes 5 miles per hour more then Smith and took one half hour longer then smith. 1 solutions Answer 153506 by ankor@dixie-net.com(15649)   on 2009-07-18 21:26:10 (Show Source): You can put this solution on YOUR website! Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one-half hour longer than Smith’s. How fast was each one traveling? : Let s = D's speed then (s+5) = J's speed : Write a time equation: Time = : Smith's time = Jones' time - .5 hrs = - .5 Multiply equation by s(s+5) s(s+5)* = s(s+5)* - .5s(s+5) Cancel out the denominators and you have: 45(s+5) = 70s - .5s^2 - 2.5s : 45s + 225 = 70s - .5s^2 - 2.5s arrange as a quadratic equation on the left .5s^2 + 2.5s + 45s - 70s + 225 = 0 : .5s^2 - 22.5s + 225 = 0 Multiply equation by 2, get rid of the decimals s^2 - 45s + 450 = 0 Factors to: (s - 15)(s - 30) = 0 Two good solutions s = 15 mph is Smith's speed, then 20 mph is Jones' speed and s = 30 mph is Smith's speed, then 35 mph is Jones' speed : : Check solutions, find the time for each trip Smith: 45/15 = 3 hr Jones: 70/20 = 3.5 hr : You can check the s=30 solution

Systems-of-equations/203394: the ratio of the tens digit to the units digit of a two-digit number is 1 to 4. the number formed by reversing the digits is 2 less than 3 times the original number. find the original number. 1 solutions Answer 153464 by ankor@dixie-net.com(15649)   on 2009-07-18 12:59:19 (Show Source): You can put this solution on YOUR website! the ratio of the tens digit to the units digit of a two-digit number is 1 to 4. the number formed by reversing the digits is 2 less than 3 times the original number. find the original number. : Let x = the tens digit Let y = units then 10x + y = the original number : "the ratio of the tens digit to the units digit of a two-digit number is 1 to 4." = cross multiply 4x = 1y : "the number formed by reversing the digits is 2 less than 3 times the original number." 10y + x = 3(10x+y) - 2 : 10y + x = 30x + 3y - 2 : 10y - 3y = 30x - x - 2 : 7y = 29x - 2 Substitute 4x for y: 7(4x) = 29x - 2 28x = 29x - 2 +2 = 29x - 28x x = 2 then y = 4(2) y = 8 : 28 = the original number. ; : Check solution in the statement: "number formed by reversing the digits is 2 less than 3 times the original number." 82 = 3(28) - 2 82 = 84 - 2