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 Miscellaneous_Word_Problems/96707: Refer to a rectangle Find an expression that represents its perimeter on top of the rectangle ___2x-1_ 5 and on the side of the rectangle __4___ 3x+1 1 solutions Answer 70494 by ankor@dixie-net.com(15653)   on 2007-09-08 15:34:19 (Show Source): You can put this solution on YOUR website!Refer to a rectangle Find an expression that represents its perimeter on top of the rectangle. (Not sure what "on top of the rectangle" means) : : Anyway: A rectangle that is by : P = 2 + 2 : P = + : Arrange over a single denominator: P = = = =
 Square-cubic-other-roots/96858: This question is from textbook Blitzer College Algebra Suppose that N= sqrt of x (only x) +3 (not under sqrt sign) models the number of cases of an infection, in millions, of a disease x years from now. a) approximately how many cases of the infection will there be 9 yrs from now? b) In how many years will there be 5 million cases? ** This is not an equation from our next book, it is one that our instructor gave us as apart of a seperate assignment1 solutions Answer 70488 by ankor@dixie-net.com(15653)   on 2007-09-08 14:28:55 (Show Source): You can put this solution on YOUR website!Suppose that N = sqrt of x (only x) + 3 (not under sqrt sign) models the number of cases of an infection, in millions, of a disease x years from now. : : a) approximately how many cases of the infection will there be 9 yrs from now? N = 3 + 3 N = 6 million cases : b) In how many years will there be 5 million cases? ; Square both sides: x = 4 years
 Polynomials-and-rational-expressions/96623: Divide the following fractions. 6p-18 ÷ 3p-9 ______ _____ 9p p²+2p 1 solutions Answer 70431 by ankor@dixie-net.com(15653)   on 2007-09-07 21:35:47 (Show Source): You can put this solution on YOUR website!: ------------ : Invert the dividing fraction and multiply: * : Factor: * : Cancel (3-p), p, * : Cancel 3 into 6 * (p+2) = : Could you follow this OK?
 Radicals/96594: find the perimeter of the triangle 4 , /5 - /3, /5 + /3 radical equations1 solutions Answer 70399 by ankor@dixie-net.com(15653)   on 2007-09-07 16:04:45 (Show Source): You can put this solution on YOUR website!find the perimeter of the triangle 4 , /5 - /3, /5 + /3 radical equations : Assume you mean the 3 sides are: 1: 4 2: 3: : Add the three sides: P = 4 + () + () : remove the brackets, group like terms P = 4 + : P = 4 + 2
 Mixture_Word_Problems/96682: A certain creme mixture contains 12 grams of creme A, 18.6 grams of petrolatum, and 30 grams univase. The pharmacist needs to make a 480-gram mixture containing the same ratio of ingredients. How much of each ingredient should she include?1 solutions Answer 70393 by ankor@dixie-net.com(15653)   on 2007-09-07 14:44:18 (Show Source): You can put this solution on YOUR website!A certain creme mixture contains 12 grams of creme A, 18.6 grams of petrolatum, and 30 grams univase. The pharmacist needs to make a 480-gram mixture containing the same ratio of ingredients. How much of each ingredient should she include? : Here is one way to do it, by proportions : Let the amt of the three ingredients be x, y, and z : Find the original total amt: 12 + 18.6 + 30 = 60.6 : Find x = Cross mult: 60.6x = 12 * 480 60.6x = 5760 x = x = 95.05 : Find y: = 60.6y = 18.6 * 480 60.6y = 8928 y = y = 147.3 : Find z = : you should be able to complete this problem : you can check the amts by adding them all up and seeing if they ~ 480
 Polynomials-and-rational-expressions/96642: Perform the indicated operations. 14x- 7 * x²+6x+8 ÷ x²+24 _______ ________ ______ x²+3-4 2x²+5x-3 x² + 2x-3 1 solutions Answer 70373 by ankor@dixie-net.com(15653)   on 2007-09-07 12:55:58 (Show Source): You can put this solution on YOUR website! 14x- 7 * x²+6x+8 ÷ x²+24 _______ ________ ______ x²+3-4 2x²+5x-3 x² + 2x-3 : Invert the dividing fraction and mulitply * * : Factor: * * : Cancel (2x-1), (x+4), (x+3) and (x-1) : 7 * (x+2) * =
 Travel_Word_Problems/96369: A funny car starts from rest and reaches a speed of 367 ft/sec in 5.5 seconds. What is the acceleration of the dragster for this quarter mile event? What is the average speed? I correctly solved the first part, but I do not know how to find average speed?1 solutions Answer 70225 by ankor@dixie-net.com(15653)   on 2007-09-06 07:37:41 (Show Source): You can put this solution on YOUR website!A funny car starts from rest and reaches a speed of 367 ft/sec in 5.5 seconds. What is the acceleration of the dragster for this quarter mile event? What is the average speed? I correctly solved the first part, but I do not know how to find average speed? : Av speed = : s = = .0454545 mi per second or .0454545 * 3600 = 163.3 mph
 Travel_Word_Problems/96260: Maria and Eduardo are traveling to a business conference. The trip takes 2 hr for Maria and 2.5 hr for Eduardo, since he lives 40 mi farther away. Eduardo travels 5 mph faster than Maria. Find their average rates.1 solutions Answer 70195 by ankor@dixie-net.com(15653)   on 2007-09-05 21:55:41 (Show Source): You can put this solution on YOUR website!Maria and Eduardo are traveling to a business conference. The trip takes 2 hr for Maria and 2.5 hr for Eduardo, since he lives 40 mi farther away. Eduardo travels 5 mph faster than Maria. Find their average rates. : Let s = M's speed Then (s+5) = E's speed : Write a distance equation: Dist = Time * speed : E's trip - M's trip = 40 2.5(s+5) - 2s = 40 : 2.5s + 12.5 - 2s = 40 : 2.5s - 2s = 40 - 12.5 : .5s = 27.5 : s = 27.5/.5 : s = 55 mph is M's speed then 55 + 5 = 60 mph is E's speed : : Check our solutions by finding the distances M: 2 * 55 = 110 mi E: 2.5 * 60 = 150 mi which is 40 mi further : Did the make sense to you. Not that hard, right?
 Travel_Word_Problems/96312: a motor boat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. What is the speed of the current?1 solutions Answer 70182 by ankor@dixie-net.com(15653)   on 2007-09-05 21:31:24 (Show Source): You can put this solution on YOUR website!a motor boat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. What is the speed of the current? : Let x = speed of the current : (16 + x) = speed downstream (16 - x) = speed upstream : Convert 20 min to hrs: 20/60 = 1/3 hr Convert 15 min to hrs: 15/60 = 1/4 hr : We know the distance upstream and distance downstream are equal Make a distance equation from that fact: Dist = time * speed : Dist downstream = dist upstream (16+x) = (16-x) : Get rid of the denominators, multiply equation by 12, results: 3(16 + x) = 4(16 - x) : 48 + 3x = 64 - 4x : 3x + 4x = 64 - 48 : 7x = 16 : x = 16/7 is the speed to the current : That's about 2.3 mph : : Check solution by finding the distances 1/4(16+2.3) = 4.6 mi 1/3(16-2.3) = 4.6 mi
 Trigonometry-basics/96400: This question is from textbook Finite mathematics An artist is painting a supply of small paintings to sell at an arts festival. He can paint three landscapes per hour and two seascapes. He can frame five paintings per hour. He has 50 hours available for painting and 25 hours for framing. How many of each type of painting should he paint and frame in order to maximize the total value of the paintings. He receives \$25 each for the landscapes and \$30 each for the seascapes.1 solutions Answer 70174 by ankor@dixie-net.com(15653)   on 2007-09-05 20:53:18 (Show Source): You can put this solution on YOUR website!An artist is painting a supply of small paintings to sell at an arts festival. He can paint three landscapes per hour and two seascapes. He can frame five paintings per hour. He has 50 hours available for painting and 25 hours for framing. : How many of each type of painting should he paint and frame in order to maximize the total value of the paintings. He receives \$25 each for the landscapes and \$30 each for the seascapes. : Let x = no. of landscapes; y = no. of seascapes ; The painting equation: x/3 + y/2 =< 50 Get rid of the denominators, multiply by 6 and you have: 2x + 3y =< 300 : The framing equation: (x + y)/5 =< 25 Get rid of the denominators, multiply equation by 5 x + y =< 125 y = y = 125 - x; use this for substitution in the Painting equation : By solving this system of equations we should be able to find the solution. : Substitute for y and find x: 2x + 3y = 300 2x + 3(125-x) = 300 2x + 375 - 3x = 300 2x - 3x = 300 - 375 -x = -75 x = 75 landscapes : y = 125 - 75 = 50 seascapes : Revenue from this: landscape\$ + seascape\$ 25(75) + 30(50) = 1875 + 1500 = \$3375 : If we graph this, it is apparent that x=75, y=50 would give us max revenue : Graph y = 125-x and y = 100 - (2/3)x : Area of feasibility, at or below the lowest graphing line. : Did this help?
 Graphs/96271: Please Help Me Find the slope and y-intercept of 2x+4y-1=01 solutions Answer 70114 by ankor@dixie-net.com(15653)   on 2007-09-05 16:58:37 (Show Source): You can put this solution on YOUR website!Find the slope and y-intercept of 2x+4y-1=0 : Put the equation in the slope intercept form (y = mx + b) where m = slope and b = y intercept : 2x + 4y - 1 = 0 : 4y - 1 = -2x; subtract 2x from both sides : 4y = -2x + 1; add 1 to both sides : y = -x + ; divide both sides by 4 : y = -x +
 Travel_Word_Problems/96261: Dave and Sam are racing in the Dallas NASCAR Race. Dave is traveling at 187 mph and Sam at 193 mph. How long will it be before Sam is 3 miles ahead of Dave?1 solutions Answer 70088 by ankor@dixie-net.com(15653)   on 2007-09-05 15:08:50 (Show Source): You can put this solution on YOUR website!Dave and Sam are racing in the Dallas NASCAR Race. Dave is traveling at 187 mph and Sam at 193 mph. How long will it be before Sam is 3 miles ahead of Dave? : Actually, you can do this in your head, The relative speed is 6 mph. How long would it take you to drive 3 mi at 6 mph? Half an hour, right?
 Linear-equations/96195: Find the slope of the line 7x + 63y = 28. Find the y-intercept of the equation1 solutions Answer 70084 by ankor@dixie-net.com(15653)   on 2007-09-05 14:53:28 (Show Source): You can put this solution on YOUR website!Find the slope of the line 7x + 63y = 28. Find the y-intercept of the equation : Put the equation in the slope/intercept form and yo have both: (y = mx + b) 7x + 63y = 28 63y = -7x + 28 : Divide equation by 63 y = -x + : Reduce fractions y = -x + : Slope = -; y intercept =
 Polynomials-and-rational-expressions/96159: Solve and check for x (x/x-2)-(x+1/x)=(8/x^2-2x)1 solutions Answer 70077 by ankor@dixie-net.com(15653)   on 2007-09-05 13:24:59 (Show Source): You can put this solution on YOUR website!Solve and check for x (x/x-2)-(x+1/x)=(8/x^2-2x) : - = : Factor (x^2 - 2x): - = : Multiplying equation by x(x-2) gets rid of the denominators and we have: x(x) - (x-2)(x+1) = 8 : x^2 - (x^2 - x - 2) = 8; FOILed (x-2)(x+1) : x^2 - x^2 + x + 2 = 8: removing the brackets changes the signs : x + 2 = 8; x^2's eliminated : x = 8 - 2 x = 6 : : Check solution by substituting 6 for x in the original equation: : - = : - = = - = Confirms our solution
 Linear_Equations_And_Systems_Word_Problems/96220: an army of soldiers is marching down a road at 5 mph. a messenger on horseback rides from the front to the rear and returns immediately, the total time taken being 10 minutes. assuming that the messenger rides at the rate of 10 mph, determine the distance from the front to the rear.1 solutions Answer 70051 by ankor@dixie-net.com(15653)   on 2007-09-05 10:38:58 (Show Source): You can put this solution on YOUR website!An army of soldiers is marching down a road at 5 mph. a messenger on horseback rides from the front to the rear and returns immediately, the total time taken being 10 minutes. assuming that the messenger rides at the rate of 10 mph, determine the distance from the front to the rear. : To convert mph to ft/min: 5280/60 = 88 : Speed in ft/min, relative to the troops: Riding against the troop direction: 88(10+5) = 1320 ft/min Riding with the troop direction: 88(10-5) = 440 ft/min : Let x = length of the troops, from front to rear, in ft: Write a time equation (in min): Time = distance/speed (in ft/min) + = 10 : Get rid of the denominators, mult equation by 1320 x + 3x = 1320(10) 4x = 13200 x = 13200/4 x = 3300 ft is the length of the troop : In miles: 3300/5280 = 5/8 of a mile : : Check our solution, find the time for the trip back, and return trip 3300/1320 = 2.5 min to the rear 3300/440 = 7.5 min return ---------------------------- total time = 10 min
 Equations/96219: There are two machines that produce aluminum cans. The newer machine can produce 72000 cans in 200 minutes. It takes the older machine 300 minutes to produce that many cans.If the two machines work together, how long will it take then to produce 7200 cans?1 solutions Answer 70046 by ankor@dixie-net.com(15653)   on 2007-09-05 09:50:10 (Show Source): You can put this solution on YOUR website!There are two machines that produce aluminum cans. The newer machine can produce 72000 cans in 200 minutes. It takes the older machine 300 minutes to produce that many cans.If the two machines work together, how long will it take then to produce 7200 cans? : A typical "shared work" problem : Let t = time for both machines to produce 72000 cans : Let the completed job = 1; (producing 72000 cans) : + = 1 : Get rid of the denominators, multiply by 600 3t + 2t = 600 5t = 600 t = 600/5 t = 120 minutes working together to produce 72000 cans : Not that hard, right?
 Age_Word_Problems/96105: Sam is 10 years older than Jack. Twice Sam's age subtracted from 6 times Jack's age is 7 more than Jack's age. Find Jack and Sam's age.1 solutions Answer 70005 by ankor@dixie-net.com(15653)   on 2007-09-04 21:47:16 (Show Source): You can put this solution on YOUR website!Sam is 10 years older than Jack. S = J+10 : Twice Sam's age subtracted from 6 times Jack's age is 7 more than Jack's age. 6J - 2S = J + 7 6J - J - 2S = 7 5J - 2S = 7 : Substitute (J+10) for S in the above equation: 5J - 2(J+10) = 7 5J - 2J - 20 = 7 5J - 2J = 7 + 20 3J = 27 J = 27/3 J = 9 yrs old, which makes S = 19 yrs old : : Check our solution in the statement: "Twice Sam's age subtracted from 6 times Jack's age is 7 more than Jack's age." 6(9) - 2(19) = 9 + 7 54 - 38 = 16 : : Does this make sense to you?
 Numbers_Word_Problems/96074: Please help me solve this problem: two consecutive integers whose product is five less than the smaller number. Thank you. Kind Regards, Bill1 solutions Answer 69998 by ankor@dixie-net.com(15653)   on 2007-09-04 21:37:47 (Show Source): You can put this solution on YOUR website!Please help me solve this problem: : I don't think this is possible, but let's go through the procedure : two consecutive integers x, (x+1) : whose product is five less than the smaller number. x(x+1) = x - 5 x^2 + x = x - 5 x^2 + x - x = -5 x^2 = -5; this shows it is not solvable
 Rate-of-work-word-problems/96092: This question is from textbook prentice hall mathematics algebra 1 ellen and kate raced on their bicycles to the library after school. they both left school at 3:00pm and bicycled along the same path. ellen rode at a speed of 12 miles per hour and kate rode at 9 miles per hour. ellen got to the library 15 minutes before kate. a. how long did it take ellen to get to the library? b. at what time did ellen get to the library? Could someone please explain this problem to me in depth?...( step by step) Thanks!1 solutions Answer 69997 by ankor@dixie-net.com(15653)   on 2007-09-04 21:25:15 (Show Source): You can put this solution on YOUR website!Ellen and Kate raced on their bicycles to the library after school. they both left school at 3:00pm and bicycled along the same path. Ellen rode at a speed of 12 miles per hour and Kate rode at 9 miles per hour. Ellen got to the library 15 minutes before Kate. : a. how long did it take Ellen to get to the library? : Let t = time for E to get to the library : It says she got there 15 min ahead of K, (change 15 min to .25 hrs), therefore (t + .25) = time for K to get to the library : Both drove the same distance so write a distance equation: Distance = speed * time : E's trip = K's trip 12t = 9(t+.25) 12t = 9t + 2.25 12t - 9t = 2.25 3t = 2.25 t = 2.25/3 t = .75 hr is E's time to the library, (.75*60 = 45 min) : b. at what time did Ellen get to the library? 3:45 pm : : Check solution by checking the distances: 12*.75 = 9 mi 9 *(.75 + .25) = 9 mi : Was this step-by-step enough for you? Any questions?
 Rate-of-work-word-problems/96088: This question is from textbook prentice hall mathematics algebra 1 juan drives to work. because of traffic conditiond, he averages 22 miles per hour. he returns home averaging 32 miles per hour. the total travel time is 2 and 1/4 hours. a. define a variable for the time juan takes to work. write an expression for the time juan takes to return home. b. write and solve an equation to find the time juan spends driving to work. I attempted to solve this problem and it was a mess. I don't understand how to solve this problem at all. Could someone explain it to me in depth please? Thanks!1 solutions Answer 69988 by ankor@dixie-net.com(15653)   on 2007-09-04 21:03:39 (Show Source): You can put this solution on YOUR website!juan drives to work. because of traffic conditions, he averages 22 miles per hour. he returns home averaging 32 miles per hour. the total travel time is 2 and 1/4 hours. a. define a variable for the time juan takes to work. Let t = time to work : "write an expression for the time juan takes to return home." It says the total time for the round trip is 2.25 hrs, therefore (2.25 - t) = time to return home : b. write and solve an equation to find the time juan spends driving to work. : We know the distance to and from his work are equal so we can write a distance equation: Distance = speed * time : 22t = 32(2.25-t) 22t = 72 - 32t 22t + 32t = 72 54t = 72 t = 72/54 t = 1 hrs, time to work : : Check our solution by finding if the distances are equal, (in decimals on a calculator) 22 * 1.33 = 29.3 miles 32(2.25 - 1.33) = 29.4 miles, : Did this make sense to you? Any questions?
 Miscellaneous_Word_Problems/96100: A farmer buys 100 live animals for \$100. How many of each doe she buy if chicks are .10 each, pigs are 42 and sheep are \$5 each?1 solutions Answer 69975 by ankor@dixie-net.com(15653)   on 2007-09-04 20:04:08 (Show Source): You can put this solution on YOUR website!I think there is typo here; pigs are not 42, I assume you meant pigs are \$2 Let c = no. of chicks; p = no. of pigs; s = no. sheep : A farmer buys 100 live animals for \$100. No. of animals equation: c + p + s = 100 : How many of each does she buy if chicks are .10 each, pigs are 42 and sheep are \$5 each? the \$\$ equation: .10c + 2p + 5s = 100 : We have two equations but 3 unknowns, however, We know there has to be a lot of chicks and the number of chicks must equal a multiple of 10, like 60, 70, 80 : Assume there are 70 chicks, they're worth \$7, our two equations then: : p + s = 100 - 70 p + s = 30 and 2p + 5s = 100 - 7 2p + 5s = 93 : Multiply the 1st equation by 2 and subtract it from the 2nd equation: 2p + 5s = 93 2p + 2s = 60 ---------------- subtracting eliminates p 0p + 3s = 33 s = 33/3 s = 11 sheep : Find p p + 11 = 30 p = 30 - 11 p = 19 pigs : c = 70 chicks (assumed) : Check using the \$\$ equation: .10(70) + 2(19) + 5(11) = 7 + 38 + 55 = 100 :
 Quadratic_Equations/96059: This question is from textbook 15. The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 27 less than the original number. Find the original number. 1 solutions Answer 69961 by ankor@dixie-net.com(15653)   on 2007-09-04 17:54:57 (Show Source): You can put this solution on YOUR website!Let x = the 10's digit and y = the units digit: : just write what it says: "The sum of the digits of a two-digit number is 11." x + y = 11 and y = (11 - x); can use for substitution : "If the digits are reversed, the new number is 27 less than the original number. Original number: 10x + y Reversed number: 10y + x : Then the equation would be: (10y + x) = 10x + y - 27 10y - y + x - 10x = -27 9y - 9x = -27 Simplify, divide equation by 9 y - x = -3 : Substitute (11-x) for y in the above equation (11 - x) - x = -3 -2x = - 3 - 11 -2x = -14 x = -14/-2 x = +7 is the 10's digit : 11 - 7 = 4 is the units digit : Check solutions 74 - 47 = 27 :