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 Quadratic_Equations/376477: describe how to solve by factoring: 1. y^3 + 2y^2 -y -2 2. a^4 b + ab^41 solutions Answer 267893 by ankor@dixie-net.com(15660)   on 2010-11-27 14:53:54 (Show Source): You can put this solution on YOUR website!describe how to solve by factoring: : 1. y^3 + 2y^2 - y -2 Group terms so that a common term can be factored out (y^3 - y) + (2y^2 - 2) Factor y(y^2 - 1) + 2(y^2 - 1) factor out (y^2-1), results: (y^2 - 1)(y + 2) ; ; 2. a^4 b + ab^4 Factor out ab ab(a^3 + b^3) Factor as the sum of cubes: ab(a+b)(a^2-ab+b^2)
 Travel_Word_Problems/376451: To deliver a package, a messenger must travel at a speed of 60mi/h on land and then use a motorboat whose speed is 20mi/h in still water. The messenger goes by land to a dock and then travels on a river against a current of 4mi/h. He reaches the destination in 4.5 hours and then returns to the starting point in 3.5 hours. How far did the messenger travel by land and how far by water? 1 solutions Answer 267892 by ankor@dixie-net.com(15660)   on 2010-11-27 14:28:58 (Show Source): You can put this solution on YOUR website!To deliver a package, a messenger must travel at a speed of 60mi/h on land and then use a motorboat whose speed is 20mi/h in still water. The messenger goes by land to a dock and then travels on a river against a current of 4mi/h. He reaches the destination in 4.5 hours and then returns to the starting point in 3.5 hours. How far did the messenger travel by land and how far by water? : Let x = distance on land Let y = distance on water : Write a time equation and simplify, for each trip : Land time + water time = total time + = 4.5 + = 4.5 Multiply by 60*16 to get rid of the denominators 16x + 60y = 4.5(960) 16x + 60y = 4320 and + = 3.5 + = 3.5 Multiply by 60*24 to get rid of the denominators 24x + 60y = 3.5(1440) 24x + 60y = 5040 : Use elimination here; subtract 16x + 60y = 4320 from the above equation 24x + 60y = 5040 16x + 60y = 4320 -------------------subtraction eliminates y find x: 8x = 720 x = x = 90 miles on land : Find y using 16x + 60y = 4320 16(90) + 60y = 4320 1440 + 60y = 4320 60y = 4320 - 1440 60y = 2880 y = y = 48 miles by water : : Check these values in the original 1st equation 90/60 + 48/16 = 1.5 + 3 = 4.5, confirms our solutions
 Expressions-with-variables/376464: A midwestern music competition awarded 41 ribbons. There was 1 less blue ribbon awarded than white and 4 more red awarded than white. How many of each kind were awarded? I have attempted many times and can not figure this one out.1 solutions Answer 267846 by ankor@dixie-net.com(15660)   on 2010-11-27 11:19:49 (Show Source): You can put this solution on YOUR website!A midwestern music competition awarded 41 ribbons. There was 1 less blue ribbon awarded than white and 4 more red awarded than white. How many of each kind were awarded? : Write an equation for each statement: : "A midwestern music competition awarded 41 ribbons." b + w + r = 41 : "There was 1 less blue ribbon awarded than white" b = w - 1 : "and 4 more red awarded than white." r = w + 4 : Using the total ribbon equation, replace b and r (w-1) + w + (w+4) = 41 3w + 3 = 41 3w = 41 - 3 3w = 38 w = w = 12.67 white, but this can't be true, the solution has to be an integer : It's no wonder you are having trouble with this problem, there is a mistake in it. : If the total ribbons were 42 instead of 41, if would work just fine 3w = 42 - 3 3w = 39 w = w = 13 white ribbons and 13 - 1 = 12 blue ribbons and 13 + 4 = 17 red ribbons, a total of 42 : This is a good method with all these type of problems
 Rate-of-work-word-problems/376475: It takes Joe 12 hours to paint a fence, but Bob can do the job in 9 hours. How long does Joe work by himself before being joined by Sam if they finish the job working 3 hours together? I've tried setting up a system of equations, but am not having much luck. I think that the first equation is x/12 + y/9 = 1, with x being the number of hours Joe works and y the number of hours Bob works, but I can't figure out the second equation.1 solutions Answer 267841 by ankor@dixie-net.com(15660)   on 2010-11-27 11:05:03 (Show Source): You can put this solution on YOUR website!It takes Joe 12 hours to paint a fence, but Bob can do the job in 9 hours. How long does Joe work by himself before being joined by Sam if they finish the job working 3 hours together? : We can do it with one equation, but I'm going to ignore Sam's contribution here : Let t = time Joe worked by himself and Bob works 3 hrs and (t+3) = total time Joe worked : Let the completed job = 1 : + = 1 Multiply by 36, results: 3(t+3) + 4(3) = 36 3t + 9 + 12 = 36 3t + 21 = 36 3t = 36 - 21 3t = 15 t = t = 5 hrs Joe works by himself ; : Let's see if that is true (Joe works 8 hrs total), 8/12 + 1/3 = 1
 Evaluation_Word_Problems/376455: The sum of three digits is 5. The first and last digits are the same. If the middle digit is exchanged with the first digit, the new number is 90 less than the original number. Find the original number.1 solutions Answer 267832 by ankor@dixie-net.com(15660)   on 2010-11-27 10:50:06 (Show Source): You can put this solution on YOUR website!The original number: 100x + 10y + z The sum of three digits is 5. x + y + z = 5 : The first and last digits are the same. x = z therefore we can write the number 100x + 10y + x : If the middle digit is exchanged with the first digit, the new number is 90 less than the original number. : 100x + 10y + x = 100y + 10x + x + 90 combine like terms 100x - 10x + x - x = 100y - 10y + 90 90x = 90y + 90 simplify, divide by 90 x = y + 1 : x + y + z = 5 Since 1st and last digit are the same (y+1) + y + (y+1) = 5 3y = 5 - 2 y = 1 then, x and z = 2 : 212 is the original number : : Check in the statement; If the middle digit is exchanged with the first digit, the new number is 90 less than the original number. 212 = 122 + 90; confirms our solution
 Travel_Word_Problems/376442: If Mindy and Mork are 6.6 miles apart and begin to walk in the same direction, it will take Mork 11 hours to overtake Mindy. If they decided to walk towards each other rather than in the same direction, they would meet in an hour. What are their speeds? I realize that there will be two equations, in which one wil be substituted into the other. I just don't know how to set them up.1 solutions Answer 267829 by ankor@dixie-net.com(15660)   on 2010-11-27 09:57:54 (Show Source): You can put this solution on YOUR website!If Mindy and Mork are 6.6 miles apart and begin to walk in the same direction, it will take Mork 11 hours to overtake Mindy. If they decided to walk towards each other rather than in the same direction, they would meet in an hour. What are their speeds? : Let m = Mork's speed Let n = Mindy's speed : Write a distance equation for each scenario, Dist = time * speed : Elimination method would be easier than substitution in this case : 11(m - n) = 6.6 and 1(m + n) = 6.6 : Divide the 1st equation by 11, add to the 2nd equation m - n = .6 m + n = 6.6 ---------------adding eliminates n, find m 2m = 7.2 m = m = 3.6 mph is Morks's speed then using the 2nd equation find n 3.6 + n = 6.6 n = 6.6 - 3.6 n = 3 mph is Mindy's speed : : Check solution in the 1st equation 11(3.6 - 3) = 6.6 11(.6) = 6.6; confirms our solutions
 Mixture_Word_Problems/376412: For extremely cold temperatures, an automobile manufacturer recommends that a 80% antifreeze and 20% water mix be used in the cooling system of a car. How many quarts of pure (100%) antifreeze and 50% antifreeze and 50% water mix should be combined to make 11 quarts of 80% antifreeze and 20% water mix?1 solutions Answer 267826 by ankor@dixie-net.com(15660)   on 2010-11-27 09:42:11 (Show Source): You can put this solution on YOUR website!an automobile manufacturer recommends that a 80% antifreeze and 20% water mix be used in the cooling system of a car. How many quarts of pure (100%) antifreeze and 50% antifreeze and 50% water mix should be combined to make 11 quarts of 80% antifreeze and 20% water mix? : Let x = amt of pure antifreeze Then (11-x) = amt of 50% antifreeze required : .50(11-x) + x = .80(11) 5.5 - .5x + x = 8.8 .5x = 8.8 - 5.5 .5x = 3.3 Multiply by 2 x = 6.6 qt of pure antifreeze and 11 - 6.6 = 4.4 quarts of 50% antifreeze ; : Check this in the original equation .5(4.4) + 6.6 = .8(11) 2.2 + 6.6 = 8.8; Confirms our answers
 Polynomials-and-rational-expressions/376386: Can someone please help me with this problen because I am totaly confused and please show all work? Consider that the age, x, of a unicorn in human equivalent years can be given by the formula (x) = - 0.0021718x^4 + 0.027326x^3 – 0.3367x^2 + 12.46x + 2.914. When a unicorn is 2.5 years old, what is its age in human equivalent years? What about when it is 12 years old? Is it similar to a dog’s approximation of multiplying by 7 to get the age in human equivalent years? Why or why not? 1 solutions Answer 267823 by ankor@dixie-net.com(15660)   on 2010-11-27 08:36:21 (Show Source): You can put this solution on YOUR website!Consider that the age, x, of a unicorn in human equivalent years can be given by the formula (x) = - 0.0021718x^4 + 0.027326x^3 – 0.3367x^2 + 12.46x + 2.914. When a unicorn is 2.5 years old, what is its age in human equivalent years? What about when it is 12 years old? : Just substitute 2.5 yrs for x in the given formula and do the tedious math: f(x) = - 0.0021718(2.5^4) + 0.027326(2.5^3) – 0.3367(2.5^2) + 12.46(2.5) + 2.914 f(x) = - 0.0021718(39.0625) + 0.027326(15.625) – 0.3367(6.25) + 12.46(2.5) + 2.914 f(x) = - .085 + .427 – 2.104 + 31.15 + 2.914 f(x) = 32.3 yrs : You can check the math, a lot chances to make a mistake here. : " What about when it is 12 years old?" Substitute 12 for x, and do the same thing : Is it similar to a dog’s approximation of multiplying by 7 to get the age in human equivalent years? Why or why not? : I don't think it is. The dog's age formula is linear
 Linear_Equations_And_Systems_Word_Problems/376371: The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning, when graphed, the function gives a line with a slope of -0.6. Suppose that the height of the candle after 20 hrs is 12 centimeters. What was the height of the candle after 15 hrs?1 solutions Answer 267783 by ankor@dixie-net.com(15660)   on 2010-11-26 22:05:45 (Show Source): You can put this solution on YOUR website!The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning, when graphed, the function gives a line with a slope of -0.6. Suppose that the height of the candle after 20 hrs is 12 centimeters. : Use the point/slope equation: y - y1 = m(x - x1) where m =-.6; x = 20; y = 12 : y - 12 = -.6(x - 20) y - 12 = -.6x + 12 y = -.6x + 12 + 12 y = -.6x + 24, is the equation (y = length after x hours) : "What was the height of the candle after 15 hrs?" y = -.6(15) + 24 y = -9 + 24 y = 15 inches after 15 hrs
 Exponential-and-logarithmic-functions/375830: Stopping an Oil Tanker: It has been shown that if an oil tanker stops its engines, then its velocity will decrease exponentially. Suppose that captin shuts off the engines when the speed of the tanker is 20 mph and one minute later the speed of the tanker is 18 mph. What is the speed of the tanker after one hour? 1 solutions Answer 267773 by ankor@dixie-net.com(15660)   on 2010-11-26 21:23:37 (Show Source): You can put this solution on YOUR website!Stopping an Oil Tanker: It has been shown that if an oil tanker stops its engines, then its velocity will decrease exponentially. Suppose that captain shuts off the engines when the speed of the tanker is 20 mph and one minute later the speed of the tanker is 18 mph. What is the speed of the tanker after one hour? : Using the decay equation 20(2^(-1/k)) = 18 2^(-1/k) = 2^(-1/k) = .9 = = -.152 k = k = 6.579: : Find the speed (s) of the tanker, when t = 60 min s = 20(2^(-60/6.579)) s = 20 * .0018 s = .036 mph
 Quadratic_Equations/376255: A window washer accidentally drops a bucket from the top of a 144 meter building. The height h of the bucket after t seconds is given by the formula . When will the bucket hit the ground? 1 solutions Answer 267741 by ankor@dixie-net.com(15660)   on 2010-11-26 19:41:42 (Show Source): You can put this solution on YOUR website!A window washer accidentally drops a bucket from the top of a 144 meter building. The height h of the bucket after t seconds is given by the formula: h = -16t^2 + 144 h = 0 when it hits the ground -16t^2 + 144 = 0 -16t^2 = -144 Divide both sides by -16 t^2 = 9 t = t = 3 seconds to hit the ground .
 test/376311: Soybean meal is 12% protein. Cornmeal I'd 6% protein. How many pounds of each should be mixed to get a 240 pound mixture that is 10% protein?1 solutions Answer 267731 by ankor@dixie-net.com(15660)   on 2010-11-26 19:15:37 (Show Source): You can put this solution on YOUR website!Soybean meal is 12% protein. Cornmeal is 6% protein. How many pounds of each should be mixed to get a 240 pound mixture that is 10% protein? : Let x = amt of 12% protein then (240-x) = amt of 6% protein : At typical mixture equation: .12x + .06(240 - x) = .10(240) .12x + 14.4 - .06x = 24 .12x - .06x = 24 - 14.4 .06x = 24 - 14.4 .06x = 9.6 x = 9.6/.06 x = 160 lb of soy meal and 240 - 160 = 80 lb of corn meal : : Check solution .12(160) + .06(80) = .10(240)
 Circles/376227: A large circular garden is surrounded by a stone wall that is 6 inches wide. The circumferance of teh OUTSIDE of teh stone wall measures 54 feet. A. Find the radius of the garden INCLUDING the stone wall. B. Find the radius of the garden WITHOUT the stone wass. C. Find the area of teh garden (not including the stone wall) in square feet. I can find the answer to A. 27ft/Pie I think the answer to B is 26ft/Pie But I can't figure out part C.1 solutions Answer 267724 by ankor@dixie-net.com(15660)   on 2010-11-26 18:56:15 (Show Source): You can put this solution on YOUR website!A large circular garden is surrounded by a stone wall that is 6 inches wide. The circumference of the OUTSIDE of the stone wall measures 54 feet. : A. Find the radius of the garden INCLUDING the stone wall. The equation: 2*pi*r = C 2*pi*r = 54 r = r = 8.6 ft is the radius including the wall : B. Find the radius of the garden WITHOUT the stone wall. 6 inches = .5 ft 8.6 - .5 = 8.1 ft radius inside the stone wall : C. Find the area of the garden (not including the stone wall) in square feet. A = pi*8.1^2 A = 206.12 sq/ft, area inside the stone wall : :
 Quadratic_Equations/376236: Hi Everyone, stuck in again on a weekend doing my maths !, having problems with this one please can someone help A circular-cylindrical oil drum is required to have a given surface area S (including its lid and base), ie S is a constant. Find the proportions of the design which contain the greatest volume V . Thank You John1 solutions Answer 267721 by ankor@dixie-net.com(15660)   on 2010-11-26 18:43:10 (Show Source): You can put this solution on YOUR website!A circular-cylindrical oil drum is required to have a given surface area S (including its lid and base), ie S is a constant. Find the proportions of the design which contain the greatest volume V . : Surface area: S = 2(pi*r^2) + (2*pi*h) : Volume: V = pi*r^2*h : Find the relationship between the surface area and the volume : = = Cancel pi*r = Therefore S = 2*(h+r) Assume a value: S = 120 2h + 2r = 120 h + r = 60 h = (60-r) : V = pi*r^2*(60-r): replace h with (60-r) Find Max volume. graph the equation y = 3.14*x^2*(60-x) Max volume occurs when r = 40 then h = 60 - 40 h = 20 : The proportion: = , we can say max volume when radius:height = 2:1
 logarithm/375902: Its a word problem and i am not sure how to solve it? A forensic specialist took the temperature of a victim's body lying in a street at 2:10 a.m. and found it to be 85.7'F. At 2:40 a.m., the temperature of the body was 84.8'F. When was the murder committed if the air temperature during the night was 55'F? [Remember, normal body temperature is 98.6'F.] HELP! Please and Thank You1 solutions Answer 267666 by ankor@dixie-net.com(15660)   on 2010-11-26 16:11:14 (Show Source): You can put this solution on YOUR website!A forensic specialist took the temperature of a victim's body lying in a street at 2:10 a.m. and found it to be 85.7'F. At 2:40 a.m., the temperature of the body was 84.8'F. When was the murder committed if the air temperature during the night was 55'F? [Remember, normal body temperature is 98.6'F.] : Find the body temp loss rate in 30 min, convert to degrees/hr 85.7 - 84.8 = .9 * 2 = 1.8 degrees/hr : Let t = no. of hrs from 98.6 (temp at death) until temp = 84.8 98.6 - 1.8t = 84.8 -1.8t = 84.8 - 98.6 -1.8t = -13.8 t = t = 7.67 hrs or 7 hr 40 min prior to 2:40 am That would place the time at 7 pm on the previous day
 Travel_Word_Problems/376209: if someone is traveling 40mph on the way to work Traveled 30mph on the way home traveling the same route What is the total miles they traveled round trip1 solutions Answer 267641 by ankor@dixie-net.com(15660)   on 2010-11-26 13:12:40 (Show Source): You can put this solution on YOUR website!Not enough information given here, you have to know the time it takes to make one way trip, or the time relationship between the two trips, or the time required to make a round trip.
 Evaluation_Word_Problems/375989: Runners Aaron and Ben leave the same oint P at a right angle to one another. Aaron runs 4 km/hr faster than Ben. After 2 hours they are 40km apart. Find the speed of each.1 solutions Answer 267634 by ankor@dixie-net.com(15660)   on 2010-11-26 11:12:55 (Show Source): You can put this solution on YOUR website!Runners Aaron and Ben leave the same point P at a right angle to one another. Aaron runs 4 km/hr faster than Ben. After 2 hours they are 40km apart. Find the speed of each. : We will use a^2 + b^2 = c^2, to solve this problem Let a = Aaron's running speed In two hrs, he will have run 2a km then (a-4) = Ben's running speed In two hrs, he will have run (2a-8)km : c = 40 : (2a)^2 + (2a-8)^2 = 40^2 4a^2 + 4a^2 - 32a + 64 = 1600 8a^2 - 32a + 64 - 1600 = 0 8a^2 - 32a - 1536 = 0; our old friend, the quadratic equation! Simplify, divide by 8 a^2 - 4a - 192 = 0 Factor this to (a-16)(a+12) = 0 positive solution a = 16 km/hr is Aaron's speed and 12 km/hr is Ben's speed ; : Check this out 32^2 + 24^2 = 40^2 1024 + 576 = 1600
 Graphs/375845: A local travel agent can sell up to 1200 travel packages for a concert. The packages will include airfare, hotel, and two types of flights: non-stop or two stop. The non-stop flight carries 150 passengers and the two stop flight carries 100 passengers. The travel agency can use no more than 10 planes. The non-stop package sells for \$1200 and the two stop flight sells for \$900. Assume that each plane will contain the maximum number of passengers. a) Write the constraints b) Find the maximum revenue for the constraints.1 solutions Answer 267616 by ankor@dixie-net.com(15660)   on 2010-11-26 09:39:27 (Show Source): You can put this solution on YOUR website!A local travel agent can sell up to 1200 travel packages for a concert. The packages will include airfare, hotel, and two types of flights: non-stop or two stop. The non-stop flight carries 150 passengers and the two stop flight carries 100 passengers. The travel agency can use no more than 10 planes. The non-stop package sells for \$1200 and the two stop flight sells for \$900. Assume that each plane will contain the maximum number of passengers. : a) Write the constraints b) Find the maximum revenue for the constraints. : Let x = number of 150 passenger planes Let y = number of 100 passenger planes : Number of airplanes: x + y =< 10 Put in the general (y=) form, to plot on a graph y =< 10 - x; (purple line) : Number of travel packages sold: 150x + 100y =< 1200 100y =< 1200 - 150x y =< 1200/100 - (150/100)x y =< 12 - 1.5x; (green line) : The graph: : Feasibility region is at or below the purple or green lines whichever is lowest : The vertices: x = 8, y = 0 x = 0, y = 10 Solve the two equation system to find the other vertici 150x + 100y = 1200 Simplify, divide by 100 1.5x + y = 12 x + y = 10 ----------------subtract, find x .5x = 2 x = 2/.5 x = 4 : Find y: 4 + y = 10 y = 6 The 3rd vertici is x = 4, y = 6, 4 ea 150 pass planes, 6 ea 100 pass planes : Revenue: 4*150*1200 = \$720,000 6*100*900 = \$540,000 -------------------- total is \$1,260,000 for 4 ea 150 pass planes and 6 ea 100 pass planes : Max revenue would be 8 full 150 pass planes at \$1,440,000
 Exponential-and-logarithmic-functions/375796: Height of tsunami waves: when waves generated by tsunamis approach shore, the height of the waves gennerally increases. Understanding the factors that contribute to this increase can aid in controlling potential damage to areas at risk. Greens law tells us how water depth affects the height of a tsunami wave. If a tsunami wave has height H at an ocean depth D, and the wave travels to a location of water depth d, then the new height h of the wave is given by h= HR^0.25, where R is the water depth ratio given by R=D/d. A.) Calculate the height of a tsunami wave in water 25 feet deep if its height is a 3 feetat its point of orgin in water 15,000 feet deep. B.) If water depth decreases by half, the depth ratio R is doubled. How is the height of the tsunami wave affected? Helpful hints: a power function has a form of: f(x)= cx^k Please help;) 1 solutions Answer 267610 by ankor@dixie-net.com(15660)   on 2010-11-26 09:26:06 (Show Source): You can put this solution on YOUR website!Height of tsunami waves: when waves generated by tsunamis approach shore, the height of the waves generally increases. Understanding the factors that contribute to this increase can aid in controlling potential damage to areas at risk. : Greens law tells us how water depth affects the height of a tsunami wave. If a tsunami wave has height H at an ocean depth D, and the wave travels to a location of water depth d, then the new height h of the wave is given by h= HR^0.25, where R is the water depth ratio given by R=D/d. : A.) Calculate the height of a tsunami wave in water 25 feet deep if its height is 3 feet at its point of origin in water 15,000 feet deep. : H=3, D=15000, d=25 : h = 3(15000/25)^.25 h = 3*600^.25 h = 3*5.0 h = 15 ft : B.) If water depth decreases by half, the depth ratio R is doubled. How is the height of the tsunami wave affected? In the above equation h = 3*1200^.25 h = 3*5.9 h = 17.657 ft :
 Miscellaneous_Word_Problems/376162: 20 people are coming for thanksgiving dinner. Aunt Rose has sent you out to buy a turkey and she wants leftovers for everyone. A cookbook said a turkey under 12 pounds will allow 1 pound per serving and for heavier birds 1/2 lb. per serving. Aunt Rose (Who I hate) says buy a turkey four pounds larger than you figure. The turkeys are on sale for .89 cents per pound. How much will it cost? And how big is it? 1 solutions Answer 267597 by ankor@dixie-net.com(15660)   on 2010-11-26 09:05:12 (Show Source): You can put this solution on YOUR website!20 people are coming for thanksgiving dinner. Aunt Rose has sent you out to buy a turkey and she wants leftovers for everyone. A cookbook said a turkey under 12 pounds will allow 1 pound per serving and for heavier birds 1/2 lb. per serving. Aunt Rose (Who I hate) says buy a turkey four pounds larger than you figure. The turkeys are on sale for .89 cents per pound. How much will it cost? And how big is it? : The small size (12 lb) won't work : Will calculate using the large size 20(.5) + 4 = 14 lb 14 * .89 = \$12.46 : But why do you hate poor Aunt Rose, who is just trying to share her vast knowledge on Turkey preparation?
 Quadratic_Equations/375890: Pauline wants to sell stainless steel water bottles as a school fundraiser. She knows that she will maximze prophits and raise 1024 dollars if she sells the bottles for 28 dollars each. she also knows that she will lose 4160 dollars if she sells the bottles for only 10 dollars each. a) Write a quadratic relation to model her profit. P in dollars if she sells the bottles for x dollars each b) What selling price will ensure that she breaks even 1 solutions Answer 267587 by ankor@dixie-net.com(15660)   on 2010-11-26 08:50:12 (Show Source): You can put this solution on YOUR website!She knows that she will maximze prophits and raise 1024 dollars if she sells the bottles for 28 dollars each. she also knows that she will lose 4160 dollars if she sells the bottles for only 10 dollars each. : Find how many bottles are being sold. Let n = no. of bottles sold 28n = 1024 10n = -4160 -------------subtract 18n - 5184 n = 5184/18 n = 288 bottles Find the profit made on each bottle 1084/288 = \$3.76 find the cost of each bottle 28 - 3.76 = \$24.24 : a) Write a quadratic relation to model her profit. P in dollars if she sells the bottles for x dollars each : P = 288(x - 24.24) : b) What selling price will ensure that she breaks even 288(x - 24.24) = 0 288x - 6981.12 = 0 288x = 6981.12 x = x = \$24.24, will break even (obviously)
 Functions/375863: Thank you so much!! Write an equation of the line containing the given point and parallel to the given line. Express in y = mx+b. (-6,2;) 6x = 5y+41 solutions Answer 267560 by ankor@dixie-net.com(15660)   on 2010-11-25 21:29:31 (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 in y = mx+b. (-6,2;) 6x = 5y+4 : Find the slope of the given equation, put it in the slope intercept form y = mx+b: 6x = 5y + 4 -5y = -6x + 4 y has to be positive, multiply by -1 5y = 6x - 4 divide by 5 y = x - : The slope = , a parallel line will have the same slope Use the point/slope form y - y1 - m(x - x1) : y - 2 = (x - (-6)) y - 2 = (x + 6) y - 2 = x + y = x + + 2 y = x + + y = x + ; is the parallel line
 Graphs/376144: One canned juice drink is 30% orange juice, another is 5% orange juice. How many liters of each should be mixed together in order to get 25 liters that is 9% of orange juice. I tried this problem and came up with some whacky numbers, i think im missing a step, any help would be great.1 solutions Answer 267550 by ankor@dixie-net.com(15660)   on 2010-11-25 20:32:48 (Show Source): You can put this solution on YOUR website!One canned juice drink is 30% orange juice, another is 5% orange juice. How many liters of each should be mixed together in order to get 25 liters that is 9% of orange juice. : Let x = amt of 30% juice required then (25-x) = amt of 5% juice : .30x + .05(25-x) = .09(25) : .30x + 1.25 - .05x = 2.25 : .30x - .05x = 2.25 - 1.25 .25x = 1 x = x = 4 liters of 30% required then 25 - 4 = 21 liters of 5% juice : : You can check these values in the original equation
 Linear-equations/376082: help me with this: write an equation in standard form of the line that contains the point (-1, 2) and is perpendicular to the line y=3x-11 solutions Answer 267546 by ankor@dixie-net.com(15660)   on 2010-11-25 20:24:18 (Show Source): You can put this solution on YOUR website!write an equation in standard form of the line that contains the point (-1, 2) and is perpendicular to the line y=3x-1 : slope of the equation, m1 = 3 : The relationship of slopes of perpendicular lines: m1*m2 = -1 3*m2 = -1 m2 = is the slope of the perpendicular line : Use point slope form to find the equation of the line, y - y1 = m(x - x1) where m2=, x1=-1, y1=2 : y - 2 = (x - (-1)) y - 2 = (x + 1) y - 2 = x - y = x - + 2 y = x - + y = x + ; is the equation of the perpendicular line But they want it in the standard form Multiply equation by 3, to get rid of the denominators 3y = -x + 5 x + 3y = 5; is the standard form : looks like this
 Numeric_Fractions/376102: A food contains three major ingredients : carbohydrate 50g, fats 15g and proteins 25g. (a) What fraction of food is carbohydrate? (b) What percentage of food is carbohydrate? (c) What fraction of food is not fat? (d) What percentage of food is fat? (e) What mass of fat is there in 60g of the food?1 solutions Answer 267543 by ankor@dixie-net.com(15660)   on 2010-11-25 20:01:01 (Show Source): You can put this solution on YOUR website!A food contains three major ingredients : carbohydrate 50g, fats 15g and proteins 25g. : Find total weight: 50 + 15 + 25 = 90g : (a) What fraction of food is carbohydrate? = : (b) What percentage of food is carbohydrate? * 100 = 55.56% : (c) What fraction of food is not fat? = = : (d) What percentage of food is fat? * 100 = 16.67% : (e) What mass of fat is there in 60g of the food? .1667 * 60 = 10 grams of fat
 Rate-of-work-word-problems/376118: two machines work at the same rate. after they work together for 7 h, one machine breaks down. the second machine requires 14 h more to finish the boxes. how long would it have taken one of the machines to fill the boxes?1 solutions Answer 267517 by ankor@dixie-net.com(15660)   on 2010-11-25 18:07:55 (Show Source): You can put this solution on YOUR website!two machines work at the same rate. after they work together for 7 h, one machine breaks down. the second machine requires 14 h more to finish the boxes. how long would it have taken one of the machines to fill the boxes? : Let x = time required by one machine to do the job : Let the completed job = 1 : One machine works a total of 21 hrs, the other machine works 7 hrs : A shared work equation: + = 1 Multiply thru by x, results: 21 + 7 = x x = 28 hrs, one machine working alone
 Equations/376031: A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total \$15,248 , and the variable costs will be \$25.50 per book. With the other method, the one-time fixed costs will total \$71,570 , and the variable costs will be \$12.00 per book. For how many books produced will the costs from the two methods be the same? 1 solutions Answer 267511 by ankor@dixie-net.com(15660)   on 2010-11-25 16:50:51 (Show Source): You can put this solution on YOUR website!A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total \$15,248 , and the variable costs will be \$25.50 per book. With the other method, the one-time fixed costs will total \$71,570, and the variable costs will be \$12.00 per book. For how many books produced will the costs from the two methods be the same? : Let n = number of books produced : Write an equation for the Cost (C) of each method: : 1: C = 25.50n + 15248 and 2: C = 12N + 71570 : Method 1 cost = Method 2 cost 25.50n + 15248 = 12n + 71570 25.50n - 12n = 71570 - 15248 13.5n = 56322 n = n = 4172 books will have the same cost
 Miscellaneous_Word_Problems/376108: The length of a poster is 10cm longer than its width. If the area of the poster is 1200cm2, what is the width of the poster. Please can someone help this quad word problem is driving me nuts.1 solutions Answer 267510 by ankor@dixie-net.com(15660)   on 2010-11-25 16:27:51 (Show Source): You can put this solution on YOUR website!The length of a poster is 10cm longer than its width. : If the area of the poster is 1200cm2, what is the width of the poster. : L = the length W = the width : Write an equation for each statement; : "The length of a poster is 10cm longer than its width." L = W+10 : "the area of the poster is 1200cm2," L * W = 1200 : what is the width of the poster. : Using the 1st equation replace L with (W+10) in the 2nd equation (W+10) * W = 1200 W^2 + 10W = 1200 A quadratic equation W^2 + 10W - 1200 = 0 This can be factored to (w+40)(w-30) = 0 The positive solution w = 30 cm is the width then L = 30 + 10 L = 40 cm is the length : : Confirms this with the area: 40 * 30 = 1200
 Equations/376093: Find measure of am angle whose compliment is 8 times its measure. I have no idea how to solve this.1 solutions Answer 267509 by ankor@dixie-net.com(15660)   on 2010-11-25 16:17:26 (Show Source): You can put this solution on YOUR website!Let x = the measure of the angle : Find measure of am angle whose compliment is 8 times its measure. : We know that the compliment of angle x = (90 - x) : Write an equation for the statement: "Find measure of an angle whose compliment is 8 times its measure." 8x = 90 - x 8x + x = 90 9x = 90 x = x = 10 degrees is the angle : : You can see that it's complement will be 8(10) which is 80 degrees 90 - 10 = 80 : This is not very hard, right?
 Travel_Word_Problems/376091: Billy and Joe are separated by 6.6 miles when they begin to walk in the same direction. It takes Billy 11 hours to overtake Joe. If they had begun to walk towards each other rather than in the same direction, they would meet up in 1 hour. What are Billy and Joe's speeds? 1 solutions Answer 267508 by ankor@dixie-net.com(15660)   on 2010-11-25 16:07:42 (Show Source): You can put this solution on YOUR website!Billy and Joe are separated by 6.6 miles when they begin to walk in the same direction, it takes Billy 11 hours to overtake Joe. If they had begun to walk towards each other rather than in the same direction, they would meet up in 1 hour. What are Billy and Joe's speeds? : Let b = Bill's speed Let j = Joe's speed : Write a distance equation for each scenario, Dist = time * speed : 11(b - j) = 6.6 and 1(b + j) = 6.6 : Divide the 1st equation by 11, add to the 2nd equation b - j = .6 b + j = 6.6 ---------------adding eliminates j, find b 2b = 7.2 b = b = 3.6 mph is Bill's speed then using the 2nd equation find j 3.6 + j = 6.6 j = 6.6 - 3.6 j = 2 mph is Joe's speed : : Check solution in the 1st equation 11(3.6 - 3) = 6.6 11(.6) = 6.6; confirms our solutions