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Quadratic_Equations/242592: The Gateway Arch in St. Louis, Missouri, has a shape similar to that of a parabola. The edge of the arch can be modeled by h= -(2/319)x^2+(92/21)x-(864/7) where x and h are measured in feet. How high is the arch? Answer in units of ft. Thanks! 1 solutions Answer 177881 by ankor@dixie-net.com(15660)   on 2009-11-26 13:51:09 (Show Source): You can put this solution on YOUR website! The Gateway Arch in St. Louis, Missouri, has a shape similar to that of a parabola. The edge of the arch can be modeled by h= -(2/319)x^2+(92/21)x-(864/7) where x and h are measured in feet. How high is the arch? Answer in units of ft. : The graph of this equation: : The axis of symmetry would be thru the highest point: The equation for this: x = -b/(2*a) : In this equation: a=-2/319, b=92/21 : x = = = = = 349.38 ft is the axis of symmetry : How high? Substitute 349.38 for x in the given equation to find the height : h= -(2/319)x^2 + (92/21)x - (864/7) h = -(2/319)(349.38^2) + (92/21)(349.38) - (864/7) I'll let you do the math here

Average/242483: The car drives 35mph for 35 miles, then 50mph for 100miles, and 53mph for 53miles. What is the car average speed for the whole trip? Thank you 1 solutions Answer 177505 by ankor@dixie-net.com(15660)   on 2009-11-24 16:54:28 (Show Source): You can put this solution on YOUR website! The car drives 35mph for 35 miles, then 50mph for 100miles, and 53mph for 53miles. What is the car average speed for the whole trip? : Find the total miles driven 35 + 100 + 53 = 188 miles : Find the total time (time = dist/speed) + + = 1 + 2 + 1 = 4 hrs : = 47 mph is the average speed

Miscellaneous_Word_Problems/242382: Hector paints a picture which is 10 inches longer than it is wide. When he frames it, the outside dimensions (that is, the length and the width) are each 2 inches longer. If the area of the picture with the frame is 40 square inches more than the area of the picture without its frame, what is the length of the original painting? 1 solutions Answer 177504 by ankor@dixie-net.com(15660)   on 2009-11-24 16:47:07 (Show Source): You can put this solution on YOUR website! Hector paints a picture which is 10 inches longer than it is wide. When he frames it, the outside dimensions (that is, the length and the width) are each 2 inches longer. If the area of the picture with the frame is 40 square inches more than the area of the picture without its frame, what is the length of the original painting? : Let x = the width of the picture then (x+10) = the length of the picture : They say that when framed it adds 2" to each dimension of the picture: (x+2) = overall width and (x+10) + 2 = (x+12) = overall length : "the area of the picture with the frame is 40 square inches more than the area of the picture without its frame," therefore: : overall area - picture area = 40 sq/in (x+12)(x+2) - x(x+10) = 40 FOIL x^2 + 2x + 12x + 24 - (x^2 + 10x) = 40 remove brackets, change signs x^2 + 14x + 24 - x^2 - 10x = 40 Combine like terms x^2 - x^2 + 14x - 10x + 24 = 40 : 4x = 40 - 24 : 4x = 16 x = x = 4 inches is the width of the picture then 4 + 10 = 14 inches is the length of the picture : : See if that is true, by finding the area of each: 16*6 = 96 14*4 = 56 ----------- diff = 40

Money_Word_Problems/242393: You invest $7,200 in two accounts paying 8% and 10% annual interest, repectively. At the end of the year, the accounts earn the same interest. How much was invested at each investment? 1 solutions Answer 177498 by ankor@dixie-net.com(15660)   on 2009-11-24 16:29:43 (Show Source): You can put this solution on YOUR website! You invest $7,200 in two accounts paying 8% and 10% annual interest, respectively. At the end of the year, the accounts earn the same interest. How much was invested at each investment? : Let x = amt invested at 8% The total investment given as 7200, therefore (7200-x) = amt invested at 10% : .08x = interest paid on the 8% account .10(7200-x) = interest paid on the 10% account : It said the interest from the two accounts are equal, therefore: .08x = .10(7200-x) .08x = 720 - .10x .08x + .10x = 720 .18x = 720 x = x = $4000 invested at 8% : I'll let you find the amt invested at 10% : Then check the interest amts on both, and ensure they are equal

Linear-systems/242408: A rectangular lot whose perimeter is 460 feet is fenced along three sides. An expensive fencing along the lot's length costs $19 per foot, and an inexpensive fencing along the two side widths costs $8 per foot. The total cost of the fencing along the three sides comes to $4130. What are the lot's dimensions? 1 solutions Answer 177482 by ankor@dixie-net.com(15660)   on 2009-11-24 15:21:21 (Show Source): You can put this solution on YOUR website! A rectangular lot whose perimeter is 460 feet is fenced along three sides. An expensive fencing along the lot's length costs $19 per foot, and an inexpensive fencing along the two side widths costs $8 per foot. The total cost of the fencing along the three sides comes to $4130. What are the lot's dimensions? : The perimeter equation (for 3 sides) L + 2W = 460 L = (460-2W) : The cost equation 19L + 8(2W) = 4130 19L + 16W = 4130 : Replace L with (460-2W), find W 19(460-2W) + 16W = 4130 8740 - 38W + 16W = 4130 -38W + 16W = 4130 - 8740 -22W = -4610 W = W = +209.5 ft is the width then 460 - 2(209.5) = 41 ft is the length : : Check solutions by finding the cost 19(41) + 8(2(209.5)) = 779 + 3352 = 4131 ~ 4130

Mixture_Word_Problems/242411: Kimberly and Andrew use a metal alloy that is 27.32% copper to make jewelry. how many ounces of a 26% alloy must be mixed with a 29% alloy to form 75 ounces of the desired alloy? I don't know how to set this one up. 1 solutions Answer 177476 by ankor@dixie-net.com(15660)   on 2009-11-24 14:44:30 (Show Source): You can put this solution on YOUR website! : Kimberly and Andrew use a metal alloy that is 27.32% copper to make jewelry. how many ounces of a 26% alloy must be mixed with a 29% alloy to form 75 ounces of the desired alloy? : Set it up this way. : Let x = amt 29% alloy required The total is to be 75 oz, therefore (75-x) = amt of 26% alloy required : .29x + .26(75-x) = .2732(75)

Miscellaneous_Word_Problems/242405: Landing speed and weight. Because the gross weight of the Piper Cheyenne depends on how much fuel and cargo are on board, the proper landing speed is not always the same. The formula V=square root of 1.496L gives the landing speed in terms of the gross weight only. a) Find the landing speed if the gross weight is 7000 lb. b) What gross weight corresponds to a landing speed of 115 ft/sec? 1 solutions Answer 177458 by ankor@dixie-net.com(15660)   on 2009-11-24 13:21:09 (Show Source): You can put this solution on YOUR website! Landing speed and weight. Because the gross weight of the Piper Cheyenne depends on how much fuel and cargo are on board, the proper landing speed is not always the same. The formula: V=square root of 1.496L gives the landing speed in terms of the gross weight only. : a) Find the landing speed if the gross weight is 7000 lb. V = V = V = 102.3 mph is the landing speed : b) What gross weight corresponds to a landing speed of 115 ft/sec? = 115 square both sides 1.496L = 115^2 1.496L = 13225 L = L = 8,840.2 lb

Linear_Equations_And_Systems_Word_Problems/242291: A child in an airport is able to cover 342 meters in 3 minutes running at a steady speed down a moving sidewalk in the direction of the sidewalk's motion. Running at the same speed in the direction opposite to the sidewalk's movement, the child is able to cover 396 meters in 6 minutes. What is the child's running speed on a still sidewalk, and what is the speed of the moving sidewalk? 1 solutions Answer 177442 by ankor@dixie-net.com(15660)   on 2009-11-24 10:56:23 (Show Source): You can put this solution on YOUR website! A child in an airport is able to cover 342 meters in 3 minutes running at a steady speed down a moving sidewalk in the direction of the sidewalk's motion. Running at the same speed in the direction opposite to the sidewalk's movement, the child is able to cover 396 meters in 6 minutes. What is the child's running speed on a still sidewalk, and what is the speed of the moving sidewalk? : let c = child's running speed let s = sidewalk speed : Effective speed (c + s) = with the sidewalk movement (c - s) = against the sidewalk ; Write two distance equations: Dist = time * speed : 3(c + s) = 342 6(c - s) = 396 ; Simplify both equations, divide the 1st by 3, and the 2nd by 6, results c + s = 114 c - s = 66 -------------adding eliminates s, find c 2c + 0 = 180 c = c = 90 meters/sec (the child) : Find s using equation c + s = 114 90 + s = 114 s = 114 - 90 s = 24 meters/sec (the sidewalk) ; : Check solution in the 2nd original equation 6(c - s) = 396 6(90-24) = 6(66) = 396

Rectangles/242218: The area of the rectangular piece of cardboard shown on the left is 198 square inches. The cardboard is used to make an open box by cutting a 2 inch square from each corner and turning up the sides. If the box is to have a volume of 196 cubic inches, find the length and width of the cardboard that must be used. 1 solutions Answer 177348 by ankor@dixie-net.com(15660)   on 2009-11-23 21:28:08 (Show Source): You can put this solution on YOUR website! The area of the rectangular piece of cardboard shown on the left is 198 square inches. The cardboard is used to make an open box by cutting a 2 inch square from each corner and turning up the sides. If the box is to have a volume of 196 cubic inches, find the length and width of the cardboard that must be used. : Area of the original piece of cardboard L * W = 198 sq/in L = : Volume L*W*H = 196 cu/in (removing 2" squares reduces the length and width by 4", height = 2" (L-4)*(W-4)*2 = 196 Simplify, divide both sides by 2 (L-4)*(W-4) = 98 FOIL LW - 4L - 4W + 16 = 98 : LW - 4L - 4W + 16 - 98 = 0 : LW - 4L - 4W - 82 = 0 : From the area equation, replace L with 198/W *W - 4* - 4W - 82 = 0 Cancel W, mult by 4 198 - - 4W - 82 = 0 : Mult by W to get rid of the denominator 198W - 792 - 4W^2 - 82W : Arrange as a quadratic equation -4W^2 + 198W - 82W - 792 = 0 : -4W^2 + 116W - 792 = 0 Divide by -2, simplify and change the signs 2W^2 - 58W + 396 = 0 This will factor (2W - 22)(W - 18}) = 0 Two solutions 2W = 22 W = 11 and W = 18 ; 18" by 11" is the cardboard used : Check the area: 18 * 11 = 198 : Check the vol of the box (18-4)*(11-4)* 2 = 196

Graphs/242219: I am supposed to graph and identify the y-intercept, but no matter how hard I try I keep getting it wrong. The equation is x + 3y = 6. I know that you have to add -x to both sides so 3y = -x + 6. The example I have says to divide by 3 and then shows y=-1/3x + 2. How did they get 1/3 if they are dividing by 3. (I know it is probably a dumb question but I am an idiot when it comes to math)If I can just figure where the fraction came from then maybe I can get the rest of it. Can someone please help? 1 solutions Answer 177316 by ankor@dixie-net.com(15660)   on 2009-11-23 19:54:53 (Show Source): You can put this solution on YOUR website! One thing to remember that when a variable like x is by itself, it is understood that the coefficient is 1. In this equation you would understand it as 3y = -1x + 6 Divide by 3 y = x + which is y = x + 2 : : Did this help?

Travel_Word_Problems/242148: at noon, car A started to travel at a uniform speed from town X to town Y which was 60KM away from town X. One and a half hours later, car B started to travel at the same uniform speed as car a from town Y to town X. They passed each other at 3P.M. What distance had they each travelled when they passed each other? 1 solutions Answer 177313 by ankor@dixie-net.com(15660)   on 2009-11-23 19:47:23 (Show Source): You can put this solution on YOUR website! at noon, car A started to travel at a uniform speed from town X to town Y which was 60KM away from town X. One and a half hours later, car B started to travel at the same uniform speed as car a from town Y to town X. They passed each other at 3 PM What distance had they each traveled when they passed each other? : We know when A meets B, their total travel dist will be 60 km : Travel time when they met a 3 PM Car A travel time = 3 hrs Car B travel time = 1.5 hrs : Let d = Car A travel distance then (60-d) = Car B travel distance : Write a speed equation Speed = dist/time (Both drive at the same speed) = Cross multiply 1.5d = 3(60-d) 1.5d = 180 - 3d 1.5d + 3d = 180 4.5d = 180 d = d = 40 km traveled by Car A and 60 - 40 = 20 km traveled by Car B : : Check solution finding the speed of each, they should be equal: 40/3 = 13 kmh 20/1.5 = 13 kmh

Polynomials-and-rational-expressions/242087: this has to do with rational expressions. 2y + 1 over y^2 - y - 6 numbers that cannot be used in place of the variable in the expression. I am lost on my whole chapter with rational expressions. 1 solutions Answer 177228 by ankor@dixie-net.com(15660)   on 2009-11-23 16:24:44 (Show Source): You can put this solution on YOUR website! numbers that cannot be used in place of the variable in the expression. : Assume you know that you cannot have the value of 0 in the denominator Another words if y^2 - y - 6 = 0 that is value for y that is forbidden : To find out what that is, we just set the denominator expression to = 0 Find out what value(s) of y that will be : y^2 - y - 6 = 0 Factor this to (y-3)(y+2) = 0 two solutions y = 3 y = -2 : the answer is that y = 3 and y = -2 are values that cannot be used

Radicals/241801: i need help simplifying the radical sqrt of 128m^6n^7 1 solutions Answer 177220 by ankor@dixie-net.com(15660)   on 2009-11-23 15:27:14 (Show Source): You can put this solution on YOUR website! i need help simplifying the radical sqrt of 128m^6n^7 Factor in a manner that will reveal the perfect squares inside the radical Extract those perfect squares, leaving

Numbers_Word_Problems/241901: The tens digit of a given two-digit positive number is two more than three times the units digit. If the digits are reversed, the new number is 13 less than half the given number. Find the given integer. 1 solutions Answer 177217 by ankor@dixie-net.com(15660)   on 2009-11-23 14:53:49 (Show Source): You can put this solution on YOUR website! Let x = the tens digit Let y = the units then 10x+y = "the number" : Write an equation for each statement, just as it says: : "The tens digit of a given two-digit positive number is two more than three times the units digit." x = 3y + 2 : "If the digits are reversed, the new number is 13 less than half the given number." 10y+x = .5(10x+y) - 13 10y + x = 5x + .5y - 13 10y - .5y = 5x - x - 13 9.5y = 4x - 13 : Find the given integer. : From the 1st statement, replace x with (3y+2) in the above equation: 9.5y = 4(3y+2) - 13 9.5y = 12y + 8 - 13 9.5y = 12y - 5 +5 = 12y - 9.5y 5 = 2.5y y = y = 2 then x = 3(2) + 2 x = 8 : 82 is the number : : Check solution in the statement: "If the digits are reversed, the new number is 13 less than half the given number." 28 = .5(82) - 13 28 = 41 - 13

Travel_Word_Problems/241922: You ride your bike to campus a distance of 5 miles and return home on the same route. Going to campus, you average 9 mph faster than on your return trip home. If the round trip takes one hour and ten minutes, what is your average rate on the return trip? 1 solutions Answer 177205 by ankor@dixie-net.com(15660)   on 2009-11-23 14:11:35 (Show Source): You can put this solution on YOUR website! You ride your bike to campus a distance of 5 miles and return home on the same route. Going to campus, you average 9 mph faster than on your return trip home. If the round trip takes one hour and ten minutes, what is your average rate on the return trip? : let s = speed on the return trip then (s+9) = speed to the campus : Write a time equation: Time = dist/speed Change time to a fraction 1 = hrs : + = Multiply equation by 6s(s+9), results 6(s+9)*5 + 6s(5) = s(s+9)*7 : 5(6s+54) + 30s = 7(s^2 + 9s) : 30s + 270 + 30s = 7s^2 + 63s Arrange as a quadratic equation 0 = 7s^2 + 63s - 60s - 270 : 7s^2 + 3s - 270 = 0 Factors to: (7s + 45)(s - 6) = 0 The positive solution s = 6 mph on the return trip ; ; Check this by finding the times 5/6 + 5/15 = 1.667; which is 1 hr 10 min

Miscellaneous_Word_Problems/241957: The number of calculators produced in a certain company varies jointly as the number of workers and the time spend working. If 200 workers can produce 1000 calculators in 8 hours, how many calculators can 500 workers produce in 40 hours? 1 solutions Answer 177150 by ankor@dixie-net.com(15660)   on 2009-11-23 09:49:41 (Show Source): You can put this solution on YOUR website! The number of calculators produced in a certain company varies jointly as the number of workers and the time spend working. If 200 workers can produce 1000 calculators in 8 hours, how many calculators can 500 workers produce in 40 hours? : Find out how many man hrs to produce 1 calc: : = 1.6 man-hrs per calc : Find out how many can be produced by 500 working 40 hrs = 12,500 calculators

Linear_Equations_And_Systems_Word_Problems/241725: math project that i have been struggling with.let x equal the cars age in years and y equal the value after x years. You buy a car for 18000 dollars and after 8 years the car is worth 4500 dollars. assuming that the depreciation is linear find an equation which gives the value of the car overtime. find two ordered pairs from the info. 1 solutions Answer 177031 by ankor@dixie-net.com(15660)   on 2009-11-22 16:51:27 (Show Source): You can put this solution on YOUR website! .let x equal the cars age in years and y equal the value after x years. You buy a car for 18000 dollars and after 8 years the car is worth 4500 dollars. assuming that the depreciation is linear find an equation which gives the value of the car overtime. find two ordered pairs from the info. : Find the slope using the slope formula: m = : assign the x,y values as follows x1=0; y1=18000 x2=8; y2= 4500 : m = = = -1687.5 : A simple equation y = -1687.5x + 18000 you can see when x=0 (the year it is new) y = 18000 (price of the car) Substitute 8 for x y = -1687.5(8) + 18000 y = -13500 + 18000 y = +4500 which is what we would expect Ordered pair 8, 4500 : How about when the car is 10 yrs old (x=10) y = -1687.5(10) + 18000 y = -16875 + 18000 y = $1125 Ordered pair 10, 1125 : interesting by this formula, a car becomes valueless in 11 years -562.5 Guess it cost that much to dispose of it!!

Quadratic_Equations/241501: A swimming pool holds 600 cubic meters of water. It can be drained at the rate of 9 minutes faster than it can be filled. If it takes half an hour to fill it than to drain it, find the drainage rate. 1 solutions Answer 176997 by ankor@dixie-net.com(15660)   on 2009-11-22 14:30:33 (Show Source): You can put this solution on YOUR website! A swimming pool holds 600 cubic meters of water. It can be drained at the rate of 9 minutes faster than it can be filled. If it takes half an hour to fill it than to drain it, find the drainage rate. : I couldn't make any sense of this problems until I add "gal/min" so it reads: : A swimming pool holds 600 cubic meters of water. It can be drained at the rate of 9 gal/min faster than it can be filled. If it takes a half an hour more to fill it than to drain it, find the drainage rate. : Let r = rate in gal/min to drain it then (r-9) = rate in gal/min to fill it : Fill time - drain time = half-hour - = 30 min Multiply equation by r(r-9), results 600r - 600(r-9) = 30r(r-9) : 600r - 600r + 5400 = 30r^2 - 270r Arrange as quadratic equation 30r^2 - 270r - 5400 = 0 Simplify, divide by 30 r^2 - 9r - 180 = 0 : Use the quadratic formula to find r: a=1; b=-9; c= -180 : The positive solution r = 18.651 gal/min to drain it ; ; Check solution - = 62.17 - 32.17 = 30 minutes

Word_Problems_With_Coins/241567: A rancher buys 100 live animals for $100. Chickens cost 50cents each, goats cost $3.50 and cows $10.00 each. How many of each did the rancher buy? Is more than one combination possible? 1 solutions Answer 176942 by ankor@dixie-net.com(15660)   on 2009-11-22 09:59:28 (Show Source): You can put this solution on YOUR website! A rancher buys 100 live animals for $100. Chickens cost 50 cents each, goats cost $3.50 and cows $10.00 each. How many of each did the rancher buy? Is more than one combination possible? : Write two equations: : No. of animals ch + g + c = 100 : Cost equation .5ch + 3.5g + 10c = 100 : Two equations, 3 unknowns We know there can't be very many cows After trying a couple values for no. of cows, came up with 4 cows, they're worth $40, our two equations then are: : ch + g = 100 - 4 ch + g = 96 and .5ch + 3.5g = 100 - 40 .5ch + 3.5g = 60 : Multiply the 2nd equation by 2 and subtract the 1st equation: ch + 7g = 120 ch + g = 96 ---------------- subtracting eliminates ch 0 + 6g = 24 g = 4 goats : Find chicks ch + 4 = 96 ch = 96 - 4 92 chickens : We have then: 4 cows, 4 goats, 92 chickens ; ; Check in the cost equation .5(92) + 3.5(4) + 10(4) = 46 + 14 + 40 = 100 Not sure if this is the only solution. You can try other values for no. of cows and see. I don't think odd number of cows will work

Linear_Equations_And_Systems_Word_Problems/241138: The semester average is computed by taking 1/3 of the midterm exam score plus 2/3 of t he final exam score. To get a C, Stacy must have a semester average between 70 and 79 inclusive. If Stacy scored only 48 on the midterm, then for what range of scores on the final exam will Stacy get a C? 1 solutions Answer 176714 by ankor@dixie-net.com(15660)   on 2009-11-21 08:18:45 (Show Source): You can put this solution on YOUR website! The semester average is computed by taking 1/3 of the midterm exam score plus 2/3 of the final exam score. To get a C, Stacy must have a semester average between 70 and 79 inclusive. If Stacy scored only 48 on the midterm, then for what range of scores on the final exam will Stacy get a C? : Let x = final exam score Since it counts twice as much as the midterm, write > 70 48 + 2x > 3(70) 48 + 2x > 210 2x > 210 - 48 2x > 162 x > x > 81 to get an over 70 average : You can find the upper limit the same way; just solve < 79

Polynomials-and-rational-expressions/241298: I am completely lost and would like the step by step play so I can understand what to do. Subtract the polynomials (-5v^2+6v+3)-(8v^2+3)= 1 solutions Answer 176711 by ankor@dixie-net.com(15660)   on 2009-11-21 07:56:57 (Show Source): You can put this solution on YOUR website! (-5v^2+6v+3)-(8v^2+3) = remove the brackets, remember, if there is a minus outside the brackets, you change all the signs inside the brackets -5v^2 + 6v + 3 - 8v^2 - 3 = : group like terms -5v^2 - 8v^2 + 6v + 3 - 3 = : Combine like terms -13v^2 + 6v

Evaluation_Word_Problems/241223: Alisha is making punch for a graduation party.The recipe requires twice as much orange juice as cranberry juice and 8 times as much ginger ale as cranberry juice.If she plans to make 165oz of punch,how much orange juice does she need? ok word problems are really hard for me,i just dont understand them at all, i have trouble on how to write them out find the answer. 1 solutions Answer 176667 by ankor@dixie-net.com(15660)   on 2009-11-20 21:29:43 (Show Source): You can put this solution on YOUR website! The recipe requires twice as much orange juice as cranberry juice and 8 times as much ginger ale as cranberry juice. If she plans to make 165oz of punch,how much orange juice does she need? : Let x = amt of cranberry juice required : It said,"Twice as much orange juice as cranberry juice." therefore 2x = amt of orange juice : It also said,"8 times as much ginger ale as cranberry juice" therefore 8x = amt of ginger ale : Find x using the total amt: x + 2x + 8x = 165 11x = 165 x = x = 15 oz of cranberry juice and 2(15) = 30 oz of orange juice which is what the asked for ; : To check our solution, find the amt of ginger ale 8(15) = 120 oz of ginger ale : 15 + 30 + 120 = 165 oz ; That was not too difficult, was it?

Miscellaneous_Word_Problems/241175: Reconciling remainders. Find a positive integer smaller than 500 that has a remainder of 3 when divided by 5, a remainder of 6 when divided by 9, and a remainder of 8 when divided by 11. 1 solutions Answer 176662 by ankor@dixie-net.com(15660)   on 2009-11-20 21:20:13 (Show Source): You can put this solution on YOUR website! Reconciling remainders. Find a positive integer smaller than 500 that has a remainder of 3 when divided by 5, a remainder of 6 when divided by 9, and a remainder of 8 when divided by 11. : we know x = multiple of 5 + 3, last digit is either 3 or 8 x = multiple of 9 + 6 x = multiple of 11 + 8, : Find a multiple of 11 + 8, last digit is 3 or 8 then test to see if it is a multiple of 9 with a remainder 6 : working downward from 500, I came up with 393 (I used the table on the TI83, with the equation y = 11x + 8, look for last digit of 3 or 8) : 393/5 = 78 r3 393/9 = 43 r6 393/11= 35 r8 : There is probably a neater way of doing this but I can't come up with it

Equations/240985: three times one number plus -7 times another number equals 21 1 solutions Answer 176647 by ankor@dixie-net.com(15660)   on 2009-11-20 19:36:21 (Show Source): You can put this solution on YOUR website! three times one number plus -7 times another number equals 21 : 3x + -7y = 21 : 3x - 7y = 21 : -7y = -3x + 21 : Multiply by -1 7y = 3x - 21 : y = x - y = x - 3 : Some integer values, ignoring 0; x=14, y=3 x=21 y=6 x=28 y=9 x=35 y=12 note as x increases by 7, y increase by 3

Finance/240975: A 67,500 estate is to be split amoung four children and a grandchildren. Each children gets the same amount and the grandchild gets half the amount. How much will each recevie? 1 solutions Answer 176643 by ankor@dixie-net.com(15660)   on 2009-11-20 19:24:24 (Show Source): You can put this solution on YOUR website! Assume it should read: A 67,500 estate is to be split among four children and a grandchild. Each child gets the same amount, and the grandchild gets half the amount. How much will each receive? : Let x = amt received by the grandchild then 2x = amt received by the children : x + 4(2x) = 67500 x + 8x = 67500 9x = 67500 x = x = $7500 received by the grandchild then 2(7500) = $15000 received the the children : : Check 4(15000) + 7500 = 67500

Mixture_Word_Problems/241134: To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist’s estimate of the size of the bear population? 1 solutions Answer 176642 by ankor@dixie-net.com(15660)   on 2009-11-20 19:15:03 (Show Source): You can put this solution on YOUR website! To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist’s estimate of the size of the bear population? : let x = estimation of no. of bears ; = cross multiply 2x = 100 * 50 2x = 5000 x = 2500 bears

Polynomials-and-rational-expressions/241131: Solve. (This one is really hard!) 3a-5/a^2+4a+3 + 2a+2/a+3 = a-3/a+1 1 solutions Answer 176637 by ankor@dixie-net.com(15660)   on 2009-11-20 19:01:19 (Show Source): You can put this solution on YOUR website! + = do some factoring here + = The common denominator is (a+3)(a+1) multiply thru by this : (a+3)(a+1)* + (a+3)(a+1)* = (a+3)(a+1)* : Cancel out the denominators, leaving: (3a - 5) + (a+1)*2(a+1) = (a+3)(a-3) : FOIL 3a - 5 + 2(a^2 + 2a+ 1) = a^2 + 3a - 3a - 9 : 3a - 5 + 2a^2 + 4a + 2 = a^2 - 9 : combine like terms on the left 2a^2 - a^2 + 3a + 4a - 5 + 2 + 9 = 0 : a^2 + 7a + 6 = 0 Factor (a + 6)(a + 1) = 0 Two solutions a = -6 a = -1 ; : Check in original equation using x=-6 + = + = + = + = ; confirms our solution ; : You can check it using x=-1

Geometry_Word_Problems/241152: A cylindrical container has 3 inches of water in it and is being filled at a rate of 1/2 inch per minute. The volume, V, of the water in the container is given by the function: V(h)=(π/4)h^3. Write a formula for the volume in terms of the time in minutes. Then, calculate the ammount of time that will take to fill the container to 70 cubic inches. please.....help!!!!! i have been working from 2 hours!!!!! and also (π = pi)mathematic pi. 1 solutions Answer 176631 by ankor@dixie-net.com(15660)   on 2009-11-20 17:41:06 (Show Source): You can put this solution on YOUR website! A cylindrical container has 3 inches of water in it and is being filled at a rate of 1/2 inch per minute. The volume, V, of the water in the container is given by the function: V(h)=(π/4)h^3. Write a formula for the volume in terms of the time in minutes. : The formula appears to be the volume of a cylinder with a radius of 1/2 inch V(h) = which is V(h) = or V(h) = : let t = time in minutes, h = 3 inches to start with, therefore the height: (3+.5t) V(t) = : Then, calculate the amount of time that will take to fill the container to 70 cubic inches. Replace V(t) with 70, solve for t = 70 Multiply both sides by (reciprocal gets rid of on the left) 3 + .5t = 70 * : 3 + .5t = 3 + .5t = 89.126 .5t = 89.126 - 3 .5t = 86.126 t = t = 172.25 min to reach 70 cu/inches ; : Check this in the volume equation: t=172.25 V(t) = V(t) = V(t) = V(t) = 69.9986 ~ 70 ; : Two hrs is a long time, hope this has helped!

Rate-of-work-word-problems/240752: One good use for rational equations is the shared work problem. This solution would be of great help in scheduling employees. For example, If Bob can mow a lawn in 3 hours and Joe can do it in 5 hours, how long would it take them together? Some people would be tempted to just average the two values and get the answer of four hours, but that would be wrong since Bob can do it by himself in 3 hours. Solve this word problem using rational equations. What is the relation of the shared work problem to the following problem?: I am filling my pool with two hoses. The larger hose can fill the pool by itself in 10 hours, The smaller hose can fill the pool in 15 hours. Unfortunately, I left the drain open in the pool and it can drain the pool in 20 hours. How long will it take before the pool is filled with both hoses running and the drain open? 1 solutions Answer 176613 by ankor@dixie-net.com(15660)   on 2009-11-20 16:09:23 (Show Source): You can put this solution on YOUR website! If Bob can mow a lawn in 3 hours and Joe can do it in 5 hours, how long would it take them together? : Let t = time required when they work together (assuming two lawn mowers) let the completed job = 1 : + = 1 clear the denominators, multiply by 15: 15* + 15* = 15(1) cancel the denominators: 5t + 3t = 15 8t = 15 t = t = 1.875 hrs or 1 + .875(60) = 1 hr 52.5 min ; : Check solution in the original shared work equation: 1.875/3 + 1.875/5 = .625 + .375 = 1 : : : The larger hose can fill the pool by itself in 10 hours, The smaller hose can fill the pool in 15 hours. Unfortunately, I left the drain open in the pool and it can drain the pool in 20 hours. How long will it take before the pool is filled with both hoses running and the drain open : Let t = time required to fill the pool with this situation Let the full pool = 1 Use + for filling and - for draining : + - = 1 Clear the denominator by multiplying by 60 : Use the 1st one as an example, you should be able to do this by yourself.

Mixture_Word_Problems/241109: Joseph has a 55% silver alloy. Ethan has a 75% silver alloy. They melted their alloys to create 160 grams of a 64% silver alloy. How many grams of each alloy? 1 solutions Answer 176603 by ankor@dixie-net.com(15660)   on 2009-11-20 15:45:05 (Show Source): You can put this solution on YOUR website! 1): Joseph has a 55% silver alloy. Ethan has a 75% silver alloy. They melted their alloys to create 160 grams of a 64% silver alloy. How many grams of each alloy? : Let x = amt of 75% alloy then (160-x) = amt of 55% alloy : Write an amt of silver equation: .75x + .55(160-x) = .64(160) : You should be able to solve this now, if not, let me know via the comment.

Unit_Conversion_Word_Problems/241156: What fraction of 2 cubic yards is 4 cubic feet? 1 solutions Answer 176601 by ankor@dixie-net.com(15660)   on 2009-11-20 15:38:29 (Show Source): You can put this solution on YOUR website! What fraction of 2 cubic yards is 4 cubic feet? : We know that 1 cubic yard = 3*3*3 = 27 cu/ft : = cu/yds is 4 cu/ft