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 Travel_Word_Problems/243019: I am stuck on this question I hope you can help Suppose that the kicker for the chargers has a punt that can be modeled by h(t)=-2t^2+200, where its height from the ground can be found based on how many seconds (t) have passed since the kick. Given this how long will it take for the foot ball to hit the ground? P.s. I can figure out to type in exponents so the 2t^2 is supposed to be 2t squared1 solutions Answer 178068 by ankor@dixie-net.com(15646)   on 2009-11-27 18:38:24 (Show Source): You can put this solution on YOUR website!Suppose that the kicker for the chargers has a punt that can be modeled by h(t)=-2t^2+200, where its height from the ground can be found based on how many seconds (t) have passed since the kick. Given this how long will it take for the foot ball to hit the ground? : this equation cannot be right, this one shows the height as 200 when t=0 : Assume the equation is h(t) = -2t^2 + 20t : When the ball hits the ground, h(t) = 0, therefore -2t^2 + 20t = 0 Factor out -2t, this also changes the signs -2t(t - 10) = 0 t = +10 sec : looks like this:
 test/242325: Had trouble with a few problems similar to this one.. Solve: 5^(x+2)= 4^(l-x)1 solutions Answer 178027 by ankor@dixie-net.com(15646)   on 2009-11-27 14:48:23 (Show Source): You can put this solution on YOUR website!Solve = Use logs = log equiv of exponents = Find the logs .69897(x+2) = .60206(1-x) : .69897x + 1.39794 = .602061 - .60206x : .69897x + .60206x = .602061 - 1.39794 : 1.30103x = -.79588 : x = x = -.61173 : : Check solution on calc: enter 5^(-.61173+2) = 9.34 enter 4^(1-(-.61173)) = 9.34; confirms our solution
 Rate-of-work-word-problems/242964: It takes 18 men 6 hours to dig a trench 720 feet long. Working at the same rate, how many feet of trench can be dug by 24 men in 8 hours?1 solutions Answer 177986 by ankor@dixie-net.com(15646)   on 2009-11-27 08:39:30 (Show Source): You can put this solution on YOUR website!It takes 18 men 6 hours to dig a trench 720 feet long. Working at the same rate, how many feet of trench can be dug by 24 men in 8 hours? : We can use man-hrs here. : 18*6 = 108 man-hrs for 720 ft that's = 6 ft per man-hr : 24 * 8 * 6 = 1280 ft
 Rate-of-work-word-problems/242971: It takes 15 workers to build 500 ft. of fencing in 6 hours. At this same rate, how many workers are needed to build 1000 ft. of fencing in 9 hours? 1 solutions Answer 177985 by ankor@dixie-net.com(15646)   on 2009-11-27 08:20:20 (Show Source): You can put this solution on YOUR website!It takes 15 workers to build 500 ft. of fencing in 6 hours. At this same rate, how many workers are needed to build 1000 ft. of fencing in 9 hours? : Use man-hrs here: It takes 15*6 = 90 man-hrs to build 500 ft of fence therefore, it will take 180 man-hrs to build 1000 ft of fence : Let m = no. of men required : 9m = 180 m = m = 20 men
 Numbers_Word_Problems/242523: could i get help with this problem please. write the verbal sentence as an equation. then solve the equation. fourteen minus the product of 3 and a number is 26.1 solutions Answer 177970 by ankor@dixie-net.com(15646)   on 2009-11-26 22:01:21 (Show Source): You can put this solution on YOUR website!write the verbal sentence as an equation. then solve the equation. : Let x = :the number" : Just write exactly what is says, (the word "is" usually means "=") : fourteen minus the product of 3 and a number is 26. 14 - 3x = 26 : subtract 14 from both sides: -3x = 26 - 14 -3x = 12 : The variable has to be positive, multiply both sides by -1 to change the signs 3x = -12 : Divide both sides by 3 x = x = -4 : : Check solution in the given statement: "fourteen minus the product of 3 and a number is 26." 14 - 3(-4) = 26 14 + 12 = 26 ( minus time a minus is plus)
 Geometry_Word_Problems/242546: A red ball and a green ball are simultaneously tossed into the air. The red ball is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is 16t2  96t feet. The green ball is given an initial velocity of 80 feet per second, and its height t seconds after it is tossed is 16t2  80t feet. a) Find a polynomial D(t) that represents the difference in the heights of the two balls. b) How much higher is the red ball 2 seconds after the balls are tossed? c) In reality, when does the difference in the heights stop increasing?1 solutions Answer 177965 by ankor@dixie-net.com(15646)   on 2009-11-26 21:41:11 (Show Source): You can put this solution on YOUR website!A red ball and a green ball are tossed into the air. The red ball is given an initial velocity of 96 feet per second and its height "t" seconds after it is tossed is -16t^2 + 96t feet. The green ball is given an initial velocity of 80 feet per second and its height "t" seconds after being tossed is -16t^2 +80t feet. : Find a polynomial D(t) that represents the difference in the heights of the two balls. D(t) = (-16t^2 + 96t) - (-16t^2 +80t) : Remove brackets D(t) = -16t^2 + 96t + 16t^2 - 80t : Group like terms: D(t) = 16t^2 + 16^2 + 96t - 80t : combine like terms: D(t) = 16t : : How much higher is the red ball 2 seconds after the balls are tossed? D(t) = 16(2) D(t) = 32 ft difference after 2 seconds : : When does the difference in the heights stop increasing? : Obviously, when one of the balls hits the ground : Find when the lowest ball hits the ground (h=0) -16t^2 + 80t = 0 Factor out -16t -16t(t - 5) = 0 t = 5 seconds when the difference stops increasing; : A graph illustrates this well
 Mixture_Word_Problems/242596: A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank? 1 solutions Answer 177949 by ankor@dixie-net.com(15646)   on 2009-11-26 21:04:25 (Show Source): You can put this solution on YOUR website!A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank? : let t = time (in minutes) to empty with both valves open : Let 1 = the completed job (an empty tank) : Plus is draining, minus is filling : - = 1 Multiply by 90, get rid of the denominators, results: 3t - 2t = 90 t = 90 minutes to empty with both valves open
 Travel_Word_Problems/242547: Jake cycled 20 km to the beach. He returned cycling 1 km/h faster. The total time for the round trip was 9 h. Find his rate for each part of the trip. 1 solutions Answer 177942 by ankor@dixie-net.com(15646)   on 2009-11-26 19:57:02 (Show Source): You can put this solution on YOUR website!Jake cycled 20 km to the beach. He returned cycling 1 km/h faster. The total time for the round trip was 9 h. Find his rate for each part of the trip. : Let r = rate to the beach then (r+1) = rate from the beach : Write a time equation: time = dist/rate : To time + from time = 9 hrs + = 9 Multiply by r(r+1), results: 20(r+1) + 20r = 9r(r+1) : 20r + 20 + 20r = 9r^2 + 9r : 40r + 20 = 9r^2 + 9r : 0 = 9r^2 + 9r - 40r - 20 : 9r^2 - 31r - 20 = 0 Factors to (9r+5)(r-4) = 0 positive solution r = 4 km/hr to the beach then 5 km/hr from the beach : : Check solution 20/4 + 20/5 = 9
 Miscellaneous_Word_Problems/242659: At the Sweet Shop, one can buy 8 Pips for a dive, 4 Quips for a quarter, and 13 Rips for a nickel. How many Rips can be purchased for the same cost as what one would pay for a total of 40 Pips and 40 Quips? 1 solutions Answer 177919 by ankor@dixie-net.com(15646)   on 2009-11-26 19:07:19 (Show Source): You can put this solution on YOUR website!At the Sweet Shop, one can buy 8 Pips for a dime, 4 Quips for a quarter, and 13 Rips for a nickel. How many Rips can be purchased for the same cost as what one would pay for a total of 40 Pips and 40 Quips? : Cost for a single item p = = q = r = : Let r = no. of rips : r = 40* + 40* : Cancel the 4's r = 10(5) + 10(25) r = 50 + 250 5r = 13(300) 5r = 3900 r = r = 780 rips
 test/242907: Two cars start out at the same point. One car starts out driving north at 25 mph. Two hours later the second car starts driving east at 20 mph. How long after the first car starts traveling does it take the two cars to be 300 miles apart?1 solutions Answer 177893 by ankor@dixie-net.com(15646)   on 2009-11-26 16:42:21 (Show Source): You can put this solution on YOUR website!Two cars start out at the same point. One car starts out driving north at 25 mph. Two hours later the second car starts driving east at 20 mph. How long after the first car starts traveling does it take the two cars to be 300 miles apart? : This is pythag problem; a^2 + b^2 = c^2 : Let t = driving time of 1st car then 25t = distance driven by the 1st car (a) : Let (t-2) = driving time of 2nd car then 20(t-2) = distance driven by the 2nd car Simplify to: (20t-40) (b) : c = 300 mi : (25t)^2 + (20t-40)^2 = 300^2 FOIL 625t^2 + (400t^2 - 1600t + 1600) = 90000 : 625t^2 + 400t^2 - 1600t + 1600 - 90000 = 0 : 1025t^2 - 1600t - 88400 = 0 : Simplify, divide by 25 41t^2 - 64t - 3536 = 0 : Solve this equation using the quadratic formula; a=41; b=-64; c=-3536 : The positive solution: x ~ 10.1 hrs after the 1st car departs
 real-numbers/242587: how do you do you get the roots of 1 solutions Answer 177890 by ankor@dixie-net.com(15646)   on 2009-11-26 16:11:51 (Show Source): You can put this solution on YOUR website!2 - y^2 = 0 Add y^2 to both sides: 2 = y^2 same as y^2 = 2 Find the square root of both sides: y = + y = -
 Human-and-algebraic-language/242517: If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?1 solutions Answer 177889 by ankor@dixie-net.com(15646)   on 2009-11-26 15:51:35 (Show Source): You can put this solution on YOUR website!f Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks? : Let t = time required all working together : Let the completed job = 1 (Mixing of 20 drinks) : A shared work equation: + + = 1 Multiply by 30, results 6t + 3t + 2t = 30 : 11t = 30 t = t = 2.73 minutes working together : : Check solution on a calc; enter (2.73/5) + 2.73/10) + (2.73/15) = 1.00; confirms our solution
 Polynomials-and-rational-expressions/242593: A rectangular storage bin is to be made from a rectangular piece of sheet metal 12 cm by 10 cm, by cutting out equal corners of side x and bending up the sides. Find x if the storage bin is to hold 90cm³(volume). - I thought it might be x(120 - 4x²)= 90cm³ which I guess would be 4x³ - 120x + 90 = 0 but I'm not sure where to go from here, or even if I'm heading in the right direction. thanks heaps manda1 solutions Answer 177888 by ankor@dixie-net.com(15646)   on 2009-11-26 15:44:06 (Show Source): You can put this solution on YOUR website!A rectangular storage bin is to be made from a rectangular piece of sheet metal 12 cm by 10 cm, by cutting out equal corners of side x and bending up the sides. Find x if the storage bin is to hold 90cm³(volume). : We know that the length and width will be decreased by 2x and height will = x : The volume, L * W * H: (12-2x)(10-2x)* x = 90 (120 - 24x - 20x + 4x^2) * x = 90 which is: x(4x^2 - 44x + 120) = 90 : 4x^3 - 44x^2 + 120x - 90 = 0 : It's difficult to solve this for x, not being an integer solution : Using the graphing calc y = 4x^3 - 44x^2 + 120x - 90 = 0 : : Two solutions: x = 1.28cm and x = 2.39cm, either value for x will give 90 cu/cm
 Geometry_Word_Problems/242491: The length of each side of an equilateral triangle is 5 centimeters more than the length of each side of a square. The perimeter of the two figures are equal. Find the lengths of the of the square and of the triangle. I really don't know where to start all I know is that you have to define the variable and write a formula and use it to solve the problem. Please and thank you !1 solutions Answer 177887 by ankor@dixie-net.com(15646)   on 2009-11-26 14:48:05 (Show Source): You can put this solution on YOUR website!The length of each side of an equilateral triangle is 5 centimeters more than the length of each side of a square. The perimeter of the two figures are equal. Find the lengths of the of the square and of the triangle. : Let x = side of the square : It says,"The length of each side of an equilateral triangle is 5 centimeters more than the length of each side of a square", therefore: : (x+5) = side of the triangle. : "The perimeter of the two figures are equal. " 4x = 3(x+5) : 4x = 3x + 15 : 4x - 3x = 15 : x = 15 : : Is this true, find the perimeter of each; (15 + 5 = 20, side of the triangle) 4(15) = 60 3(20) = 60
 Problems-with-consecutive-odd-even-integers/242519: the largest 3 consecutive integers for which the first is increased by twice the second exceeds the third by less than 25. (have to solve algrebraically) I do not know how to put "exceeds" in an equation. Please give me the answer and a detailed explanation of it!1 solutions Answer 177885 by ankor@dixie-net.com(15646)   on 2009-11-26 14:40:20 (Show Source): You can put this solution on YOUR website!Three consecutive integers, x, (x+1), (x+2); : the largest 3 consecutive integers for which the first is increased by twice the second exceeds the third by less than 25. : Exeeds by less than 25 so try 24, : x + 2(x+1) = (x+2) + 24 x + 2x + 2 = x + 26 x + 2x - x = 26 - 2 2x = 24 x = 12 : 12, 13, 14 are the integers : See if that is true in the given statement first is increased by twice the second exceeds the third by less than 25. 12 + 2(13) = 14 + 24 12 + 26 = 38
 Quadratic_Equations/242335: A rectangle has a length 2 meters less than twice its width. When 5 meters is added to the width, the result is a square with an area of 144 square meters. Find the dimensions of the original rectangle1 solutions Answer 177884 by ankor@dixie-net.com(15646)   on 2009-11-26 14:07:13 (Show Source): You can put this solution on YOUR website!A rectangle has a length 2 meters less than twice its width. When 5 meters is added to the width, the result is a square with an area of 144 square meters. Find the dimensions of the original rectangle. : Let x = the width It says,"A rectangle has a length 2 meters less than twice its width.", therefore: L = 2x - 2 : "When 5 meters is added to the width, the result is a square with an area of 144 square meters." : (x + 5)*(2x - 2) = 144 FOIL 2x^2 - 2x + 10x - 10 = 144 : 2x^2 + 8x - 10 - 144 = 0 : 2x^2 + 8x - 154 = - Simplify, divide by 2 x^2 + 4x - 77 = 0 Factors to (x + 11)(x - 7) = 0 Positive solution x = 7 m is the original width : Find the dimensions of the original rectangle : L = 2(7) - 2 = 12 m is the original length : : Will adding 5 m to the width make a square with 144 sq/m? 7 + 5 = 12, then: 12 * 12 = 144 sq/m
 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(15646)   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 you1 solutions Answer 177505 by ankor@dixie-net.com(15646)   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(15646)   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(15646)   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(15646)   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(15646)   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(15646)   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(15646)   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(15646)   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(15646)   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(15646)   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(15646)   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^71 solutions Answer 177220 by ankor@dixie-net.com(15646)   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(15646)   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(15646)   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