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 Polynomials-and-rational-expressions/103381: This question is from textbook Beginning Algebra The price of an item is given by p=2x^2 - 100 Find the polynomial that represents the revenue generated from the sale of x items. If you could please tell me what you are doing step by step, that would really help me to understand the way this equation is solved. 1 solutions Answer 75204 by ankor@dixie-net.com(15747)   on 2007-10-10 15:36:08 (Show Source): You can put this solution on YOUR website!The price of an item is given by p=2x^2 - 100 Find the polynomial that represents the revenue generated from the sale of x items. ; They don't want to solve it, just write an equation that will give you the amt of revenue for a given number of items sold (x) : They tell you two things Price (p) = 2x^2 - 100 and The number of items is given as the value of x : We know that revenue (R) = number of items sold (x) * the price (p), therefore: R = x * (2x^2 - 100) : Multiply what's inside the brackets and you have: R = 2x^3 - 100x; this is what they want : Did this help you?
 Square-cubic-other-roots/103258: Simplify: the square root of 48 x squared y to the 6th1 solutions Answer 75194 by ankor@dixie-net.com(15747)   on 2007-10-10 14:36:32 (Show Source): You can put this solution on YOUR website!Simplify: the square root of 48 x squared y to the 6th : : Factor this inside the radical to recognize the perfect squares: : Extract the square roots and you have:
 Miscellaneous_Word_Problems/103130: A projectile is thrown upward at the rate of 42 feet per second from a platform 150 feet high. How long does it take to hit ground? 1 solutions Answer 75190 by ankor@dixie-net.com(15747)   on 2007-10-10 14:25:31 (Show Source): You can put this solution on YOUR website!A projectile is thrown upward at the rate of 42 feet per second from a platform 150 feet high. : How long does it take to hit ground? Let t = time in seconds ; The three parts of this equation are: Gravity (downward): -16t^2 Velocity up-ward: 42t Platform ht: 150 : The height of the ground is 0, find t when the equation = 0: -16t^2 + 42t + 150 = 0 : Unfortunately, this has to be solved by using the quadratic formula: a = -16; b = 42; c = 150, find t: : : : : : Two solutions: t = -2.01, we don't want the negative solution and t = +4.64375 seconds to hit the ground : : You can check this by substituting 4.64375 for t in the original equation
 Linear-equations/103246: Hello out there,I need some help with some problems,the first one is,Use substitution to solve:x=3y-2 and 2x+4y=16.The next one is,Use substitution to solve:2x+y=7 and 5x-2y=4.The third one is,Find the solution of the system,y=x^2+5 and y=2x+4.And the last one is,Solve the system of equations by graphing:y=x^2-4 and y=x-2.Thanks to whoever can help.1 solutions Answer 75187 by ankor@dixie-net.com(15747)   on 2007-10-10 13:34:46 (Show Source): You can put this solution on YOUR website!Use substitution to solve: x = 3y - 2 2x + 4y = 16. Substitute (3y-2) for x in the second equation, solve for y 2(3y-2) + 4y = 16 6y - 4 + 4y = 16 6y + 4y = 16 + 4 10y = 20 y = 20/10 y = 2 Find x substitute 2 for y x = 3(2) - 2 x = 6 - 2 x = 4 : : Use substitution to solve: 2x + y = 7 y = (7 - 2x); we can substitute (7-2x) for y in the next equation, find x 5x - 2y = 4 5x - 2(7-2x) = 4 5x - 14 + 4x = 4; remember a neg outside the brackets changes the signs inside 5x + 4x = 4 + 14 9x = 18 x = 18/2 x = 2 Find y using y = (7-2x) y = 7 - 2(2) y = 7 - 4 y = 3 : : Find the solution of the system, y = x^2 + 5 y = 2x + 4 Substitute (x^2 + 5) from the 1st equation, for y in the 2nd equation: x^2 + 5 = 2x + 4 x^2 - 2x + 5 - 4 = 0 x^2 - 2x + 1; a quadratic equation that we can factor to: (x-1)(x-1) x = 1 Find y using the 2nd equation: y = 2(1) + 4 y = 2 + 4 y = 6 Check it by substitution in the 1st equation : : Solve the system of equations by graphing: y = x^2 - 4 y = x - 2 Plot these. substitute for x = -3 to x = +3 The first equation table x | y ------- -3 | +5 -2 | 0 -1 | -3 0 | -4 +1 | -3 +2 | 0 +3 | +5 Note that this is a parabola : The 2nd equation is linear, two points are sufficient x | y ------- -3 |-5 +3 |+1 : The graph should look like this: : There are two solutions, where the two graphs intersect. I'll let you figure out what they are from the graph. When you have decided what they are, check by substitution in the original equations.
 Mixture_Word_Problems/103148: radiator holds 5 gallons. The coolant in the radiator is a mixture of antifreeze and water. Presently, 40% of the mixture is pure antifreeze. The proper mixture to prevent freezing and rust formation is when antifreeze is 50% of the mixture. The radiator is now full to the top. In order to add antifreeze, some of the present mixture must be drained out to make room. How much mixture should be drained out to make just enough room to add the correct amount of pure antifreeze to give a resulting mixture in the radiator of 50%?1 solutions Answer 75083 by ankor@dixie-net.com(15747)   on 2007-10-09 19:30:37 (Show Source): You can put this solution on YOUR website! radiator holds 5 gallons. The coolant in the radiator is a mixture of antifreeze and water. Presently, 40% of the mixture is pure antifreeze. The proper mixture to prevent freezing and rust formation is when antifreeze is 50% of the mixture. The radiator is now full to the top. In order to add antifreeze, some of the present mixture must be drained out to make room. How much mixture should be drained out to make just enough room to add the correct amount of pure antifreeze to give a resulting mixture in the radiator of 50%? : Let x = amt to be removed; & amt of pure antifreeze to be added : .40(5-x) + 1.0x = .50(5) : 2 - .4x + 1x = 2.5 : .6x = 2.5 - 2 : .6x = .5 : x = .5/.6 : x = gal removed, and gal of pure antifreeze added: : : Check solution using decimals = .833: : 5 - .833 = 4.167 gal of 40% solution : .4(4.167) + 1.0(.833) = .5(5) 1.67 + .833 = 2.50, confirms our solution
 Percentage-and-ratio-word-problems/103173: Dear Sir/Madam: This is from a worksheet that I received from the teacher. Origination unknown. The denominator of a fraction is one more than the numerator. When 4 is added to the numerator and 6 is added to the denominator the result equals 3/4. Find the fraction. this is what I have: x/x+1 + 4/6 = (x + 4)/(1x + 6) = 4 / 2x + 7 I feel stuck. What did I not capture correctly out of the word problem? Thank you so very much. 1 solutions Answer 75032 by ankor@dixie-net.com(15747)   on 2007-10-09 15:20:28 (Show Source): You can put this solution on YOUR website!The denominator of a fraction is one more than the numerator. When 4 is added to the numerator and 6 is added to the denominator the result equals 3/4. Find the fraction. this is what I have: , this is right : Right here you should have: = : = : Cross multiply and you have: 4(x+4) = 3(x+7) : 4x + 16 = 3x + 21 4x - 3x = 21 - 16 : x = 5 : : Checking our solution using the original statement: = =
 Polynomials-and-rational-expressions/103172: Think of a real-life situation that can be translated to a polynomial function and solve the problem. 1 solutions Answer 75029 by ankor@dixie-net.com(15747)   on 2007-10-09 14:56:44 (Show Source): You can put this solution on YOUR website!Think of a real-life situation that can be translated to a polynomial function and solve the problem. : you have to earn at least \$3000 this summer, to be able to return to college: : You found a construction job that will let you take home \$120 per day. : The job site is 50 miles from your home. You must drive 100 mi every day. : The car you own costs 25 cents a mile to operate (It's an old one). : You bring your own lunch (using your parents food) so no expense there. : How many days will you have to work to have \$3000 at the end of the summer. : Let x = number of days worked, f(x) = 3000 : f(x) = 120x - x(.25*100) : Wages - car expense = required amt 120x - x(.25*100) = 3000 120x - x(25) = 3000 120x - 25x = 3000 95x = 3000 x = 3000/95 x = 31.58 days, so let's say you must work 32 days to reach your goal goal : : Check it using 32 days 120(32) - 32(25) = 3840 - 800 = \$3040.00 : Actually this is a real life situation that occurred not too long ago
 Quadratic_Equations/102942: x^2 - x/ x^2 + 3x + 2 / x^2-1/x^2+2X1 solutions Answer 75022 by ankor@dixie-net.com(15747)   on 2007-10-09 14:14:21 (Show Source): You can put this solution on YOUR website!x^2 - x/ x^2 + 3x + 2 / x^2-1/x^2+2X : Assume you mean: ------------- : Can be factored to: ------------- : Invert the dividing fraction and multiply: * : CAncel the (x-1)'s and (x+2)'s and you have: * =
 Polynomials-and-rational-expressions/103008: 1 solutions Answer 75006 by ankor@dixie-net.com(15747)   on 2007-10-09 11:59:33 (Show Source): You can put this solution on YOUR website! - = 1 : You can see that (x^2-1) is the difference of squares so factor that: - = 1 : Common denominator would be (x-1)(x+1), multiply equation by that: (x-1)(x+1) - (x-1)(x+1) = 1(x-1)(x+1) : Cancel out the denominators and you have; 3(x+1) - 6 = (x-1)(x+1) : Multiply what's inside the brackets on the left, FOIL the right 3x + 3 - 6 = x^2 - 1 3x - 3 = x^2 - 1 : Arrange as a quadratic equation: x^2 - 3x - 1 + 3 = 0 x^2 - 3x + 2 = 0 : Factors to: (x-2)(x-1) = 0 Two solutions: x = +2 x = +1 : However x = 1, cannot be a solution. Note that if you substitute 1 for x, both fractions have division by 0 : x = 2 is the only solution, check by subsitution : - = 1 3 - = 1 :
 Miscellaneous_Word_Problems/102964: If two inlet pipes are both open, they can fill a pool in 1 hour and 12 minutes. ONe of the pipes can fill the pool by itself in 2 hours. How long would it take the other pipe to fill the pool by itself1 solutions Answer 74986 by ankor@dixie-net.com(15747)   on 2007-10-09 08:09:47 (Show Source): You can put this solution on YOUR website!If two inlet pipes are both open, they can fill a pool in 1 hour and 12 minutes. one of the pipes can fill the pool by itself in 2 hours. How long would it take the other pipe to fill the pool by itself : Change 1 hr 12 min to hrs. 12/60 = .2 > 1.2 hrs : Let x = time for other pipe to fill by itself : Let the full pool = 1 : + = 1 : Multiply equation by 2x: 2x* + 2x* = 2x*1 ; Cancel out the denominators and you have 1.2x + 1.2(2) = 2x : 2.4 = 2x - 1.2x : 2.4 = .8x : x = 2.4/.8 : x = 3 hrs required by the other pipe alone : : Check solution: + = .6 + .4 = 1
 Linear-systems/103058: well my mean math teacher got mad at me so im stuck simplifing the equation 3x+2n=(4y-2+3x)1 solutions Answer 74951 by ankor@dixie-net.com(15747)   on 2007-10-08 21:47:07 (Show Source): You can put this solution on YOUR website!Simplify: : 3x + 2n = (4y-2+3x) : 3x + 2n = 4y - 2 + 3x : Subtract 3x from both sides: 2n = 4y - 2 : Divide equation by 2 and you have: n = 2y - 1
 Linear-systems/102734: a steamer going downstream in a river covers the distance between two towns in 20 hour coming back upstream it covers this distance in 25 hours the speed of water is 4 km/h. find the distance between the two town. (hint : first find the speed of steamer in still water.)1 solutions Answer 74947 by ankor@dixie-net.com(15747)   on 2007-10-08 21:39:18 (Show Source): You can put this solution on YOUR website!a steamer going downstream in a river covers the distance between two towns in 20 hour coming back upstream it covers this distance in 25 hours the speed of water is 4 km/h. find the distance between the two town. : Let s = speed of the boat in still water then (s-4) = speed upstream and (s+4) = speed downstream ; Distance both ways is equal. Make a distance equation; Distance = Time * speed Up distance = down distance 25(s-4)= 20(s+4) : 25s - 100 = 20s + 80 25s - 20s = +100 + 80 5s = 180 s = 180/5 s = 36 mph : Find the distance: Dist = time * speed downstream: d = 20(36+4) = 800 mi and Upstream: d = 25(36-4) = 800 mi also
 Polynomials-and-rational-expressions/102786: This question is from textbook Intermediate Algebra Everytime I try to solve this problem, nothing comes out the same and I can't seem to figure out where my mistake is to determine if any of my solutions are correct. Can someone please show me the correct way to solve this problem? . Divide: x2 – 3x + 2 / x2 – 1 7x – 14 / 7x + 7 NOTE: there should be a line between the upper and lower terms on each side of the division symbol.1 solutions Answer 74895 by ankor@dixie-net.com(15747)   on 2007-10-08 15:44:23 (Show Source): You can put this solution on YOUR website!Every time I try to solve this problem, nothing comes out the same and I can't seem to figure out where my mistake is to determine if any of my solutions are correct. Can someone please show me the correct way to solve this problem? . Divide: Assume you mean ------------ : Let's do the numerator fraction and the denominator fraction separately: : Simplify the numerator fraction: : Note that you can factor both denominator and numerator to: : Note that the (x-1)'s will cancel leaving you with: : : Simplify the denominator fraction : Note that you can factor out the 7's : 7's cancel, leaving you with: : Put it all back together and you have: --------- : Remember you invert the dividing fraction and multiply: * = 1 : Note that everything cancels : Did this help?
 Equations/102788: Having trouble solevin: 3 less than the quotient of a number and 7 is 6.1 solutions Answer 74888 by ankor@dixie-net.com(15747)   on 2007-10-08 14:38:17 (Show Source): You can put this solution on YOUR website! solve : 3 less than the quotient of a number and 7 is 6. : Just write what it says, (the word "is" usually means =) : Let x = "a number" : The quotient of a number and 7 = : The equation: - 3 = 6 : Add 3 to both sides: = 6 + 3 : = 9 : Multiply equation by 7 7* = 7*9 : Cancel the 7's and you have: x = 63 : : Check solution in original equation: - 3 = 6 9 - 3 = 6
 Quadratic_Equations/102961: Suuppose that Wendy rides her bicycle 30 miles in the same time that it takes kim to ride her bicycle 20 miles. IF wendy rides 5 miles per hour faster than kim, find the rate of each.1 solutions Answer 74887 by ankor@dixie-net.com(15747)   on 2007-10-08 14:25:32 (Show Source): You can put this solution on YOUR website!Suppose that Wendy rides her bicycle 30 miles in the same time that it takes Kim to ride her bicycle 20 miles. IF Wendy rides 5 miles per hour faster than Kim, find the rate of each. : Let s = K's speed then (s+5) = W's speed : Since they tell us the the two times are the same, we can make a simple time equation from this fact: Time = Distance/Speed : K's time = W's time = : Cross multiply 30s = 20(s+5) : 30s = 20s + 100 : 30s - 20s = 100 : 10s = 100 : s = 10 mph is K's speed and 15 mph is W's speed : : Check solution by find the time of each: 20/10 = 30/15 2 = 2
 Rate-of-work-word-problems/102963: Ryan can mow a lawn in 1 hour, and his son, Malik, can mow the same lawn in 50 minutes. ONe day Malik wtarted mowing the lawn by himself and worked for 30 minutes. Than ryan joined him and they finished the lawn. HOw long did take them to finsh mowing the lawn after Ryan started to help?1 solutions Answer 74885 by ankor@dixie-net.com(15747)   on 2007-10-08 14:14:59 (Show Source): You can put this solution on YOUR website!Ryan can mow a lawn in 1 hour, and his son, Malik, can mow the same lawn in 50 minutes. One day Malik started mowing the lawn by himself, and worked for 30 minutes. Then Ryan joined him, and they finished the lawn. How long did it take them to finish mowing the lawn, after Ryan started to help? : Assuming they have two lawn mowers. : Let x = time required to finish the lawn, together Let the completed job = 1 : : M, by himself + the two together = completed job + + = 1 : Multiply equation by 300 to get rid of the denominators: 300* + 300* + 300* = 300*1 : Cancel out the denominators and you have: 6(30) + 6x + 5x = 300 : 180 + 11x = 300 : 11x = 300 - 180 : x = 120/11 : x = 10.91 minutes : : Check solution on a calc: + + = .6 + .2182 + .1818 = 1.0000
 Numbers_Word_Problems/102939: At exactly what time (to the fraction of a minute) between 7:00 and 8:00 do the hands of a clock form a straight angle?1 solutions Answer 74876 by ankor@dixie-net.com(15747)   on 2007-10-08 11:45:52 (Show Source): You can put this solution on YOUR website!At exactly what time (to the fraction of a minute) between 7:00 and 8:00 do the hands of a clock form a straight angle? : Let x = no. of minutes : Convert minutes to degrees, 360/60 = 6 deg/min : Convert hours to degrees, 360/12 = 30 deg/hr : 7 o'clock = 7 * 30 = 210 degrees : Portion of an hr = (x/60) * 30 = x/2 or .5x : Hr hand degrees - minute hand degrees = 180 210 + .5x - 6x = 180 : -5.5x = 180 - 210 : -5.5x = -30 : x = -30/-5.5 : x = 5.45 minutes. The time would be 07:05.45 for a straight line of the hands : Check our solution 210 + (5.45/60)30 - 5.45(6) = 210 + 2.7 - 32.7 = 180