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Unit_Conversion_Word_Problems/554576: A bicycle wheel has a diameter of 26 in. If the bicycle needs to travel 59 ft, how many revolutions of the wheel need to take place? Round to the nearest whole number. 1 solutions Answer 361493 by ankor@dixie-net.com(15624)   on 2012-01-09 19:36:34 (Show Source): You can put this solution on YOUR website! A bicycle wheel has a diameter of 26 in. If the bicycle needs to travel 59 ft, how many revolutions of the wheel need to take place? : Change ft to inches, divide by the circumference = 8.667 ~ 9 revolutions

Rational-functions/554487: Please help me out with this one, "In this exercise, solve the equation containing a rational exponent on the variable." x^3/4= 125 1 solutions Answer 361355 by ankor@dixie-net.com(15624)   on 2012-01-09 09:03:07 (Show Source): You can put this solution on YOUR website! Find the cube root of both sides and you have Raise both sides to the 4 power x = 5^4 x = 625

Linear-equations/553939: find the slope for the following: x/4 + 2y - 1 = 6 1 solutions Answer 361303 by ankor@dixie-net.com(15624)   on 2012-01-08 20:52:12 (Show Source): You can put this solution on YOUR website! find the slope for the following: + 2y - 1 = 6 We can rewrite it and then put it in the slope/intercept form x + 2y - 1 = 6 x + 2y = 6 + 1 x + 2y = 7 2y = x + 7 divide both sides by 2 y = x + slope =

Linear-systems/554120: Eight years ago, Albert was 3/4 of Bilbos age. in 22 years he will be 9/10 of Bilbos age. How old is Bilbo now? 1 solutions Answer 361295 by ankor@dixie-net.com(15624)   on 2012-01-08 19:18:16 (Show Source): You can put this solution on YOUR website! Eight years ago, Albert was 3/4 of Bilbos age. in 22 years he will be 9/10 of Bilbos age. How old is Bilbo now? : Let a = Al's present age Let b = Bil's : "Eight years ago, Albert was 3/4 of Bilbos age." a - 8 = (b-8) multiply both sides by 4 4(a-8) = 3(b-8) 4a - 32 = 3b - 24 4a = 3b - 24 + 32 4a = 3b + 8 divide both sides by 4 a = .75b + 2 : "in 22 years he will be 9/10 of Bilbos age. " a + 22 = (b+22) multiply both sides by 10 10(a + 22) = 9(b + 22) 10a + 220 = 9b + 198 10a = 9b + 198 - 220 10a = 9b - 22 Replace a with (.75b+2) 10(.75b + 2) = 9b - 22 7.5b + 20 = 9b - 22 20 + 22 = 9b - 7.5b 42 = 1.5b b = 42/1.5 b = 28 is Bil's age : : : Find a, then check the solutions in both statements: a = .75(28) + 2 a = 23 is Al's age

Travel_Word_Problems/554171: Going at 37miles a hr. how far will i get in 8sec. 10sec. 15sec. and 25sec. 1 solutions Answer 361292 by ankor@dixie-net.com(15624)   on 2012-01-08 18:59:52 (Show Source): You can put this solution on YOUR website! Going at 37miles a hr. how far will i get in 8sec. 10sec. 15sec. and 25sec : Convert 37 mph to ft/sec = 54.267 ft/sec : 8 * 54.267 = 434.1 ft 10* 54.267 = 542.7 ft 15* 54.267 = 814.0 ft 25* 54.267 = 1356.7 ft

Travel_Word_Problems/554135: If I am driving at 65 miles per hour how many kilometers per hour would I be driving. I was able to find how many yards are in a mile and how many yards are in a kilometer. But I don't know how to use this information determine miles and kilometers. 1 solutions Answer 361285 by ankor@dixie-net.com(15624)   on 2012-01-08 18:34:00 (Show Source): You can put this solution on YOUR website! If I am driving at 65 miles per hour how many kilometers per hour would I be driving. : To convert miles to km, multiply by 1.609 : 1.609 * 65 = 104.6 km/hr

Polynomials-and-rational-expressions/553935: This needs to be answered in scientific notation and I just don't understand it. The mass of mars is 6.421x10^(20) metric tons.The mass of the sun is 1.998x10^(27) metric tons. about how many times the mass of marsis the mass of the sun? Round to the nearest tenth. 1 solutions Answer 361119 by ankor@dixie-net.com(15624)   on 2012-01-07 22:02:12 (Show Source): You can put this solution on YOUR website! This needs to be answered in scientific notation and I just don't understand it. The mass of mars is 6.421x10^(20) metric tons.The mass of the sun is 1.998x10^(27) metric tons. about how many times the mass of marsis the mass of the sun? Round to the nearest tenth. : Write it as a proportion Divide the numerical portion as you do normally, when you divide powers of 10, subtract the exponent of the dividing value, write it in scientific notation = = the sun is times the mass of mars

Travel_Word_Problems/553934: Joe drove at the speed of 45 miles per hour for a certain distance. He then drove at the speed of 55 miles per hour for the same distance. What is the average speed for the whole trip? 1 solutions Answer 361118 by ankor@dixie-net.com(15624)   on 2012-01-07 21:47:46 (Show Source): You can put this solution on YOUR website! Joe drove at the speed of 45 miles per hour for a certain distance. He then drove at the speed of 55 miles per hour for the same distance. What is the average speed for the whole trip? : Let d = distance driven at each speed then 2d = distance of the whole trip : let a = the average speed for the whole trip : Write a time equation; time = dist/speed : 45mph time + 55mph time = total time + = Multiply by the LCM of 45 and 55, 495a 495a* + 495a* = 495a cancel the denominators; 11ad + 9ad = 495(2d) 20ad = 990d divide both sides by d 20a = 990 a = 990/20 a = 49.5 mph is the average speed for the trip : ; : Let's check this out, using an assigned distance of 200 mi + = 2.22 + 1.82 = 4.04 4.04 = 4.04; confirms our average speed of 49.5 mph

Average/553601: Please Help. 16y^2/3y^2-24y+48 * 3y-12/4y 1 solutions Answer 361113 by ankor@dixie-net.com(15624)   on 2012-01-07 21:07:56 (Show Source): You can put this solution on YOUR website! * Factor the 1st denominator * Note that we can cancel: 3y-12 and 4y, results:

Triangles/553680: I am buying an "A" frame trailer coupler. I am using it a little different than sometimes used. So I know that the angle of the the coupler is 50 degrees. I need to know that if I attach to steel channels to it, and it's going out at 50 degrees, about how far can I go until the width of the ends is about 70 inches. To state it in plain mathematical terms, if I have a triangle where the top angle is 50 degrees, how far will the two sides be so that the bottom of the triangle is 70 inches long? 1 solutions Answer 361013 by ankor@dixie-net.com(15624)   on 2012-01-07 08:49:19 (Show Source): You can put this solution on YOUR website! if I have a triangle where the top angle is 50 degrees, how far will the two sides be so that the bottom of the triangle is 70 inches long? : We know the two other angles will be = 65 degrees angles B & C : Using the law of sines where A=50 degrees, a = 70 inches, find b or c = = = Cross multiply .766b = 70 * .9063 .766b = 63.44 b = b = 82.8 ~ 83 inches, the length of the two sides, the ends will be 70 inches apart

Miscellaneous_Word_Problems/553656: A man makes out his will, stating that if his wife gives birth to a boy, his estate is to be divided in the proportion of two-thirds to the son and one-third to his wife. If his wife gives birth to a daughter, the daughter gets one-fourth of the estate and the wife, three-fourths. The wife gives birth to twins, a boy and a girl. How would the estate be divided so that the proportions in the will are properly considered? There are two possible solutions to this problem. Find both of them. 1 solutions Answer 360974 by ankor@dixie-net.com(15624)   on 2012-01-06 21:57:24 (Show Source): You can put this solution on YOUR website! A man makes out his will, stating that if his wife gives birth to a boy, his estate is to be divided in the proportion of two-thirds to the son and one-third to his wife. If his wife gives birth to a daughter, the daughter gets one-fourth of the estate and the wife, three-fourths. The wife gives birth to twins, a boy and a girl. How would the estate be divided so that the proportions in the will are properly considered? There are two possible solutions to this problem. Find both of them. : Here's one solution, I'll let you find the other one Divide the estate into twelfths, 6/12 for son scenario and 6/12 for daughter scenario : the son, * = = for the son * = = for the wife the daughter * = = for the daughter * = = for the wife : Summarize: Son gets of the estate daughter gets of the estate wife gets + = + = of the estate

Radicals/553602: 3 over Radical(2) plus 5 over Radical (6)? 1 solutions Answer 360972 by ankor@dixie-net.com(15624)   on 2012-01-06 21:31:54 (Show Source): You can put this solution on YOUR website! 3 over Radical(2) plus 5 over Radical (6)? : + Place of a common denominator = =

Average/553562: If i wanted to go on a trip, i have to pass class with an 82.5%. I had 71% last semester . What would i have to get this semester? they take the average of both semesters. 1 solutions Answer 360962 by ankor@dixie-net.com(15624)   on 2012-01-06 19:57:45 (Show Source): You can put this solution on YOUR website! If i wanted to go on a trip, i have to pass class with an 82.5%. I had 71% last semester . What would i have to get this semester? they take the average of both semesters. : Let x = grade required in the 2nd semester to get 82.5 average of the year = 82.5 Multiply both sides by 2 71 + x = 165 x = 165 - 71 x = 94% and you pack your bags for the trip

Coordinate-system/553555: No idea if I am asking this in the correct area. We are solving for coordinates to map on the Rectangular Coordinate section. I'm not very good at this and have chosen a practice problem to see broken down. 8x + 2/9Y = 29 Solving for ( ,18) 1 solutions Answer 360933 by ankor@dixie-net.com(15624)   on 2012-01-06 16:42:27 (Show Source): You can put this solution on YOUR website! 8x + Y = 29 Solving for ( ,18) replace y with 18, find x 8x + (18) = 29 8x + 2(2) = 29 8x + 4 = 29 8x = 29 - 4 8x = 25 x = x = 3.125 : The ordered pair for this equation would be: 3.125, 18

Equations/553517: A sample of phosphorus-32 has a half-life of 14.28 days. If 55 g of this radioisotope remain unchanged after approximately 57 days, what was the mass of the original sample? could someone please help? 1 solutions Answer 360929 by ankor@dixie-net.com(15624)   on 2012-01-06 16:22:56 (Show Source): You can put this solution on YOUR website! A sample of phosphorus-32 has a half-life of 14.28 days. If 55 g of this radioisotope remain unchanged after approximately 57 days, what was the mass of the original sample? : Using the radioactive decay formula: A = Ao*2^(-t/h), where A = resulting amt after t time Ao = initial amt (t=0) t = time h = half-life of substance : We want to find Ao: Ao*2^(-57/14.28) = 55 using a calc to find 2^(-57/14.28) .062865Ao = 55 Ao = Ao = 875 grams was the initial amt : : We can check this solution on our calculator; enter: 875*2^(-57/14.28) results: 55.00 grams

Travel_Word_Problems/553372: Hello, I need help on this problem, if you don't mind may you please show most of the steps? Thanks! Two trains leave Sacramemto at the same time. One travel East at 40mph. The other traveled West at 60mph.Write amd solve a system of linear equations that can be used to determine when the trains are 280 miles apart. Thank You!!! 1 solutions Answer 360898 by ankor@dixie-net.com(15624)   on 2012-01-06 13:28:29 (Show Source): You can put this solution on YOUR website! Two trains leave Sacramemto at the same time. One travel East at 40mph. The other traveled West at 60mph. Write amd solve a system of linear equations that can be used to determine when the trains are 280 miles apart. : Let t = travel time required for them to be 280 mi apart : write a distance equation; dist = speed * time : train 1 dist + train 2 dist = 280 mi 40t + 60t = 280 100t = 280 t = 280/100 t = 2.8 hrs, they will be 280 mi apart : : Check this by finding the distance that each traveled 2.8*40 = 112 mi 2.8*60 = 168 ---------------- total: 280 mi

Graphs/552413: I am trying to help my daughter with her homework from 1300 miles away please help! The problem is find the equation of a line in slope intercept form with an undefined slope and passes though (3,-2). Thank you so much, it's been a long time since I've done this stuff. 1 solutions Answer 360250 by ankor@dixie-net.com(15624)   on 2012-01-03 21:52:26 (Show Source): You can put this solution on YOUR website! find the equation of a line in slope intercept form with an undefined slope and passes though (3,-2). : a line with a undefined slope is a vertical line, the equation: x=3 It passes thru all values for y including y=-2. it's parallel to the y axis so the slope/intercept form seems rather meaningless

Volume/552241: If a rectangular prism has a square On the base with 5 inches, how tall does it need. To be to have a total volume of 700 inches cubed? Hello! Can u help me, I understand the question bt I don't know how 2 do it... 1 solutions Answer 360219 by ankor@dixie-net.com(15624)   on 2012-01-03 19:51:53 (Show Source): You can put this solution on YOUR website! If a rectangular prism has a square On the base with 5 inches, how tall does it need To be to have a total volume of 700 inches cubed? : let h = the height of the rectangular prism then 5 * 5 * h = 700 cu/in 25h = 700 h = 700/25 h = 28 inches high : : Check this 5 * 5 * 28 = 700

Square-cubic-other-roots/552258: Please help me simplify the square root of (5g)^4. I've done all of the other problems just fine but this one has stumped me because of the parenthesis and the fact that I'm struggling in this chapter. The other problems have been easy because they have numbers that go into them evenly like: the square root of 49m^6=7m^3 and the square root of 64a^8=8a^4. And also, is it free to register? Thank you for all of your help!! 1 solutions Answer 360200 by ankor@dixie-net.com(15624)   on 2012-01-03 16:55:46 (Show Source): You can put this solution on YOUR website! simplify the square root of (5g)^4. : raise both terms to the 4th power = ; Factor inside the radical to reveal some perfect squares : extract the square root of each perfect square: 5 * 5 * g * g = 25g^2; the greatly simplified version : You could probably see this just by looking at it, but perhaps a step-by-step procedure will help you understand what when on here : Everything on this forum is free!

Rational-functions/552233: Need help with this one please: q+8/3 + q-5/5=13/3 1 solutions Answer 360195 by ankor@dixie-net.com(15624)   on 2012-01-03 16:20:24 (Show Source): You can put this solution on YOUR website! + = Multiply by 15 15* + 15* = 15* cancel the denominators and you have 5(q+8) + 3(q-5) = 5(13) : 5q + 40 + 3q - 15 = 65 8q + 25 = 65 8q = 65 - 25 8q = 40 q = 40/8 q = 5 : : Check this in the original problem where q=5 + = + =

Radicals/552025: express 5 square root 3x^3 minus 2 square root 27x^3 in simplest radical form 1 solutions Answer 360194 by ankor@dixie-net.com(15624)   on 2012-01-03 16:12:05 (Show Source): You can put this solution on YOUR website! express 5 square root 3x^3 minus 2 square root 27x^3 in simplest radical form : factor to reveal some perfect squares inside the radicals extract the square root of those perfect squares which is, and are like terms, so just do the math =

Surface-area/552027: What is the missing length in a box with 1480 suface area and 18 and 10 as two of the side lengths 1 solutions Answer 360193 by ankor@dixie-net.com(15624)   on 2012-01-03 15:59:31 (Show Source): You can put this solution on YOUR website! What is the missing length in a box with 1480 surface area and 18 and 10 as two of the side lengths : Formula for surface area of a box: S.A. = 2(L*W) + 2(L*H) + 2(W*H) Let L = 18 Let W = 10 Let H = the unknown value Given the surface area as 1480: : 2(18*10) + 2(18H) + 2(10h) = 1480 Simplify, divide thru by 2 (18*10) + (18H) + (10h) = 740 180 + 28H = 740 28H = 740 - 180 28H = 560 H = H = 20 units is the missing length : : Check the solution in the original S.A. equation.

Average/552156: Harold calculated the mean of 5 numbers to be 68. Then he found that he made an error and had written 70 for one of the numbers when he should have written 80. What is the mean of the correct 5 numbers? 1 solutions Answer 360148 by ankor@dixie-net.com(15624)   on 2012-01-03 13:05:48 (Show Source): You can put this solution on YOUR website! Harold calculated the mean of 5 numbers to be 68. Let n = sum of the 5 numbers = 68 n = 5*68 n = 340 Then he found that he made an error and had written 70 for one of the numbers when he should have written 80. This raises n by 10, 350 is the correct sum = 70 is the correct mean

Linear-equations/551997: I have a question on writing equations of parallel lines I understand that in order for an equation to be parallel with another, they must have the same slope. here is the problem. (3,-2),y=2/3x+1 1 solutions Answer 360118 by ankor@dixie-net.com(15624)   on 2012-01-03 08:33:46 (Show Source): You can put this solution on YOUR website! I have a question on writing equations of parallel lines I understand that in order for an equation to be parallel with another, they must have the same slope. here is the problem. (3,-2), y = 2/3x + 1 : You know from the equation that the slope m = : Use the point/slope formula: y - y1 = m(x - x1) the points given: x1=3, y1=-2 y - (-2) = (x - 3) y + 2 = x - 2 y = x - 2 - 2 y = x - 4 is the equation : Check the equation using x=3, ensure that y = -2

Age_Word_Problems/551945: The sum of the present ages of Joey and his mother is 46 years. In 4 years, Joey will be 3 years older than one-half as old as his mother at that time. Find the present ages of Joey and his mother. 1 solutions Answer 360116 by ankor@dixie-net.com(15624)   on 2012-01-03 08:21:54 (Show Source): You can put this solution on YOUR website! he sum of the present ages of Joey and his mother is 46 years. In 4 years, Joey will be 3 years older than one-half as old as his mother at that time. Find the present ages of Joey and his mother. : Let m = mom's present age Let j = Joey's : write an equation for each statement: : "The sum of the present ages of Joey and his mother is 46 years." m + j = 46 j = (46-m); we can use this form for substitution : " In 4 years, Joey will be 3 years older than one-half as old as his mother at that time." j + 4 = .5(m + 4) + 3 j + 4 = .5m + 2 + 3 j = .5m + 5 - 4 j = .5m + 1 Replace j with (46-m) 46-m = .5m + 1 46 - 1 = .5m + m 45 = 1.5m m = m = 30 yrs is mom's age then j = 46 - 30 j = 16 yrs is Joey's age : : Check this in the statement: "In 4 years, Joey will be 3 years older than one-half as old as his mother at that time. " 16 + 4 = .5(30+4) + 3 20 = .5(34) + 3 20 = 17 + 3

Equations/551918: Over a 3 day weekend, you take a 592-mile trip. If you average 32 mi/gal on the trip how may gasoline did you use? 1 solutions Answer 360037 by ankor@dixie-net.com(15624)   on 2012-01-02 22:01:47 (Show Source): You can put this solution on YOUR website! a 592-mile trip. If you average 32 mi/gal on the trip how much gasoline did you use? : = 18.5 gal

Quadratic_Equations/551924: "You are making a frame of uniform width for a picture that is to be displayed at the local museum. The picture is 3.25 feet tall and 3 feet wide. The museum has allocated 15 square feet of wall space to display the picture. What should the width be of the frame in order to us all of the allocated space?" 1 solutions Answer 360022 by ankor@dixie-net.com(15624)   on 2012-01-02 21:08:37 (Show Source): You can put this solution on YOUR website! You are making a frame of uniform width for a picture that is to be displayed at the local museum. The picture is 3.25 feet tall and 3 feet wide. The museum has allocated 15 square feet of wall space to display the picture. What should the width be of the frame in order to us all of the allocated space?" : Let x = the width of the frame If you draw this (a rectangle inside a rectangle) you will see the overall dimensions will be twice the width of the frame plus the picture dimension then the over all dimensions will be (3.25+2x) by (3+2x) : The overall area equation (2x+3.25)(2x+3) = 15 FOIL 4x^2 + 6x + 6.5x + 9.75 = 15 4x^2 + 12.5x + 9.75 - 15 = 0 A quadratic equation 4x^2 + 12.5x - 5.25 = 0 we have to use the quadratic formula here in this equation: a=4, b=12.5, c=-5.25 : : Two solutions, but we only want the positive one x = x = .375 ft, which would be .375(12) = 4.5 inches is the width of the frame : : : Confirm this by finding the area (2*.375 = .75) (3.25+.75)*(3+.75) = 15 sq/ft

Money_Word_Problems/551848: Please help me on this problem im so lost and confused: A gas station has just raised its prices. The attendant resets the pump but forgets to record the old prices. Rather then revealing her forgetfulness by asking her boss, she consults yesterday's sales report. she finds that 450 liters of regular and 320 liters of unleaded were sold for a total of $384.83. Regular was 5 cents per liter cheaper than unleaded. What were the two prices per liter yesterday? 1 solutions Answer 359991 by ankor@dixie-net.com(15624)   on 2012-01-02 17:01:19 (Show Source): You can put this solution on YOUR website! A gas station has just raised its prices. The attendant resets the pump but forgets to record the old prices. Rather then revealing her forgetfulness by asking her boss, she consults yesterday's sales report. she finds that 450 liters of regular and 320 liters of unleaded were sold for a total of $384.83. Regular was 5 cents per liter cheaper than unleaded. What were the two prices per liter yesterday? : Let x = price of regular then (x+.05) = price of the unleaded : reg amt + unl amt = $384.83 450x + 320(x+.05) = 384.83 450x + 320x + 16 = 384.83 770x = 384.83 - 16 770x = 368.83 x = x = $.479 for regular and .479+.05 = .529 for unleaded : : You can confirm this .479(450) + .529(320) =

expressions/551784: Short Answer: Raise the quantity in parentheses to the indicated exponent, and simplify the resulting expression. Express answers with positive exponents (32x^-5y/128x^-5y^4)^3 (32x^-5y)^3 ------------- (128x^-5y^4) Equation has parentheses around entire problem not around both equation only around entire problem. 1 solutions Answer 359987 by ankor@dixie-net.com(15624)   on 2012-01-02 16:29:30 (Show Source): You can put this solution on YOUR website! Raise the quantity in parentheses to the indicated exponent, and simplify the resulting expression. Express answers with positive exponents (32x^-5y/128x^-5y^4)^3 : x^-5, cancel reduce the numeric fraction combine the y = = =

Radicals/551684: Write the inverse variation equation of the following. Y varies inversely with x and y = 9 when x = 14 1 solutions Answer 359974 by ankor@dixie-net.com(15624)   on 2012-01-02 15:44:41 (Show Source): You can put this solution on YOUR website! Write the inverse variation equation of the following. Y varies inversely with x and y = 9 when x = 14 : k = constant of variation y = y = 9, x = 14, find k = 9 k = 14*9 k = 126 : y = is the equation

Numbers_Word_Problems/551749: A number is doubled and then the product is increased by 6. This sum is then multiplied by -3, and the result is 54 greater than three times the opposite of the number. What is the number? 1 solutions Answer 359949 by ankor@dixie-net.com(15624)   on 2012-01-02 14:30:03 (Show Source): You can put this solution on YOUR website! A number is doubled and then the product is increased by 6. This sum is then multiplied by -3, and the result is 54 greater than three times the opposite of the number. What is the number? : Let x = the number then -x = the opposite of the number : -3(2x+6) = 3(-x) + 54 -6x - 18 = -3x + 54 -18 - 54 = -3x + 6x -72 = 3x x = x = -24 is the number : : Confirm this in the original statement: -3(2(-24) + 6 = 3(24) + 54 -3(-48 + 6) = 72 + 54 -3(-42) = 126 126 = 126; confirms our solution of x=-24