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Travel_Word_Problems/623724: a word problem for 40/5 1 solutions Answer 392251 by ankor@dixie-net.com(15746)   on 2012-06-25 14:14:25 (Show Source): You can put this solution on YOUR website! a word problem for 40/5 : How long would it take to ride your bike 40 miles if you average 5 mph? Time = dist/speed you can do the rest

test/623439: Full tank with 3 one inch holes drains in 7.2 hours. Same size tank full has 7 one inch holes, how long will it take to drain? 1 solutions Answer 392146 by ankor@dixie-net.com(15746)   on 2012-06-24 21:28:33 (Show Source): You can put this solution on YOUR website! Full tank with 3 one inch holes drains in 7.2 hours. Same size tank full has 7 one inch holes, how long will it take to drain? : Let t = time to drain with 7 holes : Inverse variation equation (the greater the number holes, the less time) = Cross multiply 7t = 3 * 7.2 7t = 21.6 t = t = 3.1 hrs

Rectangles/623373: a rectangle has a length that is 1m less than twice its width. increasing the width by 3m and decreasing the length by 1m results in a square. find the dimensions of the rectangle. 1 solutions Answer 392135 by ankor@dixie-net.com(15746)   on 2012-06-24 20:00:47 (Show Source): You can put this solution on YOUR website! a rectangle has a length that is 1m less than twice its width. L = 2W-1 : increasing the width by 3m and decreasing the length by 1m results in a square Then the length and width will be equal; therefore: L-1 = W+3 L = W + 3 + 1 L = W + 4 Replace L with (2W-1), find W 2W - 1 = W + 4 2W - W = 4 + 1 W = 5 units is the width then 2(5) - 1 = 9 units is the length : find the dimensions of the rectangle. 9 by 5 : : You can check this by finding what the side of the square is Subtract 1 from 9 and add 3 to 5

Travel_Word_Problems/623475: A man drove 60 km in one hour. The next day, he started 15 minutes later. At what speed must he drive to arrive at the same destination as that of before at the same time? 1 solutions Answer 392133 by ankor@dixie-net.com(15746)   on 2012-06-24 19:45:15 (Show Source): You can put this solution on YOUR website! man drove 60 km in one hour. The next day, he started 15 minutes later. At what speed must he drive to arrive at the same destination as that of before at the same time? : He has to cover 60 km in 45 min which is .75 hrs let s = the required speed to do this : .75s = 60 s = 60/.75 s = 80 km/hr

Polynomials-and-rational-expressions/623479: Please help! I dont know what to do next! Simplify. Here is what I have so far. Reduces to: Reduces to: That is what I have so far, what do I do next? 1 solutions Answer 392122 by ankor@dixie-net.com(15746)   on 2012-06-24 18:34:06 (Show Source): You can put this solution on YOUR website! the reciprocal gets rid of the neg exponent = = : I think you are making this harder than it is, remember you have to raise 4 to the third power also, but it looks like you know what you are doing

Polynomials-and-rational-expressions/623466: Please help! I was able to do some of the problem myself but I am not sure what to do next. 3xy(to the -2 power) over x(to the 3 power) times the power of 2 Here is what I have so far: Reduces to: Reduces to: Thats all I have so far what do I do next? 1 solutions Answer 392121 by ankor@dixie-net.com(15746)   on 2012-06-24 18:17:39 (Show Source): You can put this solution on YOUR website! We can clean this up a bit, cancel the x The reciprocal gets rid of the neg exponent =

test/623438: 8 person work crew completes a job in 18 hours. What is the fewest number of workers needed to do the same job in 7 hours? 1 solutions Answer 392119 by ankor@dixie-net.com(15746)   on 2012-06-24 17:20:20 (Show Source): You can put this solution on YOUR website! 8 person work crew completes a job in 18 hours. Find the number of man-hrs to complete the job: 8 * 18 = 144 man-hrs : What is the fewest number of workers needed to do the same job in 7 hours? Let w = no. of workers required to do the job in 7 hrs 7w = 144 w = 144/7 w ~ 21 workers

Functions/623428: if f(x)-2/3x+5, determine a formula for f^-1(x). draw the graph of each function on one set of axes? 1 solutions Answer 392109 by ankor@dixie-net.com(15746)   on 2012-06-24 15:38:18 (Show Source): You can put this solution on YOUR website! if f(x)-2/3x+5, determine a formula for f^-1(x). : y = x + 5; Red Swap x and y, find y y + 5 = x y = x - 5 Multiply both sides by y = x + ; Green draw the graph of each function on one set of axes?

logarithm/623305: 1 solutions Answer 392100 by ankor@dixie-net.com(15746)   on 2012-06-24 14:22:54 (Show Source): You can put this solution on YOUR website! the exponent equiv of logs 3x - 4 = 3x - 4 = 8 3x = 8 + 4 3x = 12 x = x = 4 : : Check in the original problem = 8

Problems-with-consecutive-odd-even-integers/623318: Please help me with I do not understand how to read word problems or how to set them up. 1 solutions Answer 392086 by ankor@dixie-net.com(15746)   on 2012-06-24 13:00:02 (Show Source): You can put this solution on YOUR website! Two numbers: a & b : write an equation for each statement: : One number is one less than twice the other. a = 2b - 1 : Their product is 120 a * b = 120 Replace a with (2b-1) b(2b-1) = 120 2b^2 - b = 120 2b^2 - b - 120 = 0 factors to (2b + 15)(b - 8) = 0 two solutions, only one integer solution b = 8 Find a a = 2(8) - 1 a = 15 : Two numbers, 15 and 8

Linear-systems/623324: Length of the rectangle exceeds its breadth by 7cm. if the length is decreased by 4cm. the area of the new rectangle is same as area of the original rectangle. find the length of original rectangle. 1 solutions Answer 392085 by ankor@dixie-net.com(15746)   on 2012-06-24 12:42:50 (Show Source): You can put this solution on YOUR website! Length of the rectangle exceeds its breadth by 7cm. if the length is decreased by 4cm. the area of the new rectangle is same as area of the original rectangle. find the length of original rectangle. : This does not seem possible, but assume it is : Let x = the width then (x+7) = the length and x(x+7) = the area : "if the length is decreased by 4cm. the area of the new rectangle is same as area of the original rectangle." x(x+3) = the new area therefore x(x+7) = x(x+3) divide both sides by x x + 7 = x + 3; no sense here

Rate-of-work-word-problems/623313: Working together, two pumps can drain a certain pool in hours. If it takes the older pump hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own? 1 solutions Answer 392083 by ankor@dixie-net.com(15746)   on 2012-06-24 12:39:57 (Show Source): You can put this solution on YOUR website! We need some numerical values here

Square-cubic-other-roots/623355: I was given the impression that this is more of a physics "problem" written in algebraic form. But since I am an undereducated 64 y/o, over drugged, bedridden invalid and saw this tattoo on the shoulder of my son's latest love interest (physics major), I am a bit concerned. It goes: C = 1 OVER THE SQUARE ROOT OF "ME". Is this a statement that she is wholly into "me" or does this imply something I might want to be concerned about. I know this is thoroughly out of the ordinary. I do appreciate anything you can tell me. Thanks. Linda Joiner (MIDASMUM@MAIL.COM) 1 solutions Answer 392078 by ankor@dixie-net.com(15746)   on 2012-06-24 12:15:52 (Show Source): You can put this solution on YOUR website! I could be referring to Einsteins famous equation e = m*c^2 where e=energy, m=mass, c=speed of light The equation can also be written c =

Numbers_Word_Problems/623345: what 4 digit number becomes 9x the original number when read backwards 1 solutions Answer 392070 by ankor@dixie-net.com(15746)   on 2012-06-24 11:03:33 (Show Source): You can put this solution on YOUR website! what 4 digit number becomes 9x the original number when read backwards : From the information given, we know that 1st digit has to be 1, then the last digit had to be 9*1 = 9 : 1st original digit = 1 (thousands) let a = 2nd original digit (100's) let b = 3rd original digit (10's) last original digit = 9 (units) : Nine times original number = reversed number : 9(1000 + 100a + 10b + 9) = 9000 + 100b + 10a + 1 9000 + 900a + 90b + 81 = 9000 + 100b + 10a + 1 combine like terms 900a + 90b + 9081 = 100b + 10a + 9001 900a - 10a + 90b - 100b + 9081 - 9001 = 0 890a - 10b + 80 = 0 simplify, divide by 10 89a - b + 8 = 0 b = 89a + 8 The only value for a that would give a single digit value for b would be 0 therefore a = 0 b = 8 Original number 1089 1089 * 9 = 9801 the reverse

Travel_Word_Problems/623178: In his motorboat, man can go downstream in 1 hour less time than he can go upstream the same distance. If the rate of the current is 5kph, how fast can he travel in still water if it takes him 2 hours to travel upstream the given distance? 1 solutions Answer 391997 by ankor@dixie-net.com(15746)   on 2012-06-23 15:34:10 (Show Source): You can put this solution on YOUR website! In his motorboat, man can go downstream in 1 hour less time than he can go upstream the same distance. If the rate of the current is 5kph, how fast can he travel in still water if it takes him 2 hours to travel upstream the given distance? : Let s = boat speed in still water then (s+5) = effective speed downstream (s-5) = effective speed upstream : write a distance equation, dist = speed/speed : Dist upstream = dist downstream 2(s-5) = 1(s+5) 2s - 10 = s + 5 2s - s = 5 + 10 s = 15 km/h in still water : : Check solution by finding the distances 2(15-5) = 20 km 1(15+5) = 20 km

Travel_Word_Problems/623135: Barry lives 26 miles from school. He walks a mile to the bus stop and takes the bus,which averages 20 mph. It takes Barry 5 minutes to walk from the campus bus stop to a classroom that is about a quarter of a mile away, and his class starts at 8:10 AM. What time does Barry have to leave home to make it to class on time? 1 solutions Answer 391959 by ankor@dixie-net.com(15746)   on 2012-06-23 12:26:25 (Show Source): You can put this solution on YOUR website! Barry lives 26 miles from school. He walks a mile to the bus stop and takes the bus, which averages 20 mph. It takes Barry 5 minutes to walk from the campus bus stop to a classroom that is about a quarter of a mile away, and his class starts at 8:10 AM. What time does Barry have to leave home to make it to class on time? : From the statement,"It takes Barry 5 minutes to walk from the campus bus stop to a classroom that is about a quarter of a mile away," 1 mi requires 4 * 5 = 20 min to walk to the bus stop : Riding the bus dist: 26 - 1 - .25 = 24.75 mi; 24.75/20 = 1.2375 * 60 = 74.25 min therefore 20 + 74.25 + 5 = 99.25 ~ 100 minutes to get to school Thats 1 hr and 40 min. He has to leave at 6:30 to make it by 8:10 :

Evaluation_Word_Problems/623150: Please help me solve this word problem of variation. The volume rate of flow R of blood through an artery varies directly as the fourth power of the radius r of the artery and inversly as the distance d along the artery. If an operation is successful in effectively increasing the radius of an artery by 25% and decreasing its length by 2%, by how much is the volume rate of flow increased? 1 solutions Answer 391949 by ankor@dixie-net.com(15746)   on 2012-06-23 11:22:09 (Show Source): You can put this solution on YOUR website! Write a proportion equation for each statement : "The volume rate of flow R of blood through an artery varies directly as the fourth power of the radius r of the artery and inversely as the distance d along the artery." R = : "If an operation is successful in effectively increasing the radius of an artery by 25% and decreasing its length by 2%, by how much is the volume rate of flow increased? : Assuming the radius and the dist were both 1, we have R = = R = 2.49 * 100 = 249% increase in blood flow

Exponents/623084: 1. Use the laws on exponents for multiplication and division in simplifying the following: a) 12m3 ● 6m7 b) (6x4 + x3)x5 c) (5y)4 d) 2x-2y4z3 8x3yz3 e) (m.1/3)12 1 solutions Answer 391941 by ankor@dixie-net.com(15746)   on 2012-06-23 11:07:17 (Show Source): You can put this solution on YOUR website! 1. Use the laws on exponents for multiplication and division in simplifying the following: ; a) 12m^3 ● 6m^7 = 72m^10; add exponents when you multiply : b) (6x^4 + x^3)x^5 = 6x^9 + x^8 : c) (5y)^4 = 5^4*y^4 = 625y^4 : d) ; divided the 2 into 8 Subtract exponents when you divide, we want our solution to have positive exponents = = = : e) = =; when you raise one exponent to another exponent, you multiply

Quadratic_Equations/623137: Glenn cuts half a rectangular lawn, 40x30, by mowing strips of equal width around the perimeter. Brad cuts the small rectangle left. How wide a strip does Glenn cut so that they share the work equally, I calculated the area of the lawn to be 1200m^2 and the perimeter to be 140m but don't know how to proceed from here. 1 solutions Answer 391931 by ankor@dixie-net.com(15746)   on 2012-06-23 10:22:30 (Show Source): You can put this solution on YOUR website! Glenn cuts half a rectangular lawn, 40x30, by mowing strips of equal width around the perimeter. Brad cuts the small rectangle left. How wide a strip does Glenn cut so that they share the work equally, : Then we know half the lawn will have an area of 600 sq/ft : Let x = the width of the strip to be cut equally around the outside of the lawn. then the remaining rectangle area: {40-2x)*(30-2x) = 600 : FOIL and arrange as a quadratic equation 1200 - 80x - 60x + 4x^2 - 600 = 0 4x^2 - 140x + 600 = 0 : Simplify, divide by 4 x^2 - 35x + 150 = 0 ; Factors to (x - 5)(x - 30) = 0 Two solutions but only one will make sense x = 5 ft strip all the way around to leave half the lawn remaining : : Check this by finding the dimensions and area of the remaining rectangle A five foot strip will subtract 10 ft from each dimension (40-10)(30-10) = 30 * 20 = 600 sq/ft : Did this makes sense to you?

Quadratic_Equations/623119: Using The Pythagorean Theorem Let a = x, and b = 2x + 4, so that c = 2x + 6. Please help 1 solutions Answer 391882 by ankor@dixie-net.com(15746)   on 2012-06-22 21:51:04 (Show Source): You can put this solution on YOUR website! Using The Pythagorean Theorem Let a = x, and b = 2x + 4, so that c = 2x + 6. : a^2 + b^2 = c^2, therefore: x^2 + (2x+4)^2 = (2x+6)^2 which is x^2 + 4x^2 + 16x + 16 = 4x^2 + 24x + 36 combine like terms on the left x^2 + 4x^2 - 4x^2 + 16x - 24x + 16 - 36 = 0 we have left x^2 - 8x - 20 = 0 Factors to (x-10)(x+2) = 0 the positive solution is what we want here x = 10 : The threes side of the triangle a = 10 b = 2(10)+4 = 24 c = 2(10)+6 = 26 : : Check this on your calc: enter results: 26

Numeric_Fractions/623117: What is the value of X if : 1/4 divided by X equals 1/6 What is the value of X ? 1 solutions Answer 391880 by ankor@dixie-net.com(15746)   on 2012-06-22 21:41:31 (Show Source): You can put this solution on YOUR website! What is the value of X if : 1/4 divided by X equals 1/6 = invert the divisor and multiply * = : = Cross multiply 4x = 6 x = 6/4 x = 3/2 or 1

Quadratic_Equations/623060: Find all the real solutions of the equation by first rewriting the equation as a quadratic equation. (Enter your answers as a comma-separated list.) x6 + x3 − 6 = 0 1 solutions Answer 391871 by ankor@dixie-net.com(15746)   on 2012-06-22 19:15:15 (Show Source): You can put this solution on YOUR website! x^6 + x^3 − 6 = 0 can be factored to (x^3 - 2)(x^3 + 3) = 0 two solutions x = . that's cube root of 2 , x = the cube root of -3

�t�e�s�t/623038: Correction: your tutor lynnlo provides wrong answers to many problems he tries to answer, last example see below. Please provide the correct solution. Question 622925: If x+1/x=4 find x^4+1/x^4 Answer by lynnlo(517) 4x^2+1/x4 1 solutions Answer 391801 by ankor@dixie-net.com(15746)   on 2012-06-22 15:05:21 (Show Source): You can put this solution on YOUR website! If = 4 x + 1 = 4x 1 = 4x -x 1 = 3x x = : find = = = = 82

Travel_Word_Problems/623022: A boat is traveling in a river at a speed of 9 miles per hour. The river has a current of 7 miles per hour. If the boat's destination is a dock located 5 miles upstream, what will be the total trip time for the boat? 1 solutions Answer 391790 by ankor@dixie-net.com(15746)   on 2012-06-22 14:40:25 (Show Source): You can put this solution on YOUR website! A boat is traveling in a river at a speed of 9 miles per hour. The river has a current of 7 miles per hour. If the boat's destination is a dock located 5 miles upstream, what will be the total trip time for the boat? : The effective speed of the boat will be 9-7 = 2 mph time = 5/2 = 2.5 hrs

Age_Word_Problems/622976: Paul and his brothers Ted and Al worked out one day that their father was 3 times as old as Ted. Also that, in three years time, he would be three times as old as Paul would be, and that in 6 years time he would be twice as old as Al would be. Al was two years older than Ted. How old is their father? 1 solutions Answer 391775 by ankor@dixie-net.com(15746)   on 2012-06-22 13:49:13 (Show Source): You can put this solution on YOUR website! Write an equation for each statement: : Paul and his brothers Ted and Al worked out one day that their father was 3 times as old as Ted. f + 3t : Also that, in three years time, he would be three times as old as Paul would be, f + 3 = 3(p+3) f + 3 = 3p + 9 f = 3p + 9 - 3 f = 3p + 6 : and that in 6 years time he would be twice as old as Al would be. f + 6 = 2(a+6) f + 6 = 2a + 12 f = 2a + 12 - 6 f = 2a + 6 : Al was two years older than Ted. a = t + 2 In the equation f = 2a + 6 replace f with 3t 3t = 2a + 6 Replace a with (t+2),find t 3t = 2(t+2) + 6 3t = 2t + 4 + 6 3t - 2t = 10 t = 10 yrs is Teds present age then 3(10) = 30 yrs is father's age, which all they wish to know :

Proportions/622912: I'm confused about percents, and obtaining specific numbers using the decimals of percents of over 100%. For example I want to obtain a product of 75,000 using 103% value. So what I do is this: (75,000 / 0.97) * 1.03 = 74932.5 I NEVER get exactly 75,000 value using the 103%. I want it exactly 75,000! Thanks in advance. 1 solutions Answer 391750 by ankor@dixie-net.com(15746)   on 2012-06-22 09:36:59 (Show Source): You can put this solution on YOUR website! obtain a product of 75,000 using 103% value. : Let x = amt required to accomplish this : 1.03x = 75000 x = x = $72,815.53

Rate-of-work-word-problems/622900: two taps can fill a tank in 15 and 12 minutes respectively.a third tap can empty it in 20 minutes.if all the taps are opened at the same time then in how much time will the tank be filled?? 1 solutions Answer 391688 by ankor@dixie-net.com(15746)   on 2012-06-21 22:26:39 (Show Source): You can put this solution on YOUR website! two taps can fill a tank in 15 and 12 minutes respectively. a third tap can empty it in 20 minutes. if all the taps are opened at the same time then in how much time will the tank be filled? : Let t = time required when all three taps are open. Let the completed job = 1; (a full tank) : A typical shared work equation. : Fill + Fill - Empty = a full tank + - = 1 multiply by 60 to clear the denominators, results 4t + 5t - 3t = 60 6t = 60 t = 60/6 t = 10 minutes with all taps open

Triangles/622846: if the angle of the triangle is 70 , 3y-20 , and y+10 . . . what does y equal 1 solutions Answer 391683 by ankor@dixie-net.com(15746)   on 2012-06-21 21:54:02 (Show Source): You can put this solution on YOUR website! if the angle of the triangle is 70 , 3y-20 , and y+10 . . . what does y equal : We know the 3 angles of a triangle add up to 180 therefore 70 + (3y-20) + (y+10) = 180 Combine like terms 3y + y + 70 - 20 + 10 = 180 : 4y + 60 = 180 : 4y = 180 - 60 : 4y = 120 y = y = 30 : : Check this by finding the other angles and their sum 70 + 3(30)- 20 + (30+10) 70 + 70 + 40 = 180

Equations/622823: what is the answer for x/ 2x+6=-50 what is the easiest way to do it ? How About the answer to (6x-8x)-3x=75? 1 solutions Answer 391674 by ankor@dixie-net.com(15746)   on 2012-06-21 20:28:26 (Show Source): You can put this solution on YOUR website! what is the answer for x/ 2x+6=-50 Multiply both sides by (2x+6) and you have x = -50(2x+6) x = -100x - 300 x + 100x = -300 101x = -300 x = x = -2.9703 : answer to (6x-8x)-3x=75? combine like terms 6x - 8x - 3x = 75 -5x = 75 divide both sides by -5 x = x = -15

Equations/622825: 1 solutions Answer 391650 by ankor@dixie-net.com(15746)   on 2012-06-21 17:12:55 (Show Source): You can put this solution on YOUR website! multiply both sides by (x+1), clear the denominators, results: 4x + x(x+1) = -6 4x + x^2 + x = -6 Arrange as a quadratic equation x^2 + 5x + 6 = 0 Factors to (x+3)(x+2) = 0 two solutions x = -3 and x = -2 ; : Check solution of x=-3 in the original problem +6 - 3 = +3; confirms our solution of x=-3 : You can can check the x=-2 solution yourself

Proportions/622824: 1 solutions Answer 391647 by ankor@dixie-net.com(15746)   on 2012-06-21 17:04:18 (Show Source): You can put this solution on YOUR website! A single fraction on each side of the equal side, we can use the "cross multiply" method 16x = 4(2-x) 16x = 8 - 4x 16x + 4x = 8 20x = 8 x = 8/20 x = .4 : : Check this in the original problem, replace x with .4 10 = 10; confirms our solution of x=.4