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 Rate-of-work-word-problems/171652: An oil tank at a refinery has two inlet pipes and one outlet pipe. One inlet pipe can fill the tank in 6h, and the other inlet pipe can fill the tank in 12h. The outlet pipe can empty the tank in 24h. How long would it take to fill the tank with all three pipes open? Please, hep me with this problem, i'm trying since friday to solve it =( Tank you1 solutions Answer 126790 by ankor@dixie-net.com(15656)   on 2008-12-06 12:45:44 (Show Source): You can put this solution on YOUR website!An oil tank at a refinery has two inlet pipes and one outlet pipe. One inlet pipe can fill the tank in 6h, and the other inlet pipe can fill the tank in 12h. The outlet pipe can empty the tank in 24h. How long would it take to fill the tank with all three pipes open? : Let the full tank = 1; + for filling, - for draining : Let t = time required when all three pipes are open: + - = 1 Multiply equation by 24 to get rid of the denominators, results: 4t + 2t - t = 24 : 5t = 24 t = t = 4.8 hrs to fill when all pipes are open : : Check solution using a calc: + - .8 + .4 - .2 = 1 : : Not that hard, right?
 test/171635: Two men start from the same corner "A", going in different directions around a field 1 mile square. The man going along AB walks 4 miles an hour, and the other man who is traveling AD goes 3 miles an hour. Where and after how long will they meet?1 solutions Answer 126789 by ankor@dixie-net.com(15656)   on 2008-12-06 12:35:32 (Show Source): You can put this solution on YOUR website!Two men start from the same corner "A", going in different directions around a field 1 mile square. The man going along AB walks 4 miles an hour, and the other man who is traveling AD goes 3 miles an hour. Where and after how long will they meet? : The perimeter (ABCD) of the square = 4 mi : The two men will have traveled a total distance of 4 mi when they meet. there: Let d = distance traveled by the 1st guy when they meet from "A" Then (4-d) = distance traveled by the 2nd guy when they meet : The travel times of both men will be the same Write time equation: Time = : A's time = B's time = Cross multiply to find d 3d = 4(4-d) 3d = 16 - 4d 3d + 4d = 16 7d = 16 d = miles traveled by the 1st guy Which would put him between C & D, actually 2/7 mi from C : Find the travel time of A, who is traveling 4 mph: * = hrs or 34.3 min : : Check solution using the 2nd man traveling 3 mph, find his distance (4-d) : 4 - = - = mi for the 2nd guy That would put him between D & C, actually 5/7 mi from D : Find the travel time of the 2nd guy who is traveling at 3 mph * = hrs or 34.3 min as it should be; : : Did this procedure make sense to you?
 Distributive-associative-commutative-properties/171489: Dividing: 2x+14/7x divided by (2x^2+14x)1 solutions Answer 126778 by ankor@dixie-net.com(15656)   on 2008-12-06 10:48:14 (Show Source): You can put this solution on YOUR website!We can write it like this: : * Factor * Factor out 2 and (x+7) * =
 Rate-of-work-word-problems/171592: Mrs.Santos can finish 4 placemats for every 3 that her daughter finishes.If Mrs. Santos finishes 16 placemats in one week,how many placemats in all can mother and daughter finish together in 4 weeks?1 solutions Answer 126738 by ankor@dixie-net.com(15656)   on 2008-12-05 21:47:12 (Show Source): You can put this solution on YOUR website!Mrs.Santos can finish 4 placemats for every 3 that her daughter finishes.If Mrs. Santos finishes 16 placemats in one week,how many placemats in all can mother and daughter finish together in 4 weeks : Find out how many placemats Mom can make in 1 day: placemats per day : Find out how many placemats daughter to make in 1 day * = placemats per day : Together they can make: + = 28/7 = 4 placemats per day : 4 weeks = 28 days, therefore: 28 * 4 = 112 placemats in 4 weeks
 Quadratic-relations-and-conic-sections/171023: Hi! I need to determine the equation of a parabola in the form y-k=a(x-h)^2 I am given 2 points on the graph (0,6) and (14,0) I am given Part of V (9,k) I have tried so many things, but nothing is even close to what it should be and I am ending up just writing the question over and over and now I am fully frustrated. I know I have to use both points given in order to get "a" and "k" and I probably have to substitute or eliminate but with two unknowns I have no idea how to go about it! Any help would be seriously appreciated!1 solutions Answer 126735 by ankor@dixie-net.com(15656)   on 2008-12-05 21:27:02 (Show Source): You can put this solution on YOUR website!determine the equation of a parabola in the form y-k=a(x-h)^2 I am given 2 points on the graph (0,6) and (14,0) I am given Part of V (9,k); I assume this means h=9 ; Two equations: : 0,6: 6 - k = a(0 - 9)^2 6 - k = 81a or 81a + k = 6 : 14, 0 0 - k = a(14-9)^2 0 - k = a(5)^2 25a + k = 0 ; Eliminate k, find a 81a + k = 6 24a + k = 0 -------------subtraction eliminates k 56a = 6 a = a = : Find k using 25a + k = 0 25*() + k = 0 + k = 0 k = : The equation: y = (x - 9)^2 - : Plots this: : Looks about right
 Expressions-with-variables/170899: Equations with two variables: Solve for x and y: 8x + 2y = 7 3x - 4y = 5 Could you please, give me the answer by parts? I will appreciate if you give me the answer, and understand the questions by parts, because I need to learn who to resolve this type equations? thank you for your help. jessica1 solutions Answer 126173 by ankor@dixie-net.com(15656)   on 2008-12-03 09:43:37 (Show Source): You can put this solution on YOUR website!Solve for x and y: 8x + 2y = 7 3x - 4y = 5 : There are two ways to solve these, elimination and substitution. Elimination: You multiply one or both equations so when the equations are added or subtracted, one of the variables is eliminated. Then it is easy to solve for the other variable: : Multiply the 1st equation by 2 and you have: 16x + 4y = 14 3x - 4y = 5 ----------------Adding will eliminate y: 19x + 0y = 19 or 19x = 19 x = x = 1 : Now substitute 1 for x in one of the original equations, we'll use the 1st one. 8(1) + 2y = 7 8 + 2y = 7 2y = 7 - 8; subtracted 8 from both sides 2y = -1 y = : Check solutions by substituting both solutions in the 2nd original equation. 3(1) - 4(-1/2) = 5 3 + 2 = 5; remember minus a minus is a plus : Did this help you understand these problems?
 Travel_Word_Problems/170799: At 7:00 a.m., Joe starts jogging at 6 mph. At 7:10 a.m., Ken starts off after him. How fast must Ken run in order to overtake him at 7:30 a.m.?1 solutions Answer 126119 by ankor@dixie-net.com(15656)   on 2008-12-02 21:59:21 (Show Source): You can put this solution on YOUR website!At 7:00 a.m., Joe starts jogging at 6 mph. At 7:10 a.m., Ken starts off after him. How fast must Ken run in order to overtake him at 7:30 a.m.? : From the information given we can say: Joe's travel time = hr Ken's travel time = hr : Let s = Ken's jogging speed : When Ken overtakes Joe, they will have traveled the same distance Write a distance equation from this fact; Dist = Time * speed : Kens dist = Joe's dist s = *6 : Multiply both sides by 6 to get rid of the denominators 2s = 3*6 2s = 18 s = 9 mph is Ken's speed : : Check solution by finding the dist: * 9 = 3 mi * 6 = 3 mi
 Age_Word_Problems/170690: Erin's age is 3 times Warren's. In 4 years she will be twice as old as he will be. How old is each now? Help, thank you.1 solutions Answer 126117 by ankor@dixie-net.com(15656)   on 2008-12-02 21:45:06 (Show Source): You can put this solution on YOUR website!Let e = Erin's age now Let w = Warren's age now ; Write an equation for each statement: : "Erin's age is 3 times Warren's." e = 3w : " In 4 years she will be twice as old as he will be." e + 4 = 2(w+4) Simplify e + 4 = 2w + 8 e = 2w + 8 - 4 e = 2w + 4 ; How old is each now? : Substitute 3w for e in the above equation 3w = 2w + 4 3w - 2w = 4 w = 4 yr is Warrens age now : I'll let you find Erin's age now : Check your solutions in the statement: "In 4 years she will be twice as old as he will be."
 Expressions-with-variables/170669: I need a little help with this one. Thanks so much. The question asks to simplify: (-2a^2b^3)^2 / (2a^2b)^3 i came up with ab^7 but i don't know for sure if it's correct. Any help would be appreciated.1 solutions Answer 126108 by ankor@dixie-net.com(15656)   on 2008-12-02 20:56:44 (Show Source): You can put this solution on YOUR website! : I'm not sure how you got that answer, but let's just go thru it. : You multiply the numerator exponents by 2; (-2^2 = +4) Multiply the denominator exponents by 3 (2^3=8) and we have : Combine the exponents of like terms, in a manner to ensure they are positive: = : did this make sense to you?
 Human-and-algebraic-language/170681: Imagine a rope wrapped around Earth at the equator (Earth's circumference C). Then think of adding d feet to the rope's length so it can now circle Earth at a distance h feet above the equator at all points. Length of rope = C + d Write an equation to model this situation.1 solutions Answer 126081 by ankor@dixie-net.com(15656)   on 2008-12-02 19:29:37 (Show Source): You can put this solution on YOUR website!Imagine a rope wrapped around Earth at the equator (Earth's circumference C). Then think of adding d feet to the rope's length so it can now circle Earth at a distance h feet above the equator at all points. Length of rope = C + d Write an equation to model this situation. : 2*pi*r = C and 2*pi*(r+h) = C+d : Substitute (2*pi*r) for C 2*pi*(r+h) = 2*pi*r + d : Multiply what's inside the brackets (2*pi*r) + (2*pi*h) = (2*pi*r) + d : Subtract (2*pi*r) from both sides 2*pi*h = d; the equation to find d : Divide both sides by 2pi h = ; the equation to find h
 Numbers_Word_Problems/170677: Find a five digit number in which the second and fourth digits are the same, the third digit is the sum of the first and second, the fifth digit is the sum of the third and fourth and the third digit is one more than the first and one less than the fifth. The sum of all the digits is 14.1 solutions Answer 126073 by ankor@dixie-net.com(15656)   on 2008-12-02 19:00:13 (Show Source): You can put this solution on YOUR website!Find a five digit number in which the second and fourth digits are the same, ABCBE : the third digit is the sum of the first and second, C = A+B : the fifth digit is the sum of the third and fourth E = C + B : the third digit is one more than the first C = A + 1 A = C - 1 : Also the third digit is one less than the fifth. C = E - 1 E = C + 1 ; The sum of all the digits is 14. A + B + C + B + E = 14 A + 2B + C + E = 14 : Looking at our equations we see: E = C + B And E = C + 1 Therefore B = 1 : Substituting 1 for B in the Sum equation A + 2(1) + C + E = 14 A + C + E = 14 - 2 A + C + E = 12 : Substitute (C-1) for A, and (C+1) for E, find C (C-1) + C + (C+1) = 12 3C = 12 C = 4 Then A = 4 - 1 A = 3 and E = 4 + 1 E = 5 : Our number is: 31415 : : Check solution: the third digit is the sum of the first and second, 4 = 3 + 1 : the fifth digit is the sum of the third and fourth 5 = 4 + 1 : and the third digit is one more than the first and one less than the fifth. 4 = 3 + 1 : The sum of all the digits is 14. 3 + 1 + 4 + 1 + 5 = 14
 Systems-of-equations/170556: Find the equation, in slope-intercept form, of the line that passes through the points (5, 2) and (-7, 3). Write the equation in slope-intercept form. 1 solutions Answer 125961 by ankor@dixie-net.com(15656)   on 2008-12-01 21:53:34 (Show Source): You can put this solution on YOUR website!Find the equation, in slope-intercept form, of the line that passes through the points (5, 2) and (-7, 3). Write the equation in slope-intercept form. : Find the slope using the slope formula: m = Assign the values as follows: x1 = 5; y1 = 2 x2 = -7; y2 = 3 : m = = = : Use the point slope formula: y - y1 = m(x - x1) : y - 2 = (x - 5) : y - 2 = x + : y = x + + 2 : y = x + + : y = x + ; the slope/intercept form
 Expressions-with-variables/170453: This question is from textbook Introductory Algebra Solve the problem. Karin biked at 13 mph for a time but got a flat tire. She then walked at 5 mph. She traveled a total of 93 miles. Had she biked the whole time, she would have gone 117 miles. How many hours did she walk?1 solutions Answer 125859 by ankor@dixie-net.com(15656)   on 2008-12-01 09:46:25 (Show Source): You can put this solution on YOUR website!Karin biked at 13 mph for a time but got a flat tire. She then walked at 5 mph. She traveled a total of 93 miles. Had she biked the whole time, she would have gone 117 miles. : How many hours did she walk? : We know that if she biked the whole way, travel time would be: 117/13 = 9 hrs : This is also the travel time of walking and riding a total of 93 mi, implied by the phrase."Had she biked the whole time" : Find the distance she walked, first. Let d = distance walked Then (93-d) = distance she rode : Write a time equation: Time = dist/speed: : walking time + riding time = 9 hrs + = 9 : Multiply equation by 65 to get rid of the denominators, results: 13d + 5(93-d) = 65(9) : 13d + 465 - 5d = 585 : 13d - 5d = 585 - 465 : 8d = 120 d = d = 15 miles walked the = 3 hrs walking : Check solution, find the distance riding: = 6 hr so we have: 3 + 6 hrs = 9 hrs
 Percentage-and-ratio-word-problems/170208: This question is from textbook A Problem Solving Approach to Mathematics for Elementary School Teachers When Professor Sum was asked by Mr. Little how many students were in his classes, he answered, All of them study either languages, physics, or not at all. One-half of them study languages only, one-fourth of them study French, one-seventh of them study physics only, and 20 do not study at all. How many students does Professor Sum have1 solutions Answer 125685 by ankor@dixie-net.com(15656)   on 2008-11-30 11:36:30 (Show Source): You can put this solution on YOUR website!All of them study either languages, physics, or not at all. One-half of them study languages only, one-fourth of them study French, one-seventh of them study physics only, and 20 do not study at all. How many students does Professor Sum have : Let x = no. of students he has : "One-half of them study languages only, .x " one-fourth of them study French," x : " one-seventh of them study physics only," x and 20 do not study at all. How many students does Professor Sum have : The French students are included with the languages, so we have: x = x + x + 20 Multiply equation by 14 14x = 7x + 2x + 280 : 14x - 9x = 280 x = x = 56 students
 Surface-area/170130: A garden is in the shape of a rectangle, 20 metres by 8 metres. Around the outside is a border of uniform width and in the middle is a square pond. The width of the border is the same as the width of the pond. The size of the area, which is not occupied by either border or pond, is 124m^2. Find the width of the border.1 solutions Answer 125637 by ankor@dixie-net.com(15656)   on 2008-11-29 21:41:49 (Show Source): You can put this solution on YOUR website!A garden is in the shape of a rectangle, 20 meters by 8 meters. Around the outside is a border of uniform width and in the middle is a square pond. The width of the border is the same as the width of the pond. The size of the area, which is not occupied by either border or pond, is 124m^2. Find the width of the border. : Let x = the width of the border and also the width of the pond Then x^2 = area of the pond and (20*8) - x^2 = (160-x^2) = area of the garden (minus the pond) therefore: 160 - x^2 = 124 -x^2 = 124 - 160 -x^2 = -36 x^2 = 36 x = x = 6 meters is the width of the border : : Check solution 20 by 8 area - pond area = 160 - 6^2 = 160 - 36 = 124
 Polynomials-and-rational-expressions/170072: perform the indicated operation 5/x^2-49 + 2x+1/x^2+7x1 solutions Answer 125635 by ankor@dixie-net.com(15656)   on 2008-11-29 21:19:16 (Show Source): You can put this solution on YOUR website! + Factor + The common denominator: x(x-7)(x+7) = =
 Expressions-with-variables/170005: Could you help me solve this problem? if y varies inversely as x^2, and y=2 when x=4, what is the constant of the variation? 2? Thank you.1 solutions Answer 125606 by ankor@dixie-net.com(15656)   on 2008-11-29 19:05:40 (Show Source): You can put this solution on YOUR website!If y varies inversely as x^2," equation for this is: y; inversely means, when x increases, y decrease : y=2 when x=4, what is the constant of the variation? : Substituting for y and x we have: 2 = 2 = Multiply both sides by 16 2*16 = k : k = 32; (the constant of variation) : : Check this: using k=32 and x=4 y = y = y = 2
 logarithm/170044: 1.find the domain of the function f(x) = ln (8x-24) 2. simplify log (1/10) 3. write as a single logarithm and simplify (no decimal approximations) 2 log 6 + log x - log 2 4. expand and simplify (no approximations: ln(ex)1 solutions Answer 125603 by ankor@dixie-net.com(15656)   on 2008-11-29 18:52:50 (Show Source): You can put this solution on YOUR website!1.find the domain of the function f(x) = ln (8x-24) : We can't have a negative value, (or 0) therefore: Domain: |x| x > 3 : : 2. simplify log (1/10) : We can use the reciprocal of (1/10): -1*log(10) : we know the log of 10 = 1 -1*1=-1 : : 3. write as a single logarithm and simplify (no decimal approximations) : 2 log 6 + log x - log 2 log(18x) : : 4. expand and simplify (no approximations: ln(ex) : ln(e) + ln(x) : We know the ln of e = 1, therefore: ln(x) + 1
 Polynomials-and-rational-expressions/170010: Please Help. Thank You. Increasing cube. Each of the three sides of a cube with sides of x centimeters is increased by a whole number of centimeters. The new volume in cubic centimeters is given by V(X)= x^3 + 10x^2 + 31x + 30. a) Find V(3). b) If the new height is x + 2 centimeters, then what are the new length and width? c) Find the volume when x =3 by multiplying the length, width, and height.1 solutions Answer 125508 by ankor@dixie-net.com(15656)   on 2008-11-28 21:52:41 (Show Source): You can put this solution on YOUR website!Increasing cube. Each of the three sides of a cube with sides of x centimeters is increased by a whole number of centimeters. The new volume in cubic centimeters is given by V(X)= x^3 + 10x^2 + 31x + 30. : a) Find V(3). : V(3)= 3^3 + 10(3^2) + 31(3) + 30. V(3) = 27 + 90 + 93 + 30 V(x) = 240 cu/cm : : b) If the new height is x + 2 centimeters, then what are the new length and width? : Divide x^3 + 10x^2 + 31x + 30 by (x+2); using synthetic division: ......________________ -2 | 1 + 10 + 31 + 30 : you get: x^2 + 8x + 15 as length * width Factor this to get the length and the width (x + 5)(x + 3) : : c) Find the volume when x = 3 by multiplying the length, width, and height : Just substitute 3 for x in (x+2), (x+5), (x+3) : Multiply these these values to find the volume
 Linear-equations/170041: Solve the non-linear system of equations. Give Exact Values: 1 solutions Answer 125506 by ankor@dixie-net.com(15656)   on 2008-11-28 20:53:50 (Show Source): You can put this solution on YOUR website! : Multiply the 1st equation by 2 and subtract from the 2nd equation: --------------------subtraction eliminates y^2 x^2 = 9 x = x = +/-3 : Find y y^2 = 16 y = y = +/-4 : : Check solutions in 2nd equation
 Numeric_Fractions/170024: Barn painting. Melanie can paint a certain barn by herself in x days. Her helper Melissa can paint the same barn by herself in 2x days. Write a rational expression for the fraction of the barn that they complete in one day by working together. Evaluate the expression for x  5.1 solutions Answer 125505 by ankor@dixie-net.com(15656)   on 2008-11-28 20:44:41 (Show Source): You can put this solution on YOUR website!Barn painting. Melanie can paint a certain barn by herself in x days. Her helper Melissa can paint the same barn by herself in 2x days. Write a rational expression for the fraction of the barn that they complete in one day by working together : Let the completed job = 1 : + = = : Evaluate the expression for x = 5 : = of the barn painted in one day :