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Quadratic_Equations/319980: A square field had 5 meters added to the length and 2 meters to its width. The field then had an area of 130 meters squared. Find the length of a side of the original field. 1 solutions Answer 229168 by ankor@dixie-net.com(15645)   on 2010-07-05 21:59:23 (Show Source): You can put this solution on YOUR website! A square field had 5 meters added to the length and 2 meters to its width. The field then had an area of 130 meters squared. Find the length of a side of the original field. : Let x = side of original field then (x+5) = the new length and (x+2) = the new width : L * W = 130 (x+5)(x+2) = 130 FOIL x^2 + 2x + 5x + 10 = 130 : x^2 + 7x + 10 - 130 = 0 : x^2 + 7x - 120 = 0 Factor (x + 15)(x - 8) = 0 The positive solution is what we want here x = 8 meters, side of original square ; : Check solution by finding the area of the new rectangle (8+5)*(8+2) = 130

Percentage-and-ratio-word-problems/319979: If cement, gravel, and sand are to be mixed in the ratio of 3:5:7 respectively, and 5 tons of cement are available, how many tons of the mixture can be made? (Assume that enough gravel and sand are available to use all the available cement.) 1 solutions Answer 229166 by ankor@dixie-net.com(15645)   on 2010-07-05 21:51:11 (Show Source): You can put this solution on YOUR website! If cement, gravel, and sand are to be mixed in the ratio of 3:5:7 respectively, and 5 tons of cement are available, how many tons of the mixture can be made? (Assume that enough gravel and sand are available to use all the available cement.) : We can do it this way, let x = the multiplier 3x:5x:7x : Find the multiplier using the cement which was given 3x = 5 x = is the multiplier : Gravel:5 * = = 8.33 tons Sand: 7 * = = 11.67 tons : Total mixture: 5 + 8.33 + 11.67 = 25 tons

Linear_Equations_And_Systems_Word_Problems/320000: If 8 is substituted for x in the rational expression x - 8/x^2 - 64, the result is 0/0. It is said, "Any number divided by itself is 1." Does this mean that this expression is equal to 1 for x=8? Explain why or why not? 1 solutions Answer 229164 by ankor@dixie-net.com(15645)   on 2010-07-05 21:38:58 (Show Source): You can put this solution on YOUR website! No, you can't divide any number by 0

Functions/319923: The function H described by H(x)=2.75x+71.48 can be used to predict the height, in centimeters, of a woman whose humerus is x cm long. Predict the height of a woman whose humerus is 32 cm long. Please help I am stuck 1 solutions Answer 229163 by ankor@dixie-net.com(15645)   on 2010-07-05 21:36:26 (Show Source): You can put this solution on YOUR website! The function H described by H(x)=2.75x+71.48 can be used to predict the height, in centimeters, of a woman whose humerus is x cm long. Predict the height of a woman whose humerus is 32 cm long. : All you have to do is replace x with 32 and do the math H(32) = 2.75(32) + 71.28

Numbers_Word_Problems/319968: Please help me solve the word problem: Find the doubling time for money invested at 3% compounded continuously. 1 solutions Answer 229160 by ankor@dixie-net.com(15645)   on 2010-07-05 21:30:39 (Show Source): You can put this solution on YOUR website! Find the doubling time for money invested at 3% compounded continuously. : The continuous interest formula = A where P = initial amt (in this problem we will use 1) r = interest rate in decimal form, (.03) t = no. of years A = resulting amt; (in this problem it will be 2) : = 2 using natural logs = ln(2) log equiv of exponents .03t*ln(e) = ln(2) Find the nat log of both side. (nat log of e = 1) .03t = .693 t = t = 23.1 yrs to double at 3% : : Confirm this on a calc: enter e^(.03*23.1) results: 1.9997 ~ 2

Square-cubic-other-roots/319751: If x-1/x =5; find the value of x+1/x 1 solutions Answer 229156 by ankor@dixie-net.com(15645)   on 2010-07-05 21:03:43 (Show Source): You can put this solution on YOUR website! If x-1/x =5; find the value of x+1/x : Find the value of x = 5 x - 1 = 5x -1 = 5x - x -1 = 4x x = x = -.25 : Substitute -.25 for x in: = = = -3

Exponential-and-logarithmic-functions/319944: Please help me solve this equation: 2log7(x-1)=4log7(2) 1 solutions Answer 229137 by ankor@dixie-net.com(15645)   on 2010-07-05 19:00:49 (Show Source): You can put this solution on YOUR website! 2log7(x-1)=4log7(2) Use the exponent form log7((x-1)^2) = log7(2^4) FOIL log7(x^2-2x+1) = log7(16) Therefore: x^2 - 2x + 1 = 16 : x^2 - 2x + 1 - 16 = 0 : x^2 - 2x - 15 = 0 Factor (x-5)(x+3) = 0 Two solutions, but only the positive solution will work here x = 5 : : You can confirm this: log7((5-1)^2) = log7(2^4) log7(4^2) = log7(16)

Word_Problems_With_Coins/319875: I have 8 pennies and some quarters, nickels, and dimes. The number of pennies plus nickels equals the number of dimes. I have 3 quarters for every 2 pennies and 3 dimes for every 2 quarters. How many coins are nickels? 1 solutions Answer 229132 by ankor@dixie-net.com(15645)   on 2010-07-05 18:41:15 (Show Source): You can put this solution on YOUR website! I have 8 pennies and some quarters, nickels, and dimes. The number of pennies plus nickels equals the number of dimes. I have 3 quarters for every 2 pennies and 3 dimes for every 2 quarters. How many coins are nickels? : "The number of pennies plus nickels equals the number of dimes." d = n + 8 : " I have 3 quarters for every 2 pennies" q = 3(8/2) q = 12 : "and 3 dimes for every 2 quarters." d = 3(2q) d = 6q : q = 12 therefore d = 6(12) d = 72 dimes : How many coins are nickels? d = n + 8 72 = n + 8 72 - 8 = n n = 64 nickels

Circles/319920: If a circle has an area of 94.99 cm2, what is the length of the radius? 1 solutions Answer 229120 by ankor@dixie-net.com(15645)   on 2010-07-05 17:44:36 (Show Source): You can put this solution on YOUR website! If a circle has an area of 94.99 cm2, what is the length of the radius? = 94.99 r = r = 5.49875 is the radius

Expressions-with-variables/319854: I can not figure out how to use elimination method can you please help me? 3r-5s=-7 5r+3s=45 Thank you 1 solutions Answer 229104 by ankor@dixie-net.com(15645)   on 2010-07-05 16:36:21 (Show Source): You can put this solution on YOUR website! use elimination method 3r - 5s = -7 5r + 3s = 45 : We are going to multiply each equation by a value that will make the coefficient of s in each equation to be equal : Multiply the 1st equation by 3, multiply the 2nd equation by 5, results 9r - 15s = -21 25r+ 15s = 225 ------------------adding eliminates s, find r 34r + 0s = 204 r = r = 6 : Use the 2nd original equation to find s, substitute 6 for r 5(6) + 3s = 45 30 + 3s = 45 3s = 45 - 30 3s = 15 s = s = 5 ; : Check solutions in the original 1st equation 9r - 15s = -21 9(6) - 15(5) = 54 - 75 = -21; confirms our solutions, Make sense to you now?

Miscellaneous_Word_Problems/319898: How do you do this algebraically? In a race, the top speed of one car is nine tenths of the top speed of another. After one half hour the faster car is 10 km ahead of the slower car. Find the rate of each car, assuming they started side by side. 1 solutions Answer 229097 by ankor@dixie-net.com(15645)   on 2010-07-05 16:06:55 (Show Source): You can put this solution on YOUR website! In a race, the top speed of one car is nine tenths of the top speed of another. After one half hour the faster car is 10 km ahead of the slower car. Find the rate of each car, assuming they started side by side. : Let s = faster car speed then .9s = speed of the slower car : Write a dist equation; dist = speed * time : Fast car dist - slower car dist = 10 km .5s - .5(.9s) = 10 .5s - .45s = 10 .05s = 10 s = s = 200 km/hr is the faster car then .9(200) = 180 km/hr is the slower car : : Check solution by finding the dist each traveled in .5 hrs .5(200) = 100 km .5(180) = 90 km ------------------ dist dif: 10 km

Circles/319662: Points A,B and C lie on a circle and form an equilateral triangle. If AB = 12 what is the circumference of the circle. 1 solutions Answer 228931 by ankor@dixie-net.com(15645)   on 2010-07-04 19:16:28 (Show Source): You can put this solution on YOUR website! Points A,B and C lie on a circle and form an equilateral triangle. If AB = 12 what is the circumference of the circle. : Draw this out. The centroid of the equilateral triangle is also the center of circle. The hypotenuse of the triangle formed by drawing the medians through the center is also the radius (r). : Cos(30) = .866r = 6 r = r = 6.93 Find the circumference C = C = 43.53

Age_Word_Problems/319636: a son is half as old as his father.12 years ago the son was one third as old as his father. how is each now? 1 solutions Answer 228905 by ankor@dixie-net.com(15645)   on 2010-07-04 12:09:27 (Show Source): You can put this solution on YOUR website! Let s = son's age Let f = father's age : Write an equation for each statement : "a son is half as old as his father." s = f : "12 years ago the son was one third as old as his father." s - 12 = (f - 12) multiply each side by 3, to get rid of the fraction 3(s - 12) = f - 12 3s - 36 = f - 12 3s = f - 12 + 36 3s = f + 24 Replace s with f, (from the 1st statement) 3(f) = f + 24 (f = f + 24 Multiply both sides by 2 to get rid of the fraction, results: 3f = 2(f + 24) 3f = 2f + 48 3f - 2f = 48 f = 48 yrs is father's present age then *48 = 24 yrs is son's present age : : Check solutions in the statement "12 years ago the son was one third as old as his father." 24 - 12 = (48 - 12) 12 = *36, confirms our solutions

Miscellaneous_Word_Problems/319408: Find a counterexample to the statement: The cube of a number added to the sum of three times the number and 3 is a prime number. Justify your solution by supporting it with step by step work. 1 solutions Answer 228904 by ankor@dixie-net.com(15645)   on 2010-07-04 11:37:29 (Show Source): You can put this solution on YOUR website! Find a counterexample to the statement: The cube of a number added to the sum of three times the number and 3 is a prime number. : x = "number" the equation y = x^3 + 3x + 3 : Substituting: x = 1, then y = 7, a prime number x = 2, then y = 17, a prime number however, x = 3, then y = 39, not a prime number

Probability-and-statistics/319651: If posts are spaced 13 feet apart, how many posts are needed for 143 feet of straight-line fence? 1 solutions Answer 228903 by ankor@dixie-net.com(15645)   on 2010-07-04 11:15:48 (Show Source): You can put this solution on YOUR website! If posts are spaced 13 feet apart, how many posts are needed for 143 feet of straight-line fence? ; 143/13 = 11 + 1 = 12 posts

Percentage-and-ratio-word-problems/319453: Soybean meal is 18% protein; cornmeal is 9% protein. How many pounds of each should be mixed together in order to get 360-lb mixture that is 11% protein? How many pounds of the cornmeal should be in the mixture? How many pounds of the soybean meal should be in the mixture? 1 solutions Answer 228854 by ankor@dixie-net.com(15645)   on 2010-07-03 21:37:35 (Show Source): You can put this solution on YOUR website! Soybean meal is 18% protein; cornmeal is 9% protein. How many pounds of each should be mixed together in order to get 360-lb mixture that is 11% protein? : Let x = amt of Soy the result is to be 360 lb, therefore (360-x) = amt of corn : An amt of protein equation .18x + .09(360-x) = .11(360) : .18x + 32.4 - .09x = 39.6 : .18x - .09x = 39.6 - 32.4 : .09x = 7.2 x = x = 80 lb of soy and 360 - 80 = 280 lb of corn : : Check solution in original mixture equation .18(80) + .09(280) = .11(360) 14.4 + 25.2 = 39.6, confirms our solution

Percentage-and-ratio-word-problems/319450: Let b represent the number of boys in a club and let g represent the number of girls. If there are 50% more boys in the club than girls, which equation is true? 1 solutions Answer 228809 by ankor@dixie-net.com(15645)   on 2010-07-03 17:11:26 (Show Source): You can put this solution on YOUR website! Let b represent the number of boys in a club and let g represent the number of girls. If there are 50% more boys in the club than girls, which equation is true? b = 1.5g or g =

Angles/319447: Seven times the complement of an angle is 6 more than the supplement of the angle. What is the measure of the angle? 1 solutions Answer 228799 by ankor@dixie-net.com(15645)   on 2010-07-03 16:33:55 (Show Source): You can put this solution on YOUR website! Seven times the complement of an angle is 6 more than the supplement of the angle. What is the measure of the angle? : Let x = the angle we know (90-x) = complement of x and (180-x)= supplement of x : The equation for the statement: "Seven times the complement of an angle is 6 more than the supplement of the angle." 7(90-x) = (180-x) + 6 630 - 7x = -x + 186 630 - 186 = -x + 7x 444 = 6x x = x = 74 degrees is the angle : : YOu can confirm the solution in the original equation

Average/319490: The average of 10 students’ test scores was 69. Three students scored 80,60, and 40 respectively. Three other students scored 90, and two students scored 50. The other two students received the same score. What were their scores? 1 solutions Answer 228798 by ankor@dixie-net.com(15645)   on 2010-07-03 16:24:59 (Show Source): You can put this solution on YOUR website! The average of 10 students’ test scores was 69. Three students scored 80,60, and 40 respectively. Three other students scored 90, and two students scored 50. The other two students received the same score. What were their scores? : Let 2x = the two unknown grades : Write an equation from the given information: = 69 Multiply both sides by 10 80+60+40+270+100+2x = 690 : 2x + 550 = 690 : 2x = 690 - 550 : 2x = 140 x = x = 70 are the unknown scores

Triangles/319443: Given the perimeter of a triangle is 180 inches. If angles of the triangle are in the ratio 5:6:7. Determine he sides. 1 solutions Answer 228797 by ankor@dixie-net.com(15645)   on 2010-07-03 16:12:32 (Show Source): You can put this solution on YOUR website! Given the perimeter of a triangle is 180 inches. If angles of the triangle are in the ratio 5:6:7. Determine he sides. : Let x = the multiplier : 5x + 6x + 7x = 180 : 18x = 180 x = x = 10 is the multiplier : 50, 60, 70 are the sides

Travel_Word_Problems/319516: It takes one employee 3 hours longer to mow a football field than it does a more experienced employee. Together they can mow the grass in 2 hours. How long does it take for each person to mow the football field working alone? 1 solutions Answer 228796 by ankor@dixie-net.com(15645)   on 2010-07-03 16:02:25 (Show Source): You can put this solution on YOUR website! It takes one employee 3 hours longer to mow a football field than it does a more experienced employee. Together they can mow the grass in 2 hours. How long does it take for each person to mow the football field working alone? : Assume they each have a mower : Let t = time required by the experienced employee alone then (t+3) = time for the other employee : Let the completed job = 1 : A shared work equation + = 1 multiply by t(t+3), results: 2(t+3) + 2t = t(t+3) : 2t + 6 + 2t = t^2 + 3t combine like terms on the right 0 = t^2 + 3t - 4t - 6 A quadratic equation t^2 - t - 6 = 0 Factors to (t - 3)(s + 2) = 0 positive solution t = 3 hrs for the experienced guy by himself and 3 + 3 = 6 hrs for the other guy by himself : : Check solution + = + = 1

Geometry_Word_Problems/319494: Let A be the ratio of the volume of a sphere to the volume of a cube each of whose face is tangent to the sphere, and let B be the ratio of the surface area of this sphere to the surface area of the cube. Then find the sum A and B. 1 solutions Answer 228781 by ankor@dixie-net.com(15645)   on 2010-07-03 13:34:59 (Show Source): You can put this solution on YOUR website! Let A be the ratio of the volume of a sphere to the volume of a cube each of whose face is tangent to the sphere, and let B be the ratio of the surface area of this sphere to the surface area of the cube. Then find the sum A and B. : From the description, the sphere is enclosed in a cube : Let r = radius of the sphere then 2r = side of the cube : Volume Ratio; sphere/cube A = = cancel r^3 A = = = = ; vol ratio : Surface area ratio; sphere/cube B = = = Cancel 4, and r^2 B = : A + B: + = =

Miscellaneous_Word_Problems/319445: twelve people purchased supplies for a ten-day camping trip with the understanding that each of the twelve will get equal daily shares .they are then joined by three more people , but make no further purchases . how long will the supplies then last if the original daily share for each person is not changed ? 1 solutions Answer 228773 by ankor@dixie-net.com(15645)   on 2010-07-03 11:33:20 (Show Source): You can put this solution on YOUR website! twelve people purchased supplies for a ten-day camping trip with the understanding that each of the twelve will get equal daily shares . they are then joined by three more people , but make no further purchases . how long will the supplies then last if the original daily share for each person is not changed ? : We can use a man-day ration (mdr) method 12 men, 10 days, require: 12 * 10 = 120 mdr's were purchased : let d = no. of days for 15 men : 15d = 120 d = d = 8 days

Numbers_Word_Problems/319415: find a number that is twice its square root,increased by 7 is 9 1 solutions Answer 228756 by ankor@dixie-net.com(15645)   on 2010-07-03 08:23:27 (Show Source): You can put this solution on YOUR website! find a number that is twice its square root,increased by 7 is 9 : + 7 = 9 : = 9 - 7 = 2 square both sides 4x = 4 x = 1 : Check solution in original equation + 7 = 9 2(1) + 7 = 9

Evaluation_Word_Problems/319127: Tim has $5.03 in quarters, nickels, dimes, pennies, and half-dollars in a desk drawer. He has fice more nickles than quarters, then number of pennies is two-thirds the number of nickles, there are half as many half-dollars as pennies, and half as many dimes as nickels. How many coins of each type does he have? 1 solutions Answer 228723 by ankor@dixie-net.com(15645)   on 2010-07-02 21:47:25 (Show Source): You can put this solution on YOUR website! Tim has $5.03 in quarters, nickels, dimes, pennies, and half-dollars in a desk drawer. He has five more nickles than quarters, then number of pennies is two-thirds the number of nickles, there are half as many half-dollars as pennies, and half as many dimes as nickels. How many coins of each type does he have? : Write a equation for each statement: "Tim has $5.03 in quarters, nickels, dimes, pennies, and half-dollars in a desk drawer." .01p + .05n + .10d + .25q + .50h = 5.03 : "He has five more nickles than quarters," n = q + 5 or q = n - 5 : "then number of pennies is two-thirds the number of nickles," p = n : "there are half as many half-dollars as pennies," h = p replace p with n h = *n h = n : " half as many dimes as nickels." d = .5n : .01p + .05n + .10d + .25q + .50h = 5.03 get rid of the decimals, multiply by 100 p + 5n + 10d + 25q + 50 = 503 Get everything in terms of n, replace p, d, q, and h n + 5n + 10(.5n) + 25(n-5) + 50*n = 503 multiply by 3, get rid of the fractions 2n + 15n + 30(.5n) + 75(n-5) + 50n = 1509 : 2n + 15n + 15n + 75n - 375 + 50n = 1509 : 157n = 1509 + 375 : 157n = 1884 n = n = 12 nickels : How many coins of each type does he have? p:*12 = 8 pennies : h: *12 = 4 half dollars : q: 12 - 5 = 7 quarters : d: .5(12) = 6 dimes : : Check the solutions, find the total .01(8) + .05(12) + .10(6) .25(7) + .50(4) = .08 + .60 + .60 + 1.75 + 2.00 = 5.03; confirms our solutions

Quadratic_Equations/319350: Type an exact answer using radicals as needed and use commas to separate answers. What is the solution? w = w^4 - 2w^2 - 2 = 0 1 solutions Answer 228715 by ankor@dixie-net.com(15645)   on 2010-07-02 20:14:17 (Show Source): You can put this solution on YOUR website! w^4 - 2w^2 - 2 = 0 : Find w^2 using the quadratic formula in this equation x=w^2, a=1, b=-2, c=-2 : : Two solutions extract the sqrt of 4 Cancel the 2's Find the square root of both sides w = ; a good solution : but we also have extract the sqrt of 4 Cancel the 2's Find the square root of both sides w = However sqrt of 3 > 1, therefore we have square root of a neg number : I'm going to say the exact solution using radicals w = +, - : Confirm this with a graph of this equation

Polynomials-and-rational-expressions/319348: The base of a triangle is 4 inches less than twice the height. The area is 35 inches^2. Find the height and the base. Please help me with this problem. Thank you. 1 solutions Answer 228679 by ankor@dixie-net.com(15645)   on 2010-07-02 16:44:00 (Show Source): You can put this solution on YOUR website! The base of a triangle is 4 inches less than twice the height. The area is 35 inches^2. Find the height and the base. : Let x = the height then (2x-4) = the base : The area: *(2x-4)*x = 35 Multiply both sides by 2, get rid of the fraction 2x^2 - 4x = 2(35) Arrange as a quadratic equation: 2x^2 - 4x - 70 = 0 simplify, divide by 2 x^2 - 2x - 35 = 0 Factors to (x-7)(x+5) = 0 The positive solution x = 7 in is the height then 2(7) - 4 = 10 in is the base : : Check the area with these values .5 * 7 * 10 = 35

Volume/319271: A factory needs a box that has a volume of 6 cubic inches. The width should be 1 inch less than the height and the length should be 3 inches greater than the height. what should the dimensions of the box be? 1 solutions Answer 228671 by ankor@dixie-net.com(15645)   on 2010-07-02 16:17:06 (Show Source): You can put this solution on YOUR website! A factory needs a box that has a volume of 6 cubic inches. The width should be 1 inch less than the height and the length should be 3 inches greater than the height. what should the dimensions of the box be? : Let x = the height of the box then "width should be 1 inch less than the height" (x-1) = the width of the box and "length should be 3 inches greater than the height." (x+3) = the length of the box : Volume equation x*(x-1)*(x+3) = 6 x(x^2 + 2x - 3) = 6 x^3 + 2x^2 - 3x = 6 x^3 + 2x^2 - 3x - 6 = 0: graph this to find the positive solution x = 1.732 is the height then .732 = the width and 4.732 = the length ; : Check solution: 4.732*.732*1.732 = 5.999 ~ 6

Polynomials-and-rational-expressions/318982: Will someone please help me with these problems. 1) Factors: -8t+xt-24x+3x^2 2) Factors: 9t+wt+9y+yw 3) factors: 5x^2+13xy-6y^2 4) Factor: tu-24t+3t^2-8u 1 solutions Answer 228668 by ankor@dixie-net.com(15645)   on 2010-07-02 15:50:05 (Show Source): You can put this solution on YOUR website! 1) Factors: -8t+xt-24x+3x^2 Group the terms as follows xt + 3x^2 - 8t - 24x factor out x and -8 x(t+3x) - 8(t+3x); a -8 changes the sign Factor out (t+3x) (t+3x)(x-8) : 2) Factors: 9t+wt+9y+yw Group as follows 9t + 9y + wt + yw Factor out 9 & w 9(t+y) + w(t+y) Factor out (t+y) (t+y)(9+w) : 3) factors: 5x^2+13xy-6y^2 This can be factored as a quadratic, we know that it will be: (5x___y)(x___y) The factors of 6 are 2 & 3, choose the signs to satisfy the middle term 13xy (5x - 2y)(x + 3y); FOIL this to check it : 4) Factor: tu-24t+3t^2-8u This is very similar to the 1st problem See if you can do this exactly the same way

Quadratic_Equations/319338: how can you determine the nature of roots of this following equation: the square root of 3x suared minus 4 suare roots of 3 equals 0? 1 solutions Answer 228659 by ankor@dixie-net.com(15645)   on 2010-07-02 15:00:50 (Show Source): You can put this solution on YOUR website! the square root of 3x squared minus 4 square roots of 3 equals 0? = 0 add to both sides : Square both sides 3x^2 = 16(3) Divide both sides by 3 x^2 = 16 x = x = 4 : : Check solution in original equation = 0 extract the square root = 0

Percentage-and-ratio-word-problems/319332: On an exam with q questions, Marie correctly answered 15 of the first 20 but just 1/3 of the rest. If her total score was 50%, what was q? 1 solutions Answer 228654 by ankor@dixie-net.com(15645)   on 2010-07-02 14:32:59 (Show Source): You can put this solution on YOUR website! On an exam with q questions, Marie correctly answered 15 of the first 20 but just 1/3 of the rest. If her total score was 50%, what was q? : .50q = 15 + (q-20) Multiply equation by 3, to get rid of the fraction, results: 3(.5q) = 3(15) + q - 20 : 1.5q - q = 45 - 20 : .5q = 25 Multiply both sides by 2 q = 50 : : Check solution 15 + 1/3(50 - 20) = 15 + 10 = 25 which is 50% of 50