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 Polynomials-and-rational-expressions/607001: Can the expression a^2-16a+28 be factored. And if so how do I do it?1 solutions Answer 382495 by ankor@dixie-net.com(15624)   on 2012-05-04 16:59:34 (Show Source): You can put this solution on YOUR website!Can the expression a^2-16a+28 be factored. And if so how do I do it? : Look at the third term, 28. What are the factors? 2,14 and 4,7, can be both positive or both negative ; Which of these pairs of factors add up to the coefficient of a, which is -16 -2 - 14 = -16, and we can see that it will be factors of: : (a-2)(a-14); FOIL this to check it
 Numbers_Word_Problems/607121: the sum of the reciprocal of a number and the reciprocal of 3 less that the number 5 time the reciprocal of the original number. find the original number1 solutions Answer 382493 by ankor@dixie-net.com(15624)   on 2012-05-04 16:45:02 (Show Source): You can put this solution on YOUR website!let x = "a number" : Write an equation for the statement: "the sum of the reciprocal of a number and the reciprocal of 3 less that the number 5 time the reciprocal of the original number." + + 3 = 5() multiply by 3x, results 1(3) + 1(x) + 3(3x) = 3(5) : 3 + x + 9x = 15 10x = 15 - 3 10x = 12 x = 12/10 x = 1.2
 Mixture_Word_Problems/606963: How many quarts if a 40% alchohol solution must be mixed with 3 quarts of pure water to make a 28% solution? This is what I am doing but I am getting a negative answer: (3*1)+(x*.3)=(3+x*.28)1 solutions Answer 382491 by ankor@dixie-net.com(15624)   on 2012-05-04 16:29:58 (Show Source): You can put this solution on YOUR website!How many quarts if a 40% alcohol solution must be mixed with 3 quarts of pure water to make a 28% solution? : Let x = amt of 40% solution required : .40x = .28(x+3) .40x = .28x + .84 .40x - .28x = .84 .12x = .84 x = .84/.12 x = 7 quarts of 40% solution required : : Check this .4(7) = .28(7+3) 2.8 = .28(10)
 Human-and-algebraic-language/606887: Mr.lin is four times as old as his daughter. The sum of their ages is twelve years less than twice the difference of their ages. How old is mr.lin? The answer choices are 12,24,36 & 481 solutions Answer 382490 by ankor@dixie-net.com(15624)   on 2012-05-04 16:22:39 (Show Source): You can put this solution on YOUR website!Mr.lin is four times as old as his daughter. The sum of their ages is twelve years less than twice the difference of their ages. How old is mr.lin? : Let L = Mr Lin's age Let d = daughter's age : Write an equation for each statement: : "Mr.lin is four times as old as his daughter." L = 4d : "The sum of their ages is twelve years less than twice the difference of their ages." L + d + 12 = 2(L-d) L + d + 12 = 2L - 2D d + 2d + 12 = 2L - L 3d + 12 = L Replace L with 4d (from the 1st statement) 3d + 12 = 4d 12 = 4d - 3d d = 12 yrs is daughters age then 4(12) = 48 is Mr Lin's age : : See if that checks out in the statement: "The sum of their ages is twelve years less than twice the difference of their ages." 48 + 12 + 12 = 2(48 - 12) 72 = 2(36)
 test/607026: 5√5x+1 =5√3x I don't understand .. I'm supposed to solve 4 x.. I need help.. thank you! 1 solutions Answer 382384 by ankor@dixie-net.com(15624)   on 2012-05-04 09:40:28 (Show Source): You can put this solution on YOUR website!5√5x+1 = 5√3x Assuming the problem is: : divide both sides by 5, results: : Square both sides 5x + 1 = 3x 5x - 3x = -1 2x = -1 x = : There is no solution, the value for x gives negative values inside the radicals
 Expressions-with-variables/606944: How do i Factor: 3x^2+4xy-6x-8y1 solutions Answer 382359 by ankor@dixie-net.com(15624)   on 2012-05-04 08:18:01 (Show Source): You can put this solution on YOUR website!How do i Factor: 3x^2 + 4xy - 6x - 8y : We can group factor here, factor out x, and -2 x(3x + 4y) - 2(3x + 4y) : Now factor out (3x+4y) and you have (3x + 4y)(x - 2); sorry about that!
 Equations/606659: Solve square root of 2x+3- square root of x+1=11 solutions Answer 382331 by ankor@dixie-net.com(15624)   on 2012-05-03 21:21:42 (Show Source): You can put this solution on YOUR website!Solve square root of 2x+3- square root of x+1=1 : : Square both sides, you have to FOIL the right side 2x + 3 = : 2x + 3 = x + 2 + : 2x - x + 3 - 2 = : (x + 1) = : Square both sides, FOIL the left side : x^2 + 2x + 1 = 4(x+1) x^2 + 2x + 1 = 4x + 4 x^2 + 2x - 4x + 1 - 4 = 0 x^2 - 2x - 3 = 0 Factors to (x-3)(x+1) = 0 Two solutions x = 3 x = -1 ; We have to check both solutions in the original equation x = -1 will not work, it would give us a neg value inside the radical Try x = 3 ; looks OK, x=3 is our solution
 Coordinate-system/606648: y=x+4 what is the value of x? 1 solutions Answer 382328 by ankor@dixie-net.com(15624)   on 2012-05-03 21:09:01 (Show Source): You can put this solution on YOUR website!y=x+4 what is the value of x? subtract 4 from both sides y - 4 = x or x = y-4
 Travel_Word_Problems/606971: Andy's average driving speed for a 4-hour trip was 45 miles per hour. During the first 3 hours he drove 40 miles per hour. what was his average speed for the last hour of his trip?1 solutions Answer 382325 by ankor@dixie-net.com(15624)   on 2012-05-03 20:57:55 (Show Source): You can put this solution on YOUR website!Andy's average driving speed for a 4-hour trip was 45 miles per hour. During the first 3 hours he drove 40 miles per hour. what was his average speed for the last hour of his trip? : let s = speed on the last hr ; Write a distance equation; dist = speed * time 40(3) + 1s = 45(4) 120 + s = 180 s = 180-120 s = 60 mph on the last hr
 Equations/606719: Please help me solve this: 2^(4x-3)=1/81 solutions Answer 382321 by ankor@dixie-net.com(15624)   on 2012-05-03 20:48:40 (Show Source): You can put this solution on YOUR website!solve this: log at this, what is 2^-3?. It's 1/8 right? therefore x = 0
 Surface-area/606934: I have a math problem where pi=22/7 and I have to find the area of a circle using pi with a diameter of 5ft 3in. Please show me how to find the area?1 solutions Answer 382318 by ankor@dixie-net.com(15624)   on 2012-05-03 20:18:10 (Show Source): You can put this solution on YOUR website!I have a math problem where pi=22/7 and I have to find the area of a circle using pi with a diameter of 5ft 3in. Please show me how to find the area? : Convert 5 ft 3 in to 5.25 ft This is the diameter, we need the radius: 5.25/2 = 2.625 ft : Area of a circle: therefore A = *; in square ft
 Travel_Word_Problems/606591: At noon, car A is 41 miles due west of car B and traveling east at a constant speed of 55 miles an hour. Meanwhile, car B is traveling north at 40 miles per hour. At what time will the two cars be closest to each other? Suggestion, minimize the square of the distance, rather than the distance itself1 solutions Answer 382317 by ankor@dixie-net.com(15624)   on 2012-05-03 20:05:45 (Show Source): You can put this solution on YOUR website!At noon, car A is 41 miles due west of car B and traveling east at a constant speed of 55 miles an hour. Meanwhile, car B is traveling north at 40 miles per hour. At what time will the two cars be closest to each other? : the relationship between the two cars form a right triangle where a = (41-55t), car a distance from reference point b = 40t, car B travel distance from the the same point c = distance between the cars at t time : c^2 = (41-55t)^2 + (40t)^2 c^2 = 1681 - 4510t + 3025t^2 + 1600t^2 c^2 = 4625t^2 - 4510t + 1681 c = Plot this equation looks like they will closest together in half an hour, about 24 miles
 percentage/606534: After 4 tests this term Jessica had a 72% average. He has 2 more tests left in the term. What average score will Jessica need on the final 2 tests to bring his average to 80%1 solutions Answer 382309 by ankor@dixie-net.com(15624)   on 2012-05-03 19:13:12 (Show Source): You can put this solution on YOUR website!After 4 tests this term Jessica had a 72% average. He has 2 more tests left in the term. What average score will Jessica need on the final 2 tests to bring his average to 80% : This means he will have a total of 6 tests Let x = average grade on the final two tests : = 80 multiply both sides by 6 4(72) + 2x = 6(80) 288 + 2x = 480 2x = 480-284 2x = 192 x = 192/2 x = 96% av on the last two tests
 Mixture_Word_Problems/606614: A 5-quart solution of sulfuric acid and water is 60% acid. If a gallon of water is added, what percent of the resulting solution is acid? A)3% B)33 1/3% C)40% d)48% E)50%1 solutions Answer 382300 by ankor@dixie-net.com(15624)   on 2012-05-03 19:01:47 (Show Source): You can put this solution on YOUR website!: A 5-quart solution of sulfuric acid and water is 60% acid. If a gallon of water is added, what percent of the resulting solution is acid? : Let x = per cent when a gallon of water is added : Change 1 gallon to 4 quarts : The amt of acid remains the same 60(5) = x(5 + 4) 300 = 9x x = 300/9 x = 33 per cent
 Travel_Word_Problems/606488: Suppose a child throws a ball upward and gives it an initial velocity of 10 feet per second. The starting height of the ball is 2.5 feet. How long will it take for the ball to reach its maximum height?1 solutions Answer 382227 by ankor@dixie-net.com(15624)   on 2012-05-03 15:33:26 (Show Source): You can put this solution on YOUR website!Suppose a child throws a ball upward and gives it an initial velocity of 10 feet per second. The starting height of the ball is 2.5 feet. How long will it take for the ball to reach its maximum height? : The formula for this: f(t) = -16t^2 + 10t + 2.5 Where f(t) = height after t time -16t^2 = force of gravity downward 10t = initial velocity upward 2.5 = initial height of the ball ; Find the max height, by finding the axis of symmetry: x = -b/(2a) t = t = .3125 sec to reach max height
 Trigonometry-basics/606419: an airplane travel at 300 mph is descending at an angle of depression of 6 degrees. How many miles will the plane descend in 2 minutes?1 solutions Answer 382191 by ankor@dixie-net.com(15624)   on 2012-05-03 13:19:29 (Show Source): You can put this solution on YOUR website!an airplane travel at 300 mph is descending at an angle of depression of 6 degrees. How many miles will the plane descend in 2 minute : Find how many miles the plane will travel in 2 min a 300 mph *300 = 10 mi : use the sine of 6 degrees, side opposite is the vertical dist (a) of descent Sin(6) = * 5280 = 5519.1 ft descent
 Travel_Word_Problems/606179: a man walks from his home at a speed of 5km/h and returns at a speed of 3km/h what is the distance he walked if the whole trip takes 4 hours 1 solutions Answer 382172 by ankor@dixie-net.com(15624)   on 2012-05-03 10:51:56 (Show Source): You can put this solution on YOUR website!a man walks from his home at a speed of 5km/h and returns at a speed of 3km/h what is the distance he walked if the whole trip takes 4 hours : Find the time each way first t = 5 mph time then (4-t) = 3 mph time : Write a time equation; time = speed * time : Go dist = return dist 5t = 3(4-t) 5t = 12 - 3t 5t + 3t = 12 t = 12/8 t = 1.5 hrs : Find the distance 5(1.5) = 7.5 mi check the dist 3(4-1.5) = 7.5 mi
 Rational-functions/605939: Could someone please help with this. I have to solve this by the elimination method and I have to show the steps. I am stumped. Please help. solve by elimination y= 5x-10 2x + 3y=21 Thank you so much for the help!1 solutions Answer 381871 by ankor@dixie-net.com(15624)   on 2012-05-01 18:44:30 (Show Source): You can put this solution on YOUR website!solve this by the elimination method solve by elimination y = 5x - 10 2x + 3y = 21 : Put the 1st equation into standard form also y = 5x - 10 subtract 5x from both sides -5x + y = -10 multiply by -3, add to the 2nd equation 15x - 3y = +30 2x + 3y = 21 -----------------adding eliminates y find x 17x = 51 x = 51/17 x = 3 : Find y using the original 1st equation y = 5(3) - 10 y = 15 - 10 y = 5 : The solution is x=3, y=5 : Confirm this in the 2nd equation 2(3) + 3(5) = 21 6 + 15 = 21
 logarithm/605777: Please help me solve this equation: 50e^-0.058x=100 Directions: find exact answer then round to four decimal places.1 solutions Answer 381862 by ankor@dixie-net.com(15624)   on 2012-05-01 17:13:36 (Show Source): You can put this solution on YOUR website!solve this equation: divide both sides by 50 : nat log of both sides log equiv of exponents ln of e is 1, therefore -.058x = ln(2) x = ; using a calc x = -11.9508
 Linear_Equations_And_Systems_Word_Problems/605513: What is the equation that will fit the following information. Gail is raising money by selling popcorn. She rents a cart for 40.00 a day. She sells each box for 1.25 but her expenses for each box is .55. I think this is a y=mx + b equation but I am not sure. Can you help?1 solutions Answer 381731 by ankor@dixie-net.com(15624)   on 2012-04-30 21:32:45 (Show Source): You can put this solution on YOUR website!What is the equation that will fit the following information. Gail is raising money by selling popcorn. She rents a cart for 40.00 a day. She sells each box for 1.25 but her expenses for each box is .55. : let x = no. of boxes sold y = amt of money raised : y = x(1.25-.55) - 40 y = .70x - 40
 Travel_Word_Problems/605484: Stephen has driven 3/5 of the distance from Waco to El Paso. If he has 270miles left to drive, how many miles has he driven?1 solutions Answer 381727 by ankor@dixie-net.com(15624)   on 2012-04-30 21:11:28 (Show Source): You can put this solution on YOUR website!Stephen has driven 3/5 of the distance from Waco to El Paso. If he has 270 miles left to drive, how many miles has he driven? : Find the total distance If he has driven 3/5, he has 2/5 left, therefore d = 270 2d = 5(270) d = 675 mi : Find no. of miles driven 675 - 270 = 405 mi
 Travel_Word_Problems/605269: Biking at 12 mph, it takes Kristen 1/2 hour to reach the train station to go to work. Kristen then takes the train to work, and it takes another 1/2 hour for her to get to work when the train travels 24 mph. How far does Kristen travel to work?1 solutions Answer 381719 by ankor@dixie-net.com(15624)   on 2012-04-30 19:57:15 (Show Source): You can put this solution on YOUR website!Biking at 12 mph, it takes Kristen 1/2 hour to reach the train station to go to work. Kristen then takes the train to work, and it takes another 1/2 hour for her to get to work when the train travels 24 mph. How far does Kristen travel to work? : Write a distance equation, dist = speed * time : Total dist = bike dist + train dist d = 12(.5) + 24(.5) d = 6 + 12 d = 18 mi
 Mixture_Word_Problems/605138: It took ten men 16 days to paint a house. At that same rate, how many men would it have taken to finish paint the house in 10 days1 solutions Answer 381563 by ankor@dixie-net.com(15624)   on 2012-04-29 21:56:04 (Show Source): You can put this solution on YOUR website!It took ten men 16 days to paint a house. Find the no. of man-days required to paint the house 10*16 = 160 man-days : At that same rate, how many men would it have taken to finish paint the house in 10 days let m = no. of men required to do it 10 days 10m = 160 m = 160/10 m = 16 men to do it in 10 days
 Travel_Word_Problems/604998: Problem: In 2 minutes, a conveyor belt moves 300 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 6 minutes. If both belts are used, find how long it takes to move the cans to the storage area. I used the following equation: 300/2 + 300/6 = 300/x My answer is 1.25 minutes. The book's answer is 1-1/2 minutes. What did I do wrong? Please explain how to set up this problem. Thanks!1 solutions Answer 381561 by ankor@dixie-net.com(15624)   on 2012-04-29 21:23:50 (Show Source): You can put this solution on YOUR website!In 2 minutes, a conveyor belt moves 300 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 6 minutes. If both belts are used, find how long it takes to move the cans to the storage area. : We can do it this way let t = time required when both belts are used to move 300 lb : Let the completed job = 1 (moving 300 lb) : + = 1 Multiply by 6 6* + 6* = 6 Cancel out the denominators 3t + t = 6 4t = 6 t = 6/4 t = 1.5 min
 logarithm/605068: how do you solve: log base 3 (x+4)+log base 3 (x-2)=31 solutions Answer 381556 by ankor@dixie-net.com(15624)   on 2012-04-29 21:02:39 (Show Source): You can put this solution on YOUR website!log base 3 (x+4)+log base 3 (x-2) = 3 Combine the logs FOIL the exponent equiv of logs : ; : Factors to (x+7)(x-5) = 0 Two solutions x = -7 x = 5, since we are dealing with logs, only the positive solution is valid
 Linear-systems/605111: Solve the following system of equations for x: 6x+7y=-8 -6x-14y=22 I need your help please. I can't figure out if there is an answer or if these equations represent parallel lines and there is no solution or if these equations represent the same line and there are infinite solutions. Thank you so much for your help!!1 solutions Answer 381553 by ankor@dixie-net.com(15624)   on 2012-04-29 20:52:01 (Show Source): You can put this solution on YOUR website! 6x + 7y = -8 -6x- 14y = 22 --------------adding eliminates x, find y -7y = 14 y = y = -2 : Find x using the 1st equation 6x + 7(-2) = -8 6x - 14 = -8 6x = -8 + 14 6x = 6 x = 1 : : Check solutions in the 2nd equation -6(1) - 14(-2) = 22 -6 + 28 = 22
 Miscellaneous_Word_Problems/605077: jeff takes 5 hours longer to build a fence than it takes bill. When they work togehter , it takes them 6 hours . How long would it take bill alone to do the job alone?1 solutions Answer 381551 by ankor@dixie-net.com(15624)   on 2012-04-29 20:44:55 (Show Source): You can put this solution on YOUR website!jeff takes 5 hours longer to build a fence than it takes bill. When they work together, it takes them 6 hours . How long would it take bill alone to do the job alone? : Let b = time required by Bill to build the fence then (b+5) = time required by Jeff : Let the completed job = 1 : + = 1 multiply by b(b+5) 6(b+5) + 6b = b(b+5) 6b + 30 + 6b = b^2 + 5b 0 = b^2 + 5b - 12b - 30 a quadratic equation b^2 - 7b - 30 = 0 (b-10)(b+3) = 0 The positive solution b = 10 hrs for Bill to do the job and 10 + 5 = 15 hrs for Jeff
 Polynomials-and-rational-expressions/605058: (x^(3) - x)/(x^(3) + 5x^(2) - 6x) Can you please help me understand how to turn around an expression with negative one and stuff like that, thank you!1 solutions Answer 381546 by ankor@dixie-net.com(15624)   on 2012-04-29 20:35:16 (Show Source): You can put this solution on YOUR website! Factor and cancel x = Factor again, cancel (x-1) =
 Money_Word_Problems/604883: the forest service must determine how many acres will be needed to make an addition of twenty-two campsites. if the existing 24-acre campground accommodates fifty-five campsites, how many additional acres will be needed?1 solutions Answer 381505 by ankor@dixie-net.com(15624)   on 2012-04-29 15:30:00 (Show Source): You can put this solution on YOUR website!the forest service must determine how many acres will be needed to make an addition of twenty-two campsites. if the existing 24-acre campground accommodates fifty-five campsites, how many additional acres will be needed? : We can use a ratio equation here. Let a = no. of additional acres required : = : = Cross multiply 55(a+24) = 24 * 77 55a + 1320 = 1848 55a = 1848 - 1320 55a = 528 a = 528/55 a = 9.6 additional acres required for 22 more campsites
 Linear_Equations_And_Systems_Word_Problems/604876: two numbers are related in this way: the number 1 is subtracted from the first number, the difference is squared, then doubled;the result is equal to the second number. the number 1 is added to the first number, and the sum is squared;the result is equal to 4 minus the second number. determine the numbers. 1 solutions Answer 381485 by ankor@dixie-net.com(15624)   on 2012-04-29 14:11:04 (Show Source): You can put this solution on YOUR website!two numbers are related in this way x & y : Step-by-step the number 1 is subtracted from the first number, the difference is squared, (x-1)^2 : then doubled; 2(x-1)^2 ; the result 2(x^2-2x+1) = 2x^2 - 4x + 2 : is equal to the second number. 2x^2 - 4x + 2 = y : the number 1 is added to the first number, and the sum is squared; (x+1)^2 = x^2 + 2x + 1 : the result is equal to 4 minus the second number x^2 + 2x + 1 = 4 - y x^2 + 2x + 1 - 4 = -y x^2 + 2x - 3 = -y 2x^2 - 4x + 2 = +y; add the 1st equation -----------------eliminates y 3x^2 - 2x - 1 = 0 Factors to (3x+1)(x-1) = 0 Two solutions x = 1 and 3x = -1 x = -.333 : find y when x = 1 y = 2(1-1)^2 y = 0 : Find y when x = -.333 y = 2(-.333-1)^2 y = 2(1.77) y = 3.54 :
 logarithm/604747: log4^n=1/21 solutions Answer 381454 by ankor@dixie-net.com(15624)   on 2012-04-29 10:59:49 (Show Source): You can put this solution on YOUR website! we can write it n = using a calc n = .8305