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 Equations/531987: How do you solve for X? example: 17x – 42 = -391 solutions Answer 350757 by ankor@dixie-net.com(15653)   on 2011-11-15 19:41:10 (Show Source): You can put this solution on YOUR website!we want to isolate x on one side by performing simple operations to both sides 17x - 42 = -39 add 42 to both sides 17x - 42 + 42 = -39 + 42 17x = +3 divide both sides by 17 x = x = : : To check this in the original equation 17x - 42 = -39 replace x with 3/17 17 - 42 = -39 17's cancel, leaving 3 - 42 = -39 -39 = -39; equality, confirm our solution of x = 3/17
 Rate-of-work-word-problems/531990: If a painter can paint a house in ½ a day and another painter can paint ¾ of a house in two days, how many houses can they paint in a month? (30 days)1 solutions Answer 350751 by ankor@dixie-net.com(15653)   on 2011-11-15 19:33:40 (Show Source): You can put this solution on YOUR website!If a painter can paint a house in ½ a day and another painter can paint ¾ of a house in two days, how many houses can they paint in a month? (30 days) : Painter 1: .5 house per day Painter 2: * = = .375 house per day : .5(30) + .375(30) = 15 + 11.25 = 26.25 houses in 30 days
 Numbers_Word_Problems/531978: Find 3 consecutive numbers such that 4 times the first is equal to 7 more than the sum of the other two. I do not understand how to work this problem. HELP!1 solutions Answer 350737 by ankor@dixie-net.com(15653)   on 2011-11-15 19:07:15 (Show Source): You can put this solution on YOUR website!Find 3 consecutive numbers such that 4 times the first is equal to 7 more than the sum of the other two. : 3 numbers: x, (x+1), (x+2) : Write an equation for the statement: "numbers such that 4 times the first is equal to 7 more than the sum of the other two. " 4x = (x+1) + (x+2) + 7 4x = 2x + 3 + 7 4x = 2x + 10 4x - 2x = 10 2x = 10 x = 5 : The three numbers, 5, 6, 7 : Check that in the given statement: "3 consecutive numbers such that 4 times the first is equal to 7 more than the sum of the other two. " 4(5) = 6 + 7 + 7
 Average/532053: The formula R = -0.075 + 3.85 can be used to predict the world record in the 1500 meter run, t years after 1930. Dertermine an inequality that identifies the years in which the world record will be < 3.7 minutes. t < ___ ? I have been bandging my head, and just cannot getthe formula, sorr to be so duh! Thanks...... have a good one1 solutions Answer 350676 by ankor@dixie-net.com(15653)   on 2011-11-15 16:44:51 (Show Source): You can put this solution on YOUR website!The formula R = -0.075 + 3.85 can be used to predict the world record in the 1500 meter run, t years after 1930. Determine an inequality that identifies the years in which the world record will be < 3.7 minutes. t < ___ ? : Assume the formula is: R = -0.075t + 3.85 : -.075t + 3.85 < 3.7 min -.075t < 3.7 - 3.85 -.075t < -.15 t had to be positive, multiply both sides by -1, this reverses the inequality sign .075t > .15 t > t > 2 yrs Add that to 1930, we can say it will be less than 3.7 min after 1932 : : We can confirm that by finding the time in 1933 (t=3) R = -0.075(3) + 3.85 R = -.225 + 3.85 R = 3.625 min, slightly less than 3.7 : : Hey! I have not heard that one before, does bandaging your head actually help?
 Percentage-and-ratio-word-problems/532080: Ms. Niemeyer is taking the train 3,240 miles to Oregon. She will travel 1/8 the distance the first day and 1/6 the distance on the second day. How far will she have left to go after two days? Please show me how to set up the equation. S/ Parent1 solutions Answer 350669 by ankor@dixie-net.com(15653)   on 2011-11-15 16:30:04 (Show Source): You can put this solution on YOUR website!Ms. Niemeyer is taking the train 3,240 miles to Oregon. She will travel 1/8 the distance the first day and 1/6 the distance on the second day. How far will she have left to go after two days? : Let d = remaining distance after two days : d = 3240 - (3240) - (3240) Both of these fraction will cancel into 3240, so you have d = 3240 - 405 - 540 d = 2295 mi to go
 Geometry_Word_Problems/531784: The volume of a rectangular box is 6 ft^3 more than twice the volume of a cube. The length of the box is 2 ft more than the length of an edge of the cube its width is equal to the length of an edge of the cube; and its height is 1 ft more than the length of an edge of the cube. What are the dimensions of the box and the cube?1 solutions Answer 350667 by ankor@dixie-net.com(15653)   on 2011-11-15 16:19:08 (Show Source): You can put this solution on YOUR website!The volume of a rectangular box is 6 ft^3 more than twice the volume of a cube. The length of the box is 2 ft more than the length of an edge of the cube its width is equal to the length of an edge of the cube; and its height is 1 ft more than the length of an edge of the cube. What are the dimensions of the box and the cube? : let x = the side of the cube Write an equation for each statement: "The volume of a rectangular box is 6 ft^3 more than twice the volume of a cube." L * W * H = 2x^3 + 6 : " The length of the box is 2 ft more than the length of an edge of the cube" L = x + 2 : "its width is equal to the length of an edge of the cube;" W = x : "its height is 1 ft more than the length of an edge of the cube." H = x + 1 : Substituting for L,W,H (x+2)*x*(x+1) = 2x^3 + 6 x(x^2 + x + 2x + 2) = 2x^3 + 6 x(x^2 + 3x + 2) = 2x^3 + 6 x^3 + 3x^2 + 2x = 2x^3 + 6 Combine like terms on the left x^3 - 2x^3 + 3x^2 + 2x - 6 = 0 -x^3 + 3x^2 + 2x - 6 = 0 : Graph this equation, there are two positive solutions but x=3 is an integer : What are the dimensions of the box and the cube? x = 3 inches the side of the cube then L = 3+2 = 5 inches W = 3 inches H = 3+1 = 4 inches : : Check this 5*3*4 = 2(3^3) + 6 60 = 2(27) + 6
 Money_Word_Problems/531788: the river boat delta duchess paddled upstream at 12 km/h, stopped for 2 hours of sight seeing, and paddled back at 18 km/h. how far upstream did the boat travel if the total time for the trip, including the stop, was 7 hours?1 solutions Answer 350658 by ankor@dixie-net.com(15653)   on 2011-11-15 14:25:41 (Show Source): You can put this solution on YOUR website!the river boat delta duchess paddled upstream at 12 km/h, stopped for 2 hours of sight seeing, and paddled back at 18 km/h. how far upstream did the boat travel if the total time for the trip, including the stop, was 7 hours : We only care about the traveling time which is 5 hrs : Let d = one way distance : Write a time equation: time = dist/speed : up time + down time = 5 hrs + = 5 Multiply by 36 to get rid of the denominators, results: 3d + 2d = 36(5) 5d = 180 d = 180/5 d = 36 miles upstream : : Check this by finding the actual time each way 36/12 = 3 hrs 36/18 = 2 hrs ------------- totals: 5 hrs
 Exponents/531816: How do I simplify, instructions are "use rational exponents to simplify" this please: ^4 sqrt x^-28 I don't understand how a NEGATIVE power will affect the ^4 sqrt x Please help. Thank you! ~Adelaide1 solutions Answer 350657 by ankor@dixie-net.com(15653)   on 2011-11-15 14:16:55 (Show Source): You can put this solution on YOUR website!simplify" this please: ^4 sqrt x^-28 Assume the problem is the 4th root of x^-28, written here like this: remember you can always get rid of negative exponent using it's reciprocal In order to understand this we can write it extract the 4th root of each and we have which is : But we can sum all this up in one sentence, the 4th root of the 28th power = 7
 Rate-of-work-word-problems/531897: A 3-men crew can do a certain job in 4 hours, while it takes a 4-men crew to do the same job 3 hours. How long will it take to complete the job if two crews work together, and one worker from the second crew was 1 hour late? Thank you1 solutions Answer 350654 by ankor@dixie-net.com(15653)   on 2011-11-15 13:55:25 (Show Source): You can put this solution on YOUR website!A 3-men crew can do a certain job in 4 hours, while it takes a 4-men crew to do the same job 3 hours. How long will it take to complete the job if two crews work together, and one worker from the second crew was 1 hour late? : We know that the job requires 12 man-hours to complete (3*4 or 4*3) : Let's try and determine how long it would take the 2nd crew to do the job if one guy was 1 hr late (h). : 3 guys work the whole time, one guy works 1 hr less 3h + 1(h-1) = 12 3h + h - 1 4h = 12 + 1 4h = 13 h = 13/4 h = 3.25 hrs to do the job under these conditions : Now using a standard, shared work equation where the completed job = 1 Crew 1 + crew 2 = completed job + = 1 multiply by 13 to clear the denominators 3.25t + 4t = 13 7.25t = 13 t = t = 1.793 hrs which is 1 hr + .793(60) ~ 1 hr 48 min : Did this make sense? Let me know if you find out I am wrong on this one. C :
 Linear-equations/531851: I need help with eliminations , 3x-y=5 x-2y=111 solutions Answer 350634 by ankor@dixie-net.com(15653)   on 2011-11-15 09:22:02 (Show Source): You can put this solution on YOUR website!3x - y = 5 x - 2y = 11 Multiply the 1st equation by -2, add to the 2nd equation -6x + 2y = -10 + x - 2y = 11 ----------------adding eliminates y, find x -5x = 1 x = x = -.2 : Use the 2nd equation to find y -.2 - 2y = 11 -2y = 11 + .2 -2y = 11.2 y = y = -5.6 : : Check those solutions in the 1st equation 3x - y = 5 3(-.2) - (-5.6) = 5 -.6 + 5.6 = 5 : Summarize: x =-.2; y = -5.6
 Permutations/531832: how many 5 digit even numbers are there?1 solutions Answer 350629 by ankor@dixie-net.com(15653)   on 2011-11-15 08:30:55 (Show Source): You can put this solution on YOUR website!how many 5 digit even numbers are there? ~ 45000
 Average/531824: If I miss 12 problems on a 41 problem test what is my score?1 solutions Answer 350628 by ankor@dixie-net.com(15653)   on 2011-11-15 08:21:03 (Show Source): You can put this solution on YOUR website!If I miss 12 problems on a 41 problem test what is my score : That means you got 41-12 = 29 problems right * 100 = 70.7 %
 Age_Word_Problems/531854: PLEASE I NEED IT ASAP! A man is 27 years older than his son and in 10 years, he will be twice as old as his son. How old is each now?1 solutions Answer 350627 by ankor@dixie-net.com(15653)   on 2011-11-15 08:14:43 (Show Source): You can put this solution on YOUR website!A man is 27 years older than his son and in 10 years, he will be twice as old as his son. How old is each now? : Let m = man's present age Let s = son's present age : Write an equation for each statement: : "A man is 27 years older than his son" m = s + 27 : "in 10 years, he will be twice as old as his son." m + 10 = 2(s+10) m + 10 = 2s + 20 m = 2s + 20 - 10 m = 2s + 10 : From the 1st statement, replace m with (s+27) s + 27 = 2s + 10 27 - 10 = 2s - s 17 = s : Son is 17 years old, I'll let you find the man's age, check your solutions in the 2nd statement : Hey! Try not to wait til the last minute! C
 Rational-functions/531361: Please help me. I am confused. How do I solve these by factoring? 3x^2 -2x = 0 and 9x^2 -1 = 0 Thanks so much!1 solutions Answer 350584 by ankor@dixie-net.com(15653)   on 2011-11-14 21:41:24 (Show Source): You can put this solution on YOUR website!Please help me. I am confused. How do I solve these by factoring? 3x^2 -2x = 0 Factor out x x(3x - 2) = 0 Two solutions x = 0 and 3x = 2 x = : and 9x^2 - 1 = 0 This is the difference of squares (3x + 1)(3x -1) = 0 Two solutions 3x = -1 x = and x =
 Polynomials-and-rational-expressions/531598: How do I factor: 7-6b-b^2= ? Thank you1 solutions Answer 350536 by ankor@dixie-net.com(15653)   on 2011-11-14 19:29:04 (Show Source): You can put this solution on YOUR website!How do I factor: 7-6b-b^2= We usually write it -b^2 - 6b + 7 = 0 Easier to factor if b^2 is positive, multiply by -1 and you have b^2 + 6b - 7 = 0 -7 only has two possible factors, we know one is neg and one positive (b _ 1)(b _ 7) = 0 Choose the signs that will give you 6 as the coefficient of b (b - 1)(b + 7) = 0 : Check this by FOILing (b+7)(b-1) = b^2 - b + 7b - 7 = b^2 + 6b - 7 Multiply by -1 to get the original problem -b^2 - 6b + 7
 Rate-of-work-word-problems/531209: A 5-horsepower (hp) pump can empty a pool in 5 hours. A smaller, 2-hp pump can empty a pool in 8 hours. The pumps are used together to begin emptying this pool. After two hours, the 2-hp pump breaks down. How long will it take the larger pump to finish emptying the pool?1 solutions Answer 350396 by ankor@dixie-net.com(15653)   on 2011-11-14 11:05:49 (Show Source): You can put this solution on YOUR website!A 5-horsepower (hp) pump can empty a pool in 5 hours. A smaller, 2-hp pump can empty a pool in 8 hours. The pumps are used together to begin emptying this pool. After two hours, the 2-hp pump breaks down. How long will it take the larger pump to finish emptying the pool? : Let t = additional time to finish emptying the pool Let the completed job = 1, (an empty pool) : + = 1 multiply by 40 to clear the denominators, results: 8(t+2) + 5(2) = 40 8t + 16 + 10 = 40 8t + 26 = 40 8t = 40 - 26 8t = 14 t = 14/8 t = 1.75 more hrs for the large pump to empty the pool : : Check that (the large pump operates for a total of 3.75 hrs) + = .75 + .25 = 1
 Numbers_Word_Problems/531119: The units digit is 1 more than 3 times the tens digit in a two digit number. The number represented when the digits are interchanged is 8 times the sum of the digits. Find the original number.1 solutions Answer 350395 by ankor@dixie-net.com(15653)   on 2011-11-14 10:54:10 (Show Source): You can put this solution on YOUR website!The units digit is 1 more than 3 times the tens digit in a two digit number. The number represented when the digits are interchanged is 8 times the sum of the digits. Find the original number. : Let x = the 10's digit Let y = the units then 10x+y = the number : Write an equation for each statement: : "The units digit is 1 more than 3 times the tens digit" y = 3x + 1 : "The number represented when the digits are interchanged is 8 times the sum of the digits." 10y + x = 8(x+y) : You should be able to solve it now
 Rate-of-work-word-problems/531211: An air rescue plane averages 300 miles per hour in still air. It carries fuel for 5 hours of flying time. If, upon takeoff, it encounters a head wind of 30 miles per hour, how far can it fly and return safely? (Assume that the wind remains constant)1 solutions Answer 350372 by ankor@dixie-net.com(15653)   on 2011-11-14 08:50:21 (Show Source): You can put this solution on YOUR website!An air rescue plane averages 300 miles per hour in still air. It carries fuel for 5 hours of flying time. If, upon takeoff, it encounters a head wind of 30 miles per hour, how far can it fly and return safely? (Assume that the wind remains constant) : 300 - 30 = 270 mph the ground speed against the wind 300 + 30 = 330 mph the ground speed with the wind : let d = the one way distance to point of no return : Write a time equation, time = dist/speed : Outbound time + return time = 5 hrs + = 5 multiply by 2970 to get rid of the denominators, results 11d + 9d = 2970(5) 20d = 14850 d = d = 742.5 mi, but it says "safely", you would never cut it that close; I would say 650 max. : : Confirm this by finding the actual time for each trip 742.5/270 = 2.75 hrs 742.5/330 = 2.25 hrs --------------------- totals time: 5 hrs
 Travel_Word_Problems/530762: A boat travels 15 miles upstream and returns. If the boat travels 14 mph in still water, find the speed of the currrent if the total trip takes 2 hours and 20 minutes. I really only want to understand how to set the problem up, I have no problem with the algebra part :). Thank you so much to whoever helps me.1 solutions Answer 350307 by ankor@dixie-net.com(15653)   on 2011-11-13 19:46:20 (Show Source): You can put this solution on YOUR website!A boat travels 15 miles upstream and returns. If the boat travels 14 mph in still water, find the speed of the current if the total trip takes 2 hours and 20 minutes. : Let c = the speed of the current then (14+c) = effective speed downstream and (14-c) = effective speed upstream : Change 2 hrs 20 min to hrs : Write a time equation: time = dist/speed : Upstream time + downstream time = 2 hrs 20 min = =
 Travel_Word_Problems/530542: A truck is 300 miles due east of a car and is traveling at a constant speed of 30 miles per hour. Meanwhile, the car is going north at a constant speed of 60 miles per hour. Express the distance between the car and truck as a function of time1 solutions Answer 350149 by ankor@dixie-net.com(15653)   on 2011-11-12 21:52:14 (Show Source): You can put this solution on YOUR website!A truck is 300 miles due east of a car and is traveling at a constant speed of 30 miles per hour. Meanwhile, the car is going north at a constant speed of 60 miles per hour. Express the distance between the car and truck as a function of time : Assuming the truck is traveling east, let t = travel time of both The distance between the two will be the hypotenuse of a right triangle f(t) =
 Exponential-and-logarithmic-functions/530286: I need you help with this question: The change in the population of a township founded in 1930 can be described by the function P(t)=10000. At what rate is the population changing every year? Ps: t is on the same line like 0.02, means 0.02 times t.1 solutions Answer 350129 by ankor@dixie-net.com(15653)   on 2011-11-12 21:00:32 (Show Source): You can put this solution on YOUR website!I need you help with this question: The change in the population of a township founded in 1930 can be described by the function P(t)=10000*e^(-0.02t). At what rate is the population changing every year? : The population would be losing 2% every year : Check on the graph, the given equation is red, -2% per year is green :