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# Recent problems solved by 'rcmcc'

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 Expressions-with-variables/187598: The weight M of an object on Mars varies directly as its weight E on Earth. A person who weighs 95 lb on Earth weighs 38 lb on Mars. How much would a 100-lb person weigh on Mars? 1 solutions Answer 140615 by rcmcc(152)   on 2009-03-20 19:35:57 (Show Source): You can put this solution on YOUR website!This is a simple ratio question, because you are looking for the ratio beween E and M you simply have to divide the two numbers. 38/95=0.4 Now that you know the ratio is .04 simply multiply it with the weight of the person on earth 0.4x100=40 A 100 lb person would weigh 40 pounds on mars.
 Mixture_Word_Problems/164107: How many kilograms of pure alcohol must be added to 40 kg of a 70% alcohol solution to produce an 85% alcohol solution?1 solutions Answer 120929 by rcmcc(152)   on 2008-10-26 17:38:01 (Show Source): You can put this solution on YOUR website!To solve this question you must first find the quantity of liquid that is not alcohol in the first solution. Because the 40kg solution is 70% alcohol 30% of the solution is a fixed variable. 30% of 40kg = 12kg. The second solution is 85% alcohol. Because we can not change the fixed variable the 15% of the new solution weighs 12kg if 15% of the new solution weigs 12kg then the entire solution weighs 80kg. because your original solution weighs 40kg, and your new solution weighs 80kg, you would need 40kg of pure alcohol added to the old solution to increase the concentration from 70% to 85%.
 Age_Word_Problems/118390: two trains traveled in opposite directions from the same starting point. one train traveled 25 mph faster than the other one. after 4 hours they were 456 miles apart. find the rate of each train.1 solutions Answer 86523 by rcmcc(152)   on 2008-01-01 15:33:56 (Show Source): You can put this solution on YOUR website!To solve this question you must first find a linear equation. Let the speed of the slower train equal (x) the faster train is 25mph faster than (x) so train 2=(X)+25 Because 4 hours elapsed we can state that (4)(X) distance has occured for the slower train and (4)(x+25) has occured for the faster train. Because we are looking for the total distance between them we can add them to find the total distance. train x+train Y= XY (4x)+(4y)=456 because y (faster train) is represented by x+25. substitute the value. your linear equation is below 4(X)+(4)(x+25)=456 expand the brackets and simplify the equation and solve 4x+4x+100=456 8x+100=456 8x=356 x=44.5 so the slower train is traveling at 44.5mph and the faster one is traveling at 69.5. You can test this by substituting the numbers into your equation (4x)+(4y)=456 (4)(44.5)+(4)(69.5)=456. Solved.
 Equations/106683: find two factors of 35 with a difference of 21 solutions Answer 77644 by rcmcc(152)   on 2007-10-28 11:27:55 (Show Source): You can put this solution on YOUR website!the quickest way to solve this is to list the factors of 35 1x35 5X7 there are only 2 sets of factors relating to 35 and only 1 set has a differece of 2 that is 5,7
 Triangles/106679: Help me this ones wrecking my brain and is stressing me out!!! The perimeter of a triangle ABC is 26m. BC is two thirds the length of AB and is 2m longer than ac. find the length of the sides.1 solutions Answer 77636 by rcmcc(152)   on 2007-10-28 11:13:31 (Show Source): You can put this solution on YOUR website!To solve this question it is easier to make a set of simple equations. because perimeter is x+y+z we can make the equation now we can make equations for the other parts of the question because BC is the length of Ab we can make the equation now we can add on the other part of the equation. because BC is 2cm longer than AC we can derive the equation now you have the 3 equations below the simplest way to solve is to substitute the 2 lower equations into the top equation in place of their respective variables. so you substitute (2/3)BC in place of AB in the top equation. you get simplify divide by 8/3 BC=9 Now because you have BC solved substitute into the other equations to solve for the remainder sides so AC=11 and AB=6 the lengths of the 3 sides of the triagle are 9,11,6
 Linear_Algebra/106669: 6x + 4(3x – 2) = 6x + 2 I am getting x=10 but I was not sure if I did it right.1 solutions Answer 77631 by rcmcc(152)   on 2007-10-28 10:56:46 (Show Source): You can put this solution on YOUR website! first thing to do with this question is to simplify brackets by expanding the 4 into them Now simplify the question remove the 6 from the right side by subtracting from both sides now bring the 8 to the other side by adding it so by dividing 12 from each side check this answer by substituting it into the first equation 7=7 Then when the equation is verified.
 Linear_Equations_And_Systems_Word_Problems/106672: One number is 4 less than another. If 10 times the smaller number minus 3 times the larger number is 51, find the two numbers. So is this x(x-4)=51 I am lost Thanks1 solutions Answer 77629 by rcmcc(152)   on 2007-10-28 10:43:21 (Show Source): You can put this solution on YOUR website!Word problems are tricky to understand. The easiest way to derive an equation is to go step by step. the first equation you can find is simple. y=x-4 where x is the larger number and y is the smaller one so if y is the smaller number 10x y subtracting 3x the larger number x looks like this 10y-3x=51 so your two equations are below y=x-4 10y-3x=51 because you have y isolated you can substitute it in for the second equation 10y-3x=51 10(x-4)-3x=51 expand the brackets 10x-40-3x=51 simplify 7x-40=51 bring the 40 to the other side 7x=91 divide by 7 x=13 because you have the larger number subtract 4 to find the smaller number your two numbers are (13 and 9)
 Proportions/99245: It takes only 0.4 seconds for the ball to travel the 60.5 feet from the pitcher's mound to home plate. How many miles per hour did the ball travel?1 solutions Answer 72200 by rcmcc(152)   on 2007-09-19 19:04:48 (Show Source): You can put this solution on YOUR website!You know that there are 5280 feet in a mile. You can find the distance in miles that the ball traveled from the pitchers mound to the plate by dividing. now you find how many hours elapsed note that 60 seconds in a min and 60 mins in an hour now by dividing the time by the distance you can find the mph of the ball the ball traveled aprox 103 mph
 Miscellaneous_Word_Problems/99126: The simple interest "I" on a principal of "P" dollars at interest rate "r" for time "t", in years, is given by I = Prt. Find the simple interest on a principal of \$6000 at 3% for 2 years. (Hint: 3%=0.03) Thank you1 solutions Answer 72138 by rcmcc(152)   on 2007-09-19 11:27:35 (Show Source): You can put this solution on YOUR website!For this question it is simple substitution P=6000 R=.03 T= 2 an. Assuming that it is not compounded after the first year you substitute the values into the simple interest formula I=PRT I=(6000)(.03)(2) I=360
 Graphs/99113: I need help with graphing an equation x-2y=6 x+4y=5 I did try but I am having problems.I have 16 problems I will try the other ones on my own, 1 solutions Answer 72136 by rcmcc(152)   on 2007-09-19 11:23:41 (Show Source): You can put this solution on YOUR website!to graph this question you first must isolate y from each side bring the x to the other side divide by -2 Repeat the same for the next line Bring x to the other side divide by 4 by substituting in your x value into your isolated equations you can find the y coordinate. ex. for the equation you are given a random x value of 4 place 4 in for x and you get the y value now plot (4,-1) on your graph, and repeat for other points until you can draw your graph.
 Travel_Word_Problems/99122: I am having trouble with this problem Please Help: Two planes leave Philadelphia at the same time. One heads due south toward Atlanta; the other heads due north toward Boston. The Atlant bound plane flies 50 mph faster than the other. In 1/2 hour the pplanes are 275 miles apart. What are their speeds?1 solutions Answer 72132 by rcmcc(152)   on 2007-09-19 11:09:59 (Show Source): You can put this solution on YOUR website!Because you are looking for the speed of the plane in mph. you should convert the data into full hours. assuming the planes stay at a constant speed. 2x the time should equal 2x the distance So if in 1/2 an hour the planes are 275 miles appart in one hour they will be 550 miles appart. because one plane travels 50 mph faster than the other, 550 is the same as x+(x+50) where x represents the speed of the slower plane. because this is a simple linear equation you can combine the terms to take the 50 to the other side divide by 2 so the slower plane is traveling at 250mph, and the faster plane is traveling 50mph faster so the second plane is traveling at 300mph you can check this answer in the question at 1/2 (250mph) plane 1 is 125miles from the origin at 1/2 (300mph) plane 2 is 150miles from the origin because they are in opposite directions they are 275 miles appart.
 Miscellaneous_Word_Problems/99119: "Suppose the temperature outside is dropping at a constant rate. At noon, the temperature is 70 degrees f and it drops to 58 degrees at 5:00 p.m. How much did the temperature change each hour?1 solutions Answer 72128 by rcmcc(152)   on 2007-09-19 11:00:24 (Show Source): You can put this solution on YOUR website!To solve this problem you need 2 pieces of data. 1. The amount of time that passes 2. The temperature drop over that amount of time Because you measure the time from noon (12) to (5) there has been a 5 hour time difference. to find the temperature change subtract 58 from 70 and you get 12 degrees. now divide the temperature by the time is your answer. in decimal form 2.4 degrees per hour.
 Angles/85161: If a right angle has a hypotenuse of the square root of 58 and a second side of 7, what is the length of the third side?1 solutions Answer 61361 by rcmcc(152)   on 2007-06-12 09:40:17 (Show Source): You can put this solution on YOUR website!The right angle triangle formula is because c= hypotenuse and you have a side a/b you can isolate the other side by making the equation by quaring the information you have you can fill in the equation and by square routing the answer you find a A=3 so your third side is equal to 3
 Equations/84692: My Problem is to 2 Solve This Verbal Equation: The product of 9 and a number plus 17 is equal to -1 Any help with this problem would be greatly appreciated ,Kia Jayy1 solutions Answer 61020 by rcmcc(152)   on 2007-06-07 13:07:07 (Show Source): You can put this solution on YOUR website!A product means that you multiply the numbers change "a number" to x and you can form the equation 9x+17=-1 subtract 17 from each side 9x=-18 divide by 9 from each side x=-2 so your number is -2
 Equations/84694: My Verbal Equation Is To Figure Out What: Twelve less than 2 times a number is equal to -1 is. Any help with this problem would be greatly appreciated=) ,Kia Jayy1 solutions Answer 61019 by rcmcc(152)   on 2007-06-07 13:04:44 (Show Source): You can put this solution on YOUR website!Start by making "a number"=x "twelve less"=-12 and "equal" to = by changing the words into their literal meaning you get the equation -12+2x=-1 add 12 to each side -12+2x=-1 +12 +12 ________________ 2x=11 divide by 2 x=5.5 or 11/2 so your number is 5.5
 Bodies-in-space/72365: How much glass in square cm is needed for aquarium 200cm deep, 600 cm long, and 300 cm wide?1 solutions Answer 51779 by rcmcc(152)   on 2007-02-27 09:51:49 (Show Source): You can put this solution on YOUR website!There are two possible answers for this question. If the aquarium has a glass lid, more glass will be needed If the aquarium has no glass lid (like normal) less glass will be needed. To find the two solutions find the area of each side. Because the sides are paired, you only have to calculate the area 3 times. We start with the sides 200cm*600cm=120000cm squared*2 =240000cm squared the small sides 200cm*300cm=60000cm*2= 120000cm squared and the top and bottom 300cm*600cm= 180000cm.... with no glass lid the amount of glass needed is 540000cm squared with a glass lid the amount of glass needed is 720000cm squared
 Miscellaneous_Word_Problems/72420: tuition for 2007 is 7% more than the price of tuition last year than it was in 2006. If tuition for 2007 was 13910 how much did it cost in 2006?1 solutions Answer 51778 by rcmcc(152)   on 2007-02-27 09:44:32 (Show Source): You can put this solution on YOUR website!To find the Tuition rate from the previous year, divide 2007s tuituion by 7% so 13910/1.07= 13000 so the tuition is 13000 in 2006
 Equations/71821: Solve the system by addition. 1 solutions Answer 51377 by rcmcc(152)   on 2007-02-23 13:20:36 (Show Source): You can put this solution on YOUR website!x + y = 1 x - y = 3 simply add all the terms 2x=4 x=2 substitute in 2 for x 2+y=1 y=-1
 Rational-functions/71896: This question is from textbook Introductory and intermediate algebra Add 7+ [1/(x-5)]1 solutions Answer 51376 by rcmcc(152)   on 2007-02-23 13:18:23 (Show Source): You can put this solution on YOUR website!To add find a common denominator for the term in this case the common denominator is (x-5) to get a common denominator multiply 7 by (x-5) when you simplify the numberator you get
 Money_Word_Problems/71900: A krispy creme assistant manager earns \$2528 each month for working a 48-hour week. Find (a) the number of hours worked each month and (b) the manager's hourly earnings. (1 month = 4.3 weeks) Round to the nearest cent.1 solutions Answer 51375 by rcmcc(152)   on 2007-02-23 13:12:06 (Show Source): You can put this solution on YOUR website!To find the amount of hours worked each month, simply multiply the weekly hours by 4.3 (4.3 weeks in a month) 48x4.3 206.4 hours to find the wage, divide the monthly salary by the amount of hours worked. \$2528/206.4 his hourly wage is \$12.25 rounded to the nearest cent.
 Graphs/71860: ```Find the horizontal asymptote of the rational function Possible answers: Thank you. Exactly what is a asymptote? Can anyone explain the simplest way to solve this problem?```1 solutions Answer 51355 by rcmcc(152)   on 2007-02-23 09:49:19 (Show Source): You can put this solution on YOUR website!Hello, Because you have a linear function with a division equation, the asymptote is located where the equation is undefined. this occurs when the function is divisable by 0. because no equation is valid when you divide by 0 that is your asymptote. to find this simply look at the bottom half of your equation the value that makes the bottom half 0 is (1/2) ... 4(1/2)-2=0 so your asymptote is 1/2
 Polynomials-and-rational-expressions/66499: perform the indicated operation. Write the result in standard decimal notation. (9.8 x 10^-4)(2.1 x 10^2)(3.1 x 10^-1)1 solutions Answer 47235 by rcmcc(152)   on 2007-01-12 14:47:26 (Show Source): You can put this solution on YOUR website! The easiest way to solve this is by converting the terms into standard form and then placing them back into notation form. 9.8E-4 is the same as 0.00098 as the decimal moves 4 forward 2.1E2 is teh same as 210 as the decimal moves 2 back 3.1E-1 is the same as 0.31 as the decimal moves 1 back multiply these to form one term 0.00098x210x0.31= 0.063798 because you are only given 2 significant digits you round to the 2nd placing in this case you round it up to 0.064 to get the term back into standard notation move the decimal back 2 places you get the answer
 Polynomials-and-rational-expressions/66506: multiply the expression (5m - 6n + 7) (2m - 3n - 4)1 solutions Answer 47234 by rcmcc(152)   on 2007-01-12 14:36:16 (Show Source): You can put this solution on YOUR website!(5m - 6n + 7)(2m - 3n - 4) to multiply out this term we use a method known as foiling. You multiply each term in the first equation by each term in the second equation. I will break this down step by step. Take 5m and multiply it. 5m(2m - 3n - 4) 10m^2-15mn-20m (hold onto this we will use it later.) now -6n -6n(2m - 3n - 4) -12mn+18n^2+24n(hold onto this we will use it later.) now we will multiply out 7. 7(2m - 3n - 4) 14m-21n-28 You now take all the results from the foil process and line them up. 10m^2-15mn-20m-12mn+18n^2+24n+14m-21n-28 you combine all like terms 10m^2+18n^2-27mn-6m+3n-28 this is your answer
 Geometric_formulas/66556: This question is from textbook Advanced mathematics A furniture salesperson is normally paid \$160 for a 40 hour week. During the week of the sale, his hourly pay was increased 25 percent and he was allowed to work 60 hours. How much did he make during the week of sale?1 solutions Answer 47233 by rcmcc(152)   on 2007-01-12 14:26:03 (Show Source): You can put this solution on YOUR website!To solve this question you must first find the amount he makes in an hour \$160/40h=\$4.00/h if it was increased by 25%, take his wage (100%) add 25% to the value. because percents are decimals, 100% can be written as 1.0 and 25% can be written as .25 to find the new value multiply \$4 by 1.25 (125%) 4x1.25 =\$5/h now multiply it by the amount of hours he will spend working (60) 5x60=\$300/week
 Polynomials-and-rational-expressions/66560: Solve simultaneously for a and b a+2b=5 a-b=01 solutions Answer 47232 by rcmcc(152)   on 2007-01-12 14:21:29 (Show Source): You can put this solution on YOUR website!Use a system of equations to solve a+2b=5 a-b=0 isolate a from the first equation a=5-2b substitute into the second formula 5-2b-b=0 5-3b=0 3b=5 b=5/3 now add this to your first equation a+(2(5/3))=5 a+10/3=5 a=5/3 both a and b are 5/3
 Graphs/66407: Technology. Driving down a mountain, Tom finds that he has descended 1800 ft in elevation by the time he is 3.25 mi horizontally away from the top of the mountain. Find the slope of his descent to the nearest hundredth.1 solutions Answer 47108 by rcmcc(152)   on 2007-01-10 14:04:10 (Show Source): You can put this solution on YOUR website!lwt us convert the whole question into feet. I mile=5280 feet so the x distance on a graph will be 17160 feet the slope of the graph can be found by the equation rise/run or Y2-Y1/X2-X1 fisrt you must find the 2 points on the graph to find the slope. these were given in your data, the first position is x, this is at zero. and Y is at 1800 feet so you have the point (0,1800) the second point is also given, where x is 17160 feet away, and where he stopped y=0 so your two points are (0,1800) and (17160,0) so in the equation you will get 0-1800/17160-0=slope the slop of your graph is (+/-)0.104895 where depending on your view is positive or negative.
 Percentage-and-ratio-word-problems/66404: The Brown's want to purchase a house that costs \$130,000. They plan to take out a \$90,000. mortgage and put \$40,000 as a down payment. The bank informs them with a 20-year mortgage their monthly cost would be \$752.40 and with a 30-year mortgage their monthly cost would be \$660.60. Determine the amount they would save on the cast of the house if they selected the 20-year mortgage rather than the 30-year mortgage. 1 solutions Answer 47107 by rcmcc(152)   on 2007-01-10 13:54:53 (Show Source): You can put this solution on YOUR website!the first information about the amount of the house is un-needed to answer the question. all you need is the amount cost per month. because the 20 year period has 240 months. it would cost 240x\$752.40=\$180 576 and the 30 year period has 360 months it would cost 360x\$660.60=\$237 816 so the home owner would save \$57 240 taking out the 20 year mortgage.
 Equations/66408: 4(8-t)=20 6(2x-1)=4(2x+5) 7(2w-3)-5(3w-1)=01 solutions Answer 47106 by rcmcc(152)   on 2007-01-10 13:46:03 (Show Source): You can put this solution on YOUR website!4(8-t)=20 6(2x-1)=4(2x+5) 7(2w-3)-5(3w-1)=0 I belive you are looking to solve for the variable in each case. on the first. 4(8-t)=20 expand the brackets. 32-4t=20 subtract 32 from each side -4t=-12 switch signs to make T positive 4t=12 divide out 4 t=3 next 6(2x-1)=4(2x+5) expand brackets 12x-6=8x+20 put similar terms on different sides 12x-8x=20+6 4x=26 divide out 4. x=6.5 the last one 7(2w-3)-5(3w-1)=0 expand the brackets 14w-21-15w+5=0 place similar terms on opposite sides 14w-15w=21-5 -w=18 switch signs to make w positive. w=-18
 Linear-equations/59106: I am running into a problem when I try to figure out this answer. What is the rule for multiplying negative and positive numbers? If you have 3 x -2, is the answer negative 6? This is the problem I have to answer: 2(x-3)-3(x+5)=3(x-2)-71 solutions Answer 40533 by rcmcc(152)   on 2006-10-31 14:20:10 (Show Source): You can put this solution on YOUR website!no, when multiplying negatives with a positive the answer is always negative, when multiplying two negatives, the answer is positive. to solve this question we must expand the terms into the brackets. we can combine these terms add x to both sides, add 13 to both sides divide out 4 to isolate x good luck
 Geometry_Word_Problems/59072: find the surface area in square centimeters of a rectangular solid 8 cm long, 5 cm wide, and 3 cm high?1 solutions Answer 40532 by rcmcc(152)   on 2006-10-31 14:14:06 (Show Source): You can put this solution on YOUR website!in a rectangular prism there is always 2 opposite sides that have the same area, to find the surface area, the sides, multiply by LxW and multiply by 2. since there are 3 sets of sides we have to make 3 calculations and add the together. LxW is one set LxH is another set WxH is the third set set 1=(2)x(8)x(5) set 1 surface area is 80cm squared set 2=(2)x(8)x(3) set 2 surface area is 48cm squared set 3=(2)x(5)x(3) set 3 surface area is 30cm squared to find the total surface area, add the numbers together. the total surface area of the cube is 158cm squared