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# Recent problems solved by 'josmiceli'

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 Rational-functions/638389: On a 1287 mile long road trip in windy conditions, a family calculates their fuel economy to be 18 miles per gallon over the 2 days it takes to reach their destination. On their 2-day return trip, with a similar wind at their backs, their calculations show a fuel economy of 26 miles per gallon. Calculate the expected fuel economy of their vehicle in ideal (non-windy) conditions (f) as well as the influence of the wind (w) in miles per gallon.1 solutions Answer 402187 by josmiceli(9654)   on 2012-08-17 22:57:21 (Show Source): You can put this solution on YOUR website! Add the equations mi/gal and mi/gal I think the 1287 mi information is not needed for the problem
 Travel_Word_Problems/638405: a trip to washington from boston will take you 5 3/4 hours. If you have traveled 1/3 of the way, how much longer will the trip take?1 solutions Answer 402183 by josmiceli(9654)   on 2012-08-17 22:45:02 (Show Source): You can put this solution on YOUR website!You have 2/3 of the distance left. As long as your speed is constant, you have of the time left. That is hrs minutes You have 3 hours and 50 minutes left
 Finance/638399: Hello Sir/Mame, I would be grateful for any assistance regarding the following question. 'In my pocket, I have some 20 cent coins and 50 cent coins. I have seven more 50 cent coins than 20 cent coins and have a total of \$16.10. how many of each coin do I have?' My teacher would like me to use algebra as a replacement of 'Trial and Error' Thank you! Sash Lack1 solutions Answer 402181 by josmiceli(9654)   on 2012-08-17 22:36:26 (Show Source): You can put this solution on YOUR website!Let = number of 20 cent coins = number of 50 cent coins given: ( in cents ) You have 18 twenty cent coins and 25 fifty cent coins check answer: OK
 Surface-area/638253: A sewing box is 24 cm by 18 cm by 6 cm. What is the total surface area?1 solutions Answer 402086 by josmiceli(9654)   on 2012-08-17 09:11:53 (Show Source): You can put this solution on YOUR website!The bottom and the top surfaces are both x Both sides are x Both the front and the back are x So I have: Total surface = Total Surface = Total Surface = 1368 cm2
 Age_Word_Problems/638254: Mary is now four times as her daughter.four years ago the product of their ages was 40 find their present ages. Thankyou1 solutions Answer 402083 by josmiceli(9654)   on 2012-08-17 09:01:44 (Show Source): You can put this solution on YOUR website!Let = Mary's age now Let = Daughter's age now given: (1) (2) ------------------------ Substitute (1) into (2) (2) (2) (2) (2) (2) (2) Daughter's age must be positive, so the Daughter is 6 and, since (1) (1) (1) The Mother is 24 -------------- check answers (2) (2) (2) (2) OK
 Age_Word_Problems/638224: In three more years, Katrina's mother will be six times as old as Katrina was last year. When Katrina's present age is added to his grandfather's present age, the total is 57. How old is each one now?1 solutions Answer 402080 by josmiceli(9654)   on 2012-08-17 08:48:35 (Show Source): You can put this solution on YOUR website!Let = Katrina's age now Let = Mother's age now Let = Grandfather's age now given: ------------ Some information must be missing. You've got 3 unknowns but only 2 equations, so it can't be solved as it stands.
 Volume/638243: Suppose every edge of a cube measures fifteen centimeters. What is the volume of the cube? 1 solutions Answer 402077 by josmiceli(9654)   on 2012-08-17 08:23:50 (Show Source): You can put this solution on YOUR website!Volume = cubic centimeters
 Triangles/638246: One of the angle of a triangle is 65. Find the remaining two angles if their difference is 251 solutions Answer 402076 by josmiceli(9654)   on 2012-08-17 08:19:57 (Show Source): You can put this solution on YOUR website!Call the unknown angles and The angles of a triangle always add up to 180 degrees, so (1) also given is (2) --------------- (2) Substitute this into (1) (1) (1) (1) (1) and, since (2) (2) (2) The remaining angles are 45 and 70 degrees check: (1) (1) (1) OK
 percentage/637969: How do I draw a shape that represents 150% ?1 solutions Answer 401949 by josmiceli(9654)   on 2012-08-16 11:42:40 (Show Source): You can put this solution on YOUR website!You could say that a square = 100% Then combine a square and a half a square and call this rectangle 150%
 Travel_Word_Problems/637973: A bus is 13 kilometers from town, going away at 80km/h. At the same moment a car leaves town going the same direction as the bus, at the same speed. x = number of hours the car and bus have been going 80x = car's distance from town 13 + 80x = bus's distance from town After how long will the bus's distance be twice the car's distance? I already know that it will happen when the bus is 26 km from town, and the car is 13 km from town, meaning they've each traveled 13km. At 80km/h this means it will happen at 13/80 of an hour, or 9.75 minutes. But I can't figure out how to write an algebraic equation showing this. Here is what I tried, and I get a negative number: 80x = 2 * 80x + 13 80x - 13 = 160x -13 = 80x -13/80 = 80x/801 solutions Answer 401947 by josmiceli(9654)   on 2012-08-16 11:40:11 (Show Source): You can put this solution on YOUR website!given: km km km * hrs ----------- * you just wrote this backwards
 Proportions/637892: Debbie and kevin share profits in the ratio of 4:3 they admit jessie into the partnership for 1/5 share of the profits. Debie and Kevin will continue to share profits in the same ratio as between themselves. What will be the profit sharing ratio of the new partnership of Debbie, Kevin and Jessie?1 solutions Answer 401934 by josmiceli(9654)   on 2012-08-16 00:51:07 (Show Source): You can put this solution on YOUR website!They keep the ratio of profit at 4:3 J has 1/5 share, so D and K have 4/5 share together. D has share K has share J has or share ----------------------------- Note that as it should The ratios now are: D:K:J = 16:12:7
 Rational-functions/637896: what is the graph to y=tan(θ/2)1 solutions Answer 401933 by josmiceli(9654)   on 2012-08-16 00:40:54 (Show Source): You can put this solution on YOUR website!As the tangent angle rotates around the unit circle, every 90 degrees it switches this way starting with 0 degrees: 0, infinity, 0, minus infinity, 0 ( which is back to 0 degrees ) Here's the plot:
 Money_Word_Problems/637539: Help on this problem would be greatly appreciated! A village wants to build a community center that is projected to cost 1.2 million dollars. Cost per resident is increased by \$3 as it is discovered that there are 225 fewer residents than when planning began 2 years ago. What is the revised cost per resident?1 solutions Answer 401750 by josmiceli(9654)   on 2012-08-14 21:11:14 (Show Source): You can put this solution on YOUR website!Let = the original number of residents Let = the original cost/resident (1) (2) ------------------------------- (2) Substitute (1) into (2) (2) (2) (2) Substitute this back into (1) (1) (1) (1) The revised cost/resident is \$131 check: (1) (1) (1) and (2) (2) {2) ------------------------ This is close but a little off. Can you see where I messed up?
 Exponents-negative-and-fractional/637367: How do you solve 2^(5/2) - 2^(3/2)? The fractions are fractional exponents (not mixed numbers). I submitted this question yesterday but I apologize it was in the wrong form (I did not include parentheses.)The answer is supposed to be 2^3/2 according to the answer key. I need to see it worked out line by line. Thanks so much!1 solutions Answer 401598 by josmiceli(9654)   on 2012-08-14 10:35:26 (Show Source): You can put this solution on YOUR website! This is the same as Factor out ------------- check: OK
 Probability-and-statistics/637333: IN HOW MANY WAYS CAN 3 COINS FALL?1 solutions Answer 401570 by josmiceli(9654)   on 2012-08-14 08:16:04 (Show Source): You can put this solution on YOUR website!H H H T T T H T T H H T T H T H T H T T H H H T -------- This is 8 ways, which is 2*2*2 You multiply because it is ( 2 choices ) AND ( 2 choices ) AND ( 2 choices ) -------- It sounds like the coins are falling all at once, and the order doesn't matter, so H T T is the same as T T H or T H T , so that means the coins can fall in 4 ways H H H T T T H H T T T H
 Trigonometry-basics/637336: solution and graph for this y= 3 + 2 sin (2x - pi/2)1 solutions Answer 401569 by josmiceli(9654)   on 2012-08-14 08:02:30 (Show Source): You can put this solution on YOUR website!Here's a chart: ----------- x . . . . . . 2x . . . . . . 2x - pi/2 . . . . . . 3 + 2sin(2x - pi/2) pi/2 . . . . pi . . . . . . . pi/2 . . . . . . . . . . 4 pi . . . . . . 2pi . . . . . . 3pi/2 . . . . . . . . . . 1 3pi/2 . . . 3pi . . . . . . 5pi/2 . . . . . . . . . . 4 ----------------------------------- It looks like y has a max of and a min of , and every pi/2 y is 1 or 4. here's the plot:
 Graphs/637114: I am studying for the GRE and have a question about f(x) equations. The problem is f(x) = 3x + 4. I haven't studied f(x) problems in quite a while. How do I figure out what the slope of f is, and what the x and y-intercepts of f is? Also, any other information about slope equations would be greatly appreciated. Thank you!1 solutions Answer 401431 by josmiceli(9654)   on 2012-08-13 14:49:13 (Show Source): You can put this solution on YOUR website!The definition of slope is ( change in y ) / ( change in x ) You need either 2 points on a curve or the equation of that curve to find the slope. When the equation is in the form , is the slope, so if the equation is , the slope is ------------- Note that , and you can use either definition.
 Polynomials-and-rational-expressions/637055: i need to show all my work when completing this problem. I tried but i cant figure out how to get the denominators the same. here is the problem. please add these to together. x^2-49/2x-1 + x^2-14x+49/1-2x1 solutions Answer 401376 by josmiceli(9654)   on 2012-08-13 11:23:53 (Show Source): You can put this solution on YOUR website!The key to this is the fact that and, since , you can rewrite this as: Factoring the polynomials: You could take it further, too
 Travel_Word_Problems/637048: a plane traveled 1386 miles to singapore and back. The trip there was with the wind. It took 9 hours. The trip back was into the wind. the trip back took 11 hours. Find the speed of the plane in still air and the speed of the wind.1 solutions Answer 401375 by josmiceli(9654)   on 2012-08-13 11:00:06 (Show Source): You can put this solution on YOUR website!Let = the speed of the wind in mi/hr Let = the speed of the plane in still air = the plane's speed going with the wind = the plane's speed going against the wind ---------------- Equation going with the wind: (1) Equation going against the wind: (2) ---------------------- (1) (1) Substitute this result into (2) (2) (2) (2) (2) (2) Substitute this result into (1) or (2) (2) (2) (2) The plane's speed in still air is 140 mi/hr The speed of the wind is 14 mi/hr check: (1) (1) (1) OK
 Miscellaneous_Word_Problems/637051: I cannot figure out how this is done: "you need a piece of lumber 5' 11" long. How much will you have left over if you cut what you need from a piece 8' 3" long"1 solutions Answer 401371 by josmiceli(9654)   on 2012-08-13 10:44:45 (Show Source): You can put this solution on YOUR website!You need to subtract feet from feet and inches from inches. The feet is easy, but how do you subtract 11 inches from 3 inches? -------------------- What you do is borrow 12 inches from the 8 feet, so now it looks like 7' 15" ------------------------ Now subtract feet from feet and inches from inches 7' 15" minus 5' 11" = 2' 4"
 Travel_Word_Problems/636921: A car travels at an average speed of 64 miles per hour. How many miles does it travel in 5 hours and 45 minutes? 1 solutions Answer 401292 by josmiceli(9654)   on 2012-08-12 19:54:14 (Show Source): You can put this solution on YOUR website! miles Note that 45 minutes is .75 hrs
 Polynomials-and-rational-expressions/636899: I'm trying to help a friend who is in a course segment called "real zeros of a polynomial function". The math is OK, but we're stymied by the vagueness of the problem wording. One portion of a problem boils down to "express 1/(3x^6 + 86x^3 + 135) as a QUOTIENT". Well, it is a quotient already. And it can't be neatly simplified or factored. What are they asking for?1 solutions Answer 401277 by josmiceli(9654)   on 2012-08-12 18:08:24 (Show Source): You can put this solution on YOUR website!All I can figure is that somehow they want you to find the value of , then plug it into the denominator, and come up with a decimal number for the fraction.
 Miscellaneous_Word_Problems/636903: Jimmy is having speaker wire run in his family room. To install the speaker wire, one company charges \$85 plus \$0.20 per foot of wire used. If Jimmy needs the cost of installation to remain below \$95, how many feet of wire can he have installed? 1 solutions Answer 401276 by josmiceli(9654)   on 2012-08-12 18:00:13 (Show Source): You can put this solution on YOUR website!Let = cost of installation Let = number of feet of wire given: The number of feet of wire must be less than 50
 Expressions-with-variables/636896: Use the equations below to find the length of the pipe. (there is a pipe separated into an a, b, and c section) a + b = 15 b - a = 3 a + b - 12 = c How do i set up an equation for this problem? Thanks!1 solutions Answer 401274 by josmiceli(9654)   on 2012-08-12 17:54:26 (Show Source): You can put this solution on YOUR website!There are 3 equations and 3 unknowns. That means this is solvable, since number of unknowns must equal number of equations to solve. ------------ (1) (2) (3) ------------------ (1) Substitute this into (2) (2) (2) (2) (2) (2) and, since (1) (1) (1) Substitute these results into (3) (3) (3) (3) (3) -----------
 Rate-of-work-word-problems/636702: A, B, and C can do a piece of work in 10 days. A and B can do it in 12 days, A and C in 20 days. How many days would it take each to do the work alone?1 solutions Answer 401180 by josmiceli(9654)   on 2012-08-12 02:18:49 (Show Source): You can put this solution on YOUR website!Let their rates of working in ( fraction of work finished ) / ( days to do it ) = , , and given: (1) (2) (3) ----------------------- (2) (3) and, by substitution, (1) (1) (1) {1) (1) ----------------- (2) (2) (2) (2) ---------------- (3) (3) (3) (3) ----------------- A takes 30 days working alone B takes 20 days working alone C takes 60 days working alone ------------------------ check: (1) (1) (1) (1) OK
 Graphs/636699: I would appreciate your help on this: f(x)=-2x^2+2x+6. Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function. This is what I have so far. x coordinate of the vertex is 1/2 the y-coordinate of the vertex is_____ the equation of the line of symmetry is x= The maximum /minimum of f(x)is_____ The value f(1/2)=13/2 is maximum1 solutions Answer 401179 by josmiceli(9654)   on 2012-08-12 01:45:31 (Show Source): You can put this solution on YOUR website! --------- Now plug this back into equation This is y-co-ordinate of vertex There is a maximum at ( 1/2. 13/2 ) is equation of line of symmetry ---------------- Here's the plot:
 �t�e�s�t/636616: 2x^2-4x+1 ----------- change to a mixed expression x+2 1 solutions Answer 401142 by josmiceli(9654)   on 2012-08-11 17:52:59 (Show Source): You can put this solution on YOUR website!The 1st term is Subtract this from The result is ----------------- The 2nd term is Subtract this from The result is ---------------- The answer is check answer: OK
 Quadratic_Equations/636499: f(x)=x2 + 2x - 9 determine whether the given quadratic function has a minmum or maximun value. then find the coordinated of the mininmun or maximun point.1 solutions Answer 401058 by josmiceli(9654)   on 2012-08-11 08:04:34 (Show Source): You can put this solution on YOUR website! Since the coefficient of the squared term is positive ( +1 ), then the function has a minimum. ------------- The value of the minimum will be at when the equation is in the form ----------------- Plug this back into the equation ------------ So the minimum is at (-1,-10) Here's a plot:
 logarithm/635521: Find all of the solutions to the equation: Could you please guide me through this? Thank you so much for helping and thank you so much for your time in helping me with this problem!1 solutions Answer 400387 by josmiceli(9654)   on 2012-08-07 17:27:08 (Show Source): You can put this solution on YOUR website! --------------------- The sine is negative in the 3rd and 4th quadrants. In the 3rd quadrant, the angle is radians or degrees ---------------- In the 4th quadrant, the angle is radians, or degrees
 Travel_Word_Problems/635016: Karen traveled 640 miles by boat and returned by plane. She spent 42 hours traveling on the trip. If the plane is 20 times faster than the rate of the boat, find each rate.1 solutions Answer 400044 by josmiceli(9654)   on 2012-08-05 20:35:09 (Show Source): You can put this solution on YOUR website!Let = time spent traveling by boat = time spent traveling by plane Let = rate by boat Let = rate by plane ------------------------ Equation for boat: (1) (2) ----------------------- (2) Substitute (1) into (2) (2) (2) ------------------ You can finish. Find and
 Linear_Equations_And_Systems_Word_Problems/634479: You have 15L of 24% acid solution. How much water should you add in order to dilute the solution so that it is 8% acid?1 solutions Answer 399657 by josmiceli(9654)   on 2012-08-03 20:55:56 (Show Source): You can put this solution on YOUR website!Let = liters of water to be added liters of acid in 24% solution 30 liters of water should be added check: OK