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Linear_Equations_And_Systems_Word_Problems/219686: Rise and run: If the rise is 3/2 and the run is 5, then what is the ratio of the rise to the run? 1 solutions Answer 165171 by solver91311(16897)   on 2009-09-30 16:29:15 (Show Source): You can put this solution on YOUR website! Saying "the ratio of to " is exactly the same as saying . So just divide by 5. John

Length-and-distance/219671: When finding the coordinates for a problem that requires the formula (x,y) -> (x+a, y+b) What does a and b stand for and How do you find it? Thank you for your help! :) 1 solutions Answer 165167 by solver91311(16897)   on 2009-09-30 16:26:51 (Show Source): You can put this solution on YOUR website! You have to share the whole problem. a and b are offsets to the original coordinates, but without the entire problem I can't tell how to determine their values. John

Human-and-algebraic-language/219675: Aside from using trial and error, how does one solve this type of problem? A large box of popcorn costs $4. A small box costs $3. 59 boxes are sold totalling $200. How many boxes of each were sold? Thanks. 1 solutions Answer 165161 by solver91311(16897)   on 2009-09-30 16:23:00 (Show Source): You can put this solution on YOUR website! Let represent the number of small boxes sold. Let represent the number of large boxes sold. Then dollars is the amount of money collected from the sale of small boxes and dollars is the amount of money collected from the sale of large boxes. We know that: because 59 boxes of both sizes were sold. We also know that: because sales totaled $200. So, since , we can say Given this relationship we can say: by substitution of for Now all you have to do is solve for to find the number of small boxes sold and then subtract that from 59 to find the number of large boxes sold. John

Polynomials-and-rational-expressions/219550: find a polynomial function of degree 3 with the given numbers -2, 3, 5 1 solutions Answer 165138 by solver91311(16897)   on 2009-09-30 15:45:48 (Show Source): You can put this solution on YOUR website! The only way this question makes any sense at all is if you really meant to say: "Find a polynomial function of degree 3 with the given numbers as zeros of the function. Therefore, I shall presume that is what you meant. However, before continuing I would like to caution you to take more care to state your questions accurately lest the tutors on this site get annoyed with your cavalier attitude and begin to ignore your requests for help. If the zeros of a 3rd degree polynomial function are -2, 3, and 5, then the factors of the polynomial must be: Hence: You will need to multiply the three binomials to get the proper final form of your answer. John

Equations/219587: if sally paints a house in 4 hours and john paints the same house in 6 hours how long will it take for them both to paint the house 1 solutions Answer 165113 by solver91311(16897)   on 2009-09-30 14:44:45 (Show Source): You can put this solution on YOUR website! Let represent the number of hours it takes Sally to paint the house. Let represent the number of hours it takes John to paint the house. If Sally can paint the house in hours, she can paint of the house in one hour. Likewise, John can paint of the house in one hour. So given both working together, the house will get painted at a rate of: of the house per hour. Therefore the entire house will be painted in: hours. Just plug in the values you were given and do the arithmetic. John

Functions/219561: I understand a and c of this problem but I cannot figure out b and d because of the month to days thing. The question is; Newborn blue whales are approximately 24 feet long and weigh 3 tons. Young whales are nursed for 7 months, and by the time of weaning they often are 53 feet long and weigh 23 tons. Let L and W denote the length (in feet) and the weight (in tons), respectively, of a whale that is t months of age. a.) If L and t are linearly related, express L in terms of t. L=mt+b 53=m(7)+24 29/7=m L=(29/7)m+24 b.) What is the daily increase in the length of a young whale? (Use 1 month= 30 days) ??? L=(29/7)?+24 c.) IF W and t are linearly related, express W in terms of t. W=mt+c 23=m(7)+3 20/7=m W=(20/7)m+3 d.) What is the daily increase in the weight of a young whale? W=(20/7)?+3 1 solutions Answer 165112 by solver91311(16897)   on 2009-09-30 14:38:29 (Show Source): You can put this solution on YOUR website! You have an error in parts A and D. I think perhaps you confused the symbol m meaning slope in a linear equation and the fact that time t is measured in months. The correct answer to part A is: And the correct answer to part D is: As to part B: The length at zero months is: The length at one month is: And the difference is: feet meaning that the whale increases its length that much each month, or each 30 days. Therefore, the whale will increase its length one-thirtieth of that amount each day, namely: feet. You can do your own arithmetic. Do part D the same way, namely take the slope number m from the weight equation and divide it by 30. John

Polynomials-and-rational-expressions/219563: please solve: f(g(x)) f(x)= 4x^3-3x g(x)= 6x-9 1 solutions Answer 165081 by solver91311(16897)   on 2009-09-30 13:31:07 (Show Source): You can put this solution on YOUR website! If , then and . So: Of course, this needs to be simplified. I'll leave that part to you. John

logarithm/219556: write the equation 2^6=64 in logarithmic form 1 solutions Answer 165079 by solver91311(16897)   on 2009-09-30 13:24:31 (Show Source): You can put this solution on YOUR website! So: John

Rate-of-work-word-problems/219554: an inlet pipe can fill a large water tank in 3 hours. an outlet pipe can empty the same tank in 5 hours. given an empty water tank at 8pm activate both pipes. at what time on the clock will it be before the tank is compeletly filled? 1 solutions Answer 165076 by solver91311(16897)   on 2009-09-30 13:18:58 (Show Source): You can put this solution on YOUR website! Let represent the number of hours it takes the inlet pipe to fill the tank. Let represent the number of hours it takes the outlet pipe to empty the tank. If the inlet can fill the tank in hours, it can fill of the tank in one hour. Likewise, the outlet can empty of the tank in one hour. So given both pipes open, the tank will fill at a rate of: per hour. Therefore the entire tank will be full in: hours. Just plug in the values you were given and do the arithmetic. Don't forget to add your answer to 8pm to get the clock time. John

Travel_Word_Problems/219376: Elisa walked a certain distance at 5mi/h and then jogged twice that distance a 8 mi/h. Her total time walking and jogging was 2 hr and 15 min. How many miles did she walk? I am trying to use the formula time= distance/ rate I set d egual to distance walked at 5mi/h and 2d to distance walked at 8mi/hr d/5+2d/8=135 Im lost at this point ,cant seem to see what im doing wrong any help would be greatly appreciated 1 solutions Answer 165070 by solver91311(16897)   on 2009-09-30 13:04:38 (Show Source): You can put this solution on YOUR website! The first thing that you are doing wrong is mixing your units of measure. You converted 2 hours 15 minutes to 135 minutes, but you left your rates of speed in terms of miles per hour. If you mix apples and grapes you get fruit salad -- or what evil mathematicians shake their heads and call a wrong answer. What you need is to realize that 15 minutes is one-quarter hour, so 2 hours 15 minutes is 2.25 hours. (An alternative would be to convert the rates of speed to miles per minute -- and -- but that would make for some really ugly arithmetic) Other than that your method works just fine. Which is the distance walked. Check: If she walked 5 miles at 5 mph, then she walked for 1 hour. That means she jogged for 2.25 - 1 = 1.25 hour. 1.25 hour times 8 mph = 10 miles which is 2 times 5 miles. Answer checks. John

Problems-with-consecutive-odd-even-integers/219500: Translate the following problem using only the variable x. Do not solve the equation Eight times the first of three consecutive odd integers is twice the second 1 solutions Answer 165050 by solver91311(16897)   on 2009-09-30 11:41:33 (Show Source): You can put this solution on YOUR website! Let represent the first of three consecutive odd integers. The next consecutive odd integer must then be and the one after that must be . Eight times the first integer is then . "Is" means "=". Twice the second consecutive odd integer is . Putting it all together: John

Money_Word_Problems/219496: How long does it take your money in your savings account to double at 8% interest rate using the formula A=Pe^rt ? 1 solutions Answer 165049 by solver91311(16897)   on 2009-09-30 11:35:58 (Show Source): You can put this solution on YOUR website! So: If the principal has doubled, then , so: Take the natural logarithm of both sides: But , so: Plug in and crank up your calculator. John

Polynomials-and-rational-expressions/219489: 3^9 . (x^2 y)^-2/ 3^3 . x^-4 y answer: 3^6/y^3 or 729/y^3 how did my math book get this answer and can anyone explain by defintions and rules for exponents i got as far as 3^6 power by quotient rule but then i got stuck by the rest 1 solutions Answer 165047 by solver91311(16897)   on 2009-09-30 11:23:38 (Show Source): You can put this solution on YOUR website! Start with and , so: Next use , so: Next use and , so: Finally, use , so: John

test/219181: compute all possible ordered pairs of positive integers (x,y)which satisfy xsquared- ysquared=45 1 solutions Answer 164909 by solver91311(16897)   on 2009-09-29 20:11:52 (Show Source): You can put this solution on YOUR website! If Then and therefore If both and are integers, then must be a positive integer and must be an integer in general. But in order for to be a positive integer in the above equation, must be a positive integer as well. So, the possibilities are: But since both and are positive integers, must be greater than , so we can eliminate the last three relationships in the above list. So: John

Circles/219100: A circle is drawn in a square whose side has a length of 40. Find the area of the shaded region in terms of pie. 1 solutions Answer 164875 by solver91311(16897)   on 2009-09-29 19:12:43 (Show Source): You can put this solution on YOUR website! Be delighted to help you if you would be so very kind as to share a description of "the shaded area." We can't see your picture. However, I will help you this much: Presuming that the circle is inscribed in the square, which is to say that all four sides of the square are tangent to the circle, then you can say this: If the side of the square is 40, then the area of the entire square is . 40 is also a diameter of the circle, hence the radius of the circle is then 20. Hence the area of the circle is . The sum of the areas of the four little corner pieces that are part of the square but not of the circle is then the area of the square minus the area of the circle, i.e., . If you only need one of those little pieces, then the area is one-fourth the area of all four of them, or Oh, and one more thing: "pie" is a dessert item, usually with a flaky crust, and frequently with a fruit filling. "pi" is the Greek letter representing the ratio of a circle's circumference to its diameter. Therefore, I am assuming that you need to express your answer to this question in terms of "pi" rather than "pie." John

Geometry_proofs/219099: finding angle measures 1 solutions Answer 164840 by solver91311(16897)   on 2009-09-29 18:02:14 (Show Source): You can put this solution on YOUR website! A truly fascinating subject. Was there a question there somewhere? John

Radicals/219094: What is the square root of 18? But it has to be simplifed. My teacher said i had to do something with factors to get the answer but he lost me. 1 solutions Answer 164839 by solver91311(16897)   on 2009-09-29 18:00:52 (Show Source): You can put this solution on YOUR website! Derive the prime factorization of the radicand. So: Because: But So: John

Travel_Word_Problems/219069: If a train traveling at 30 m/s brakes to a stop in 1 minute, what is it's acceleration? 1 solutions Answer 164831 by solver91311(16897)   on 2009-09-29 17:51:33 (Show Source): You can put this solution on YOUR website! For this problem the initial speed is 30 m/s, and the final speed is 0. Since the speed is expressed in meters per second, the time must be expressed in seconds. One minute = 60 seconds, so: Solve for , remember to pay attention to your units of measure, and check your answer for reasonability. John

Rectangles/219082: The length of rectangle is 9 more than the width. If the perimeter of the rectangle is 46 in, find the length and width of the rectangle. 1 solutions Answer 164828 by solver91311(16897)   on 2009-09-29 17:39:41 (Show Source): You can put this solution on YOUR website! This is exactly the same as problem 218299 using different numbers.

Linear-equations/218459: the height H (in feet) of a ball thrown into the air from top of a building after t seconds is givin by H=-16t^2+59t=224...Estimate the height of the ball after 4.5seconds 1 solutions Answer 164559 by solver91311(16897)   on 2009-09-28 17:45:37 (Show Source): You can put this solution on YOUR website! Replace t in your function with 4.5 and then do the arithmetic. John

Linear-equations/218475: Solving Radical equations It says check whether the given x-value is a solution of the equation 1 solutions Answer 164557 by solver91311(16897)   on 2009-09-28 17:38:58 (Show Source): You can put this solution on YOUR website! Since you didn't bother to share "the given -value," I can't actually do the problem. You take the given value, put it in place of the and then do the arithmetic. If it becomes a true statement, then the given value is a solution, otherwise not. John

Probability-and-statistics/218462: Four standard six-sided dice are rolled. What is the probability that the product of the numbers on the top faces of all four dice is a prime number? Express your answer as a common fraction 1 solutions Answer 164556 by solver91311(16897)   on 2009-09-28 17:35:35 (Show Source): You can put this solution on YOUR website! There are different results for rolling 4 six-sided dice. The only way the product of the four upper faces can be prime is if three of the upper faces show a 1 and the remaining upper face shows a prime number less than 6, namely 2, 3, or 5. Here are the possibilities 1, 1, 1, 2 1, 1, 1, 3 1, 1, 1, 5 1, 1, 2, 1 1, 1, 3, 1 1, 1, 5, 1 1, 2, 1, 1 1, 3, 1, 1 1, 5, 1, 1 2, 1, 1, 1 3, 1, 1, 1 5, 1, 1, 1 for 12 possible successful outcomes. John

Numbers_Word_Problems/218455: Please help me solve this equation: The sum of three consecutive whole numbers is eighteen. How do I write that? 1 solutions Answer 164551 by solver91311(16897)   on 2009-09-28 17:26:39 (Show Source): You can put this solution on YOUR website! Let represent the first number. Then the next consecutive whole number must be and the following consecutive whole number must be The sum is 18: John

Triangles/218432: How do you find the range for the measure of the third side of a triangle given the measures of two sides? 1 solutions Answer 164541 by solver91311(16897)   on 2009-09-28 17:13:45 (Show Source): You can put this solution on YOUR website! The 3rd side must be less than the sum of the other two sides John

Triangles/218448: How does a triangle with sides 13, 18, and 31 have an area of 0. 1 solutions Answer 164538 by solver91311(16897)   on 2009-09-28 17:11:24 (Show Source): You can put this solution on YOUR website! To begin with, your first presumption is incorrect. You don't have a triangle in the first place. You cannot have a triangle unless the sum of the two shortest legs is greater than the longest leg. In this case, the sum of the two shortest legs is EQUAL to the longest leg - ergo, no triangle. John

Equations/218371: Suppose you scored 80% on a test and answered 32 questions correctly. How many questions were on the test? and i was wondering if you could do this problem step by step for me so i can see how to do it? 1 solutions Answer 164473 by solver91311(16897)   on 2009-09-28 15:20:12 (Show Source): You can put this solution on YOUR website! Let represent the number of questions on the test. 80% of the questions on the test must then be which is equal to 32, so: Divide both sides by 0.8. John

Angles/218373: Find the measure of angle T if the measure of angle T is 20 more than four tiems it's supplement. 1 solutions Answer 164472 by solver91311(16897)   on 2009-09-28 15:16:55 (Show Source): You can put this solution on YOUR website! Let represent the measure of angle T. Then is the supplement of angle T. But: Solve for John

Rectangles/218289: I need to know if my answer is correct for the following: If it isn't, I need to know why. thanks Solve the system of equations x+2y=1 3x-2y=11 My answer is (3,-1) Thank you very much! 1 solutions Answer 164469 by solver91311(16897)   on 2009-09-28 15:12:19 (Show Source): You can put this solution on YOUR website! Spot on.

Geometry_proofs/218341: What is the side splitting theorem proof? 1 solutions Answer 164434 by solver91311(16897)   on 2009-09-28 14:05:16 (Show Source): You can put this solution on YOUR website! If a line is constructed parallel to one side of a triangle that intersects the other two sides in distinct points, then the other two sides each form a transversal where the corresponding angles are equal. Since you now have two triangles with two pairs of angles equal because of equal corresponding angles of a transversal and the third angle is in common, you have two triangles that have all three angles congruent. Since all three angles are congruent, the triangles must be similar (AAA). Since the triangles are similar, their corresponding sides are in proportion by definition of similarity. John

Travel_Word_Problems/218316: Two row boats are traveling at a steady speed of 10 miles/hr straight toward each other. At the moment when they are 40 miles apart, a messenger pigion takes off from one of the boats and flies at a steady speed of 25 miles/hr directly to the other boat. It touches the second boat, turns around instantly, and returns at the same steady speed to the first boat. When it touches the first boat, it instantly turns around again and heads directly back to the second boat. The pegion repeats this back and forth flight pattern over and over again at the same speed until the boats meet. From the moment the pigion took off from the firts boat until the final meting of the boats, how much was the pegions total mileage? Justify your answer. 1 solutions Answer 164429 by solver91311(16897)   on 2009-09-28 13:56:57 (Show Source): You can put this solution on YOUR website! Since each boat is traveling at a 10 mph steady state, the boats are closing with each other at a rate of 20 mph. That means that the distance between them will be reduced to zero in 2 hours. (40 miles divided by 20 mph is 2 hours). Now I don't know what a pegion or a pigion is, but presuming you actually meant pigeon, the bird would be flying at a steady state of 25 mph for 2 hours, or 50 miles would be the theoretical distance traveled. Of course that presumes the completely ludicrous idea that a bird of any kind can actually be traveling 25 miles per hour in one direction and then instantaneously reverse its direction and begin flying 25 miles per hour in the opposite direction. In practical terms, the distance traveled by the bird would be much less because of the time it would actually take for the animal to slow down, stop, turn around, and reacquire speed again. John

Miscellaneous_Word_Problems/218324: Select the correct answer: 1st 2nd 3rd 4th "The Point (-6,3) would be graphed in this quadrent." Please help if you can! THANKS! 1 solutions Answer 164414 by solver91311(16897)   on 2009-09-28 13:32:05 (Show Source): You can put this solution on YOUR website! (-6, 3) is in the II quadrant. Notice the correct spelling of 'quadrant' not 'quadrent'. Yes, this is mathematics, but we still have to communicate, so spelling, grammar, punctuation , and all of the other niceties of English written communications count. John