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 Numbers_Word_Problems/275864: how do i find the solution for the following problem? The sum of two consecutive integers is 146. Find the numbers.1 solutions Answer 201144 by solver91311(16877)   on 2010-03-01 19:34:43 (Show Source): You can put this solution on YOUR website! Your problem has no solution as stated. If you have two consecutive integers, one of them must be odd and the other must be even in some order. The sum of an even number and an odd number must be odd -- but 146 is even. Now if you meant two consecutive even integers, it would work out. But that isn't what you said, and I don't want to guess. John
 Divisibility_and_Prime_Numbers/275854: I need some help with a proof. Let p & q be 2 consecutive primes. Then p+q=2n for some n. Is n always composite. I have some examples but not sure how to write proof. Examples: 11, 13 11+13=24 13,17 13+17=30 Thank you1 solutions Answer 201143 by solver91311(16877)   on 2010-03-01 19:30:33 (Show Source): You can put this solution on YOUR website! All you need to do to prove that it is NOT true is to find a counter-example. 2 plus 3 = 5. 5 is prime. On the other hand, if you exclude 2 by saying p and q are 2 consecutive odd primes, then the theorem is true. Except for 2, all primes are odd and of the form . So we can say that and for some and . Then which is clearly an even, and therefore composite, number. John
 Money_Word_Problems/275838: Write an equation of the line containing the given point and parallel to the given line. Express you answer in the form of y=mx+b. (7,8);x +8y=9. The equation of the line is y=???1 solutions Answer 201138 by solver91311(16877)   on 2010-03-01 19:18:53 (Show Source): You can put this solution on YOUR website! Step 1: Determine the slope of the line represented by the given equation. Put the given equation into slope-intercept form: Add to both sides, then multiply both sides by . Once the given equation is in slope-intercept form, the slope of the line will be equal to the coefficient on . Step 2: Use the point-slope form of the equation of a line, namely: where are the coordinates of the given point and is the slope calculated in Step 1. You can use the same slope number because parallel lines have equal slopes, in other words: Step 3: Once you have plugged in the values for the coordinates of the given point and for the calculated slope, solve the resulting equation for (similar to the process used to rearrange the equation in step 1) to put the desired equation into slope-intercept form. John
 Travel_Word_Problems/275840: if a train is traveling at 72 mph how far will it go in 40 minutes1 solutions Answer 201136 by solver91311(16877)   on 2010-03-01 19:10:43 (Show Source): You can put this solution on YOUR website! Hint: 40 minutes is of 1 hour. John
 Numbers_Word_Problems/275833: Points A, B, C, and D lie in consecutive order on a line. If AC=4/3AB and BD=6BC, then what is AB/CD?1 solutions Answer 201135 by solver91311(16877)   on 2010-03-01 19:09:45 (Show Source): You can put this solution on YOUR website! so and since we can say: Therefore Furthermore, Substituting: Now we have both AB and CD in terms of BC, so: John
 Money_Word_Problems/275829: Find the slope intercept equation of the line that has the given characteristics. Slpe 3 and y-intercept (0,2). The slope-intercept equation is y=??1 solutions Answer 201130 by solver91311(16877)   on 2010-03-01 18:55:17 (Show Source): You can put this solution on YOUR website! The slope-intercept form of the equation of a line is: where is the slope of the line and is the -coordinate of the point where the graph of the line intersects the -axis. You are given the two numbers directly -- just substitute them. John
 Rate-of-work-word-problems/275821: I had a question about a work word problem. It says: Jane, Paul, and Peter can finish a painting in 2 hours. Jane can paint the same painting in 5 hours. Paul can paint it alone in 6 hours. How long would it take Peter to paint it on his own? the equation was 1/5+1/6+1/x=1/2 and I dont understand where they got the 1/2 from.......If you could help me with this it would be great. Thanks!!!1 solutions Answer 201127 by solver91311(16877)   on 2010-03-01 18:52:45 (Show Source): You can put this solution on YOUR website! If person A can complete an entire job in time periods, then that person can complete of the job in one time period. Jane can do the whole job in 5 hours, so she can do of the job in one hour. Likewise, Paul is 6 hours and of the job, while Peter is hours and of the job. In the same way, the three of them working together can do the job in 2 hours, which is to say that the three of them working together can do of the job in one hour. The equation works out to "The fraction of the job that Jane can do in one hour" plus "The fraction of the job that Paul can do in one hour" plus "The fraction of the job that Peter can do in one hour" adds up to "The fraction of the job that the three of them working together can do in one hour" John
 Volume/275816: Decreasing cube. Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is given by V(s)= s^3  13s^2 + 54s  72. a) Find V(10). b) If the new width is s  6 centimeters, then what are the new length and height? c) Find the volume when s=10 by multiplying the length, width, and height. Can someone help me please!1 solutions Answer 201122 by solver91311(16877)   on 2010-03-01 18:35:35 (Show Source): You can put this solution on YOUR website! Show the signs in your polynomial John
 Trigonometry-basics/275801: how do i solve this i need like a step by step breakdown 5 cos^2(theta)-4 sin(theta)-4 = 01 solutions Answer 201121 by solver91311(16877)   on 2010-03-01 18:34:48 (Show Source): You can put this solution on YOUR website! Remember Therefore So substitute Simplify: Let represent Factor the quadratic: Hence, or But since or And finally, considering the interval : or and John
 Inequalities/275798: how do you work out the problem, d - 1 _> 61 solutions Answer 201108 by solver91311(16877)   on 2010-03-01 18:12:03 (Show Source): You can put this solution on YOUR website! Just add 1 to both sides. Then is 7 or anything larger than 7. John
 Volume/275797: Decreasing cube. Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is given by V(s)= s^3  13s^2 + 54s  72. a) Find V(10). b) If the new width is s  6 centimeters, then what are the new length and height? c) Find the volume when s=10 by multiplying the length, width, and height.1 solutions Answer 201106 by solver91311(16877)   on 2010-03-01 18:10:24 (Show Source): You can put this solution on YOUR website! You left out the signs in your polynomial expression. John
 Triangles/275796: a right triangle has sides of 4 ft, 5 ft, and 1 yd. what is its perimeter in feet?1 solutions Answer 201105 by solver91311(16877)   on 2010-03-01 18:09:32 (Show Source): You can put this solution on YOUR website! 1 yard is 3 feet. Add the measures of the three sides in feet to get the perimeter in feet. John
 Quadratic_Equations/275778: x^2+6x+27 help me can you solve it for me1 solutions Answer 201103 by solver91311(16877)   on 2010-03-01 18:08:37 (Show Source): You can put this solution on YOUR website! In a word, no. You can't "solve" something that doesn't have an equals sign in it somewhere. Now if your problem is really: That is another story altogether. But you didn't say that, and I'm not going to guess. John
 Polygons/275785: why do you think each letter in a polygon's name can be used only once1 solutions Answer 201098 by solver91311(16877)   on 2010-03-01 17:58:39 (Show Source): You can put this solution on YOUR website! What makes you think your premise is true in the first place? Counterexample: nonagon, also known as an enneagon. John
 Probability-and-statistics/275782: Two shaded circles are inside a rectangle that has one side that is 2" and the bottom side is 4". What is the probibilty of an object landing randomly on the figure in the shaded circle. " Express the probability as a percent."1 solutions Answer 201091 by solver91311(16877)   on 2010-03-01 17:48:10 (Show Source): You can put this solution on YOUR website! That would depend a great deal on the size of the circles in relation to the size of the rectangle and whether the random falling of objects is constrained to inside the rectangle or not. Presuming the rectangle as a universal constraint, find the area of each of the circles. Add the two areas of the circles. The sum of the areas of the two circles is the numerator of your probability fraction. The area of the rectangle is your denominator. John
 Quadratic_Equations/275775: i need help on this problem x^2+5x-251 solutions Answer 201090 by solver91311(16877)   on 2010-03-01 17:44:21 (Show Source): You can put this solution on YOUR website! You have a handsome little quadratic trinomial there. What would you like to do with it? John
 Surface-area/275765: Why can you find an excact Surface Area measurement for a prism but not a cylinder1 solutions Answer 201089 by solver91311(16877)   on 2010-03-01 17:40:03 (Show Source): You can put this solution on YOUR website! The underlying premise of your question is not true in general. In the first place, you can never find the exact measurement of anything. ALL measurements are approximate, no matter how precisely taken. Therefore you can never exactly represent the surface area of a prism because the measurements of the edges begin as approximations. On the other hand, who says you cannot represent the surface area of a cylinder exactly? Typically the surface area calculation for a cylinder involves , the ratio of the circumference of a circle to its diameter. is a transcendental irrational number, and irrational numbers can never be represented by an exact decimal fraction. However, that is not to say that you cannot represent a quantity involving exactly, because you can. All you need to do is leave the result in terms of and you have your exact representation. So presuming an ideal theoretical cylinder whose height was exactly and base radius exactly , you would have a lateral surface area of exactly or a total surface area of exactly . Example: If you had a cylinder that was purported to be exactly 5 units in height and exactly 2 units in radius (even though no one would ever be able to measure it and determine whether it was indeed 5 high and 2 in radius), then the lateral surface area would be exactly , and the total surface area would be exactly John
 Volume/275761: Decreasing cube. Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is given by V(s)= s^3  13s^2 + 54s  72. a) Find V(10). b) If the new width is s  6 centimeters, then what are the new length and height? c) Find the volume when s=10 by multiplying the length, width, and height.1 solutions Answer 201086 by solver91311(16877)   on 2010-03-01 17:21:32 (Show Source): You can put this solution on YOUR website! Why do you insist on leaving the signs out of your expressions? John