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solver91311 answered: 16865 problems
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Rate-of-work-word-problems/232146: Pump A can fill a water jar two times faster than Pump B. Working together, the two pumps fill water jars in five hours. How long does it take for each pump to fill a water jar individually? I don't know how to solve, or the equations I would need. 1 solutions Answer 171674 by solver91311(16877)   on 2009-10-27 19:53:25 (Show Source): You can put this solution on YOUR website! Let represent the number of hours it would take A to fill the jar by itself. Since A pumps twice as fast as B, it would take B two times longer to fill the jar, so represents the number of hours it would take B to fill the jar by itself. Since is the amount of time for A to fill the jar, is the amount of the jar that A can fill in 1 hour. Likewise, B can fill in one hour. And together they can fill: of the jar in 1 hour. Add 'em up: And we know it takes 5 hours to fill the jar working together, so we can conclude that together they can fill of the jar in 1 hour, therefore: Solve for to get the time for A to fill the jar by itself (Hint cross-multiply). B is twice that value. John

Proofs/232217: j→i ~j→k ~k Prove: i 1 solutions Answer 171667 by solver91311(16877)   on 2009-10-27 19:38:00 (Show Source): You can put this solution on YOUR website! The contrapositive has the same truth value as the statement. Given Because Because John

Functions/232209: How do you find the domain and range for the following Points? {(1,3) (1,0) (1,-2) ( 1,8)} And is it a function. Thank you 1 solutions Answer 171664 by solver91311(16877)   on 2009-10-27 19:30:24 (Show Source): You can put this solution on YOUR website! The domain is the set of values that can be taken by the independent or input variable -- generally the . You have four ordered pairs in your set, and all of the -coordinates are equal to 1. Therefore the domain is . The range is the set of all values of the dependent variable resulting from all values of the independent variable. Therefore the range is , which are the four -coordinates. A relation is a function if and only if every element in the domain corresponds to one and only one element in the range. Here you have the element 1 in the domain that corresponds to 4 different elements in the range. Not a function. If you graphed these four points, you would find that you would be able to draw a vertical line that would contain more than one of the points (in fact, the line would contain all four points). Any time you can find such a vertical line, your relation is NOT a function. John

Rational-functions/232188: How do you solve i^6? 1 solutions Answer 171661 by solver91311(16877)   on 2009-10-27 19:19:32 (Show Source): You can put this solution on YOUR website! In general (definition of ) Where is the remainder when integer is divided by integer 6 divided by 4 leaves a remainder of 2, so , so John

Geometry_proofs/232123: how do i solve for a proof? 1 solutions Answer 171642 by solver91311(16877)   on 2009-10-27 18:21:30 (Show Source): You can put this solution on YOUR website! Start with what you are given, then proceed in logical steps showing the axiomatic or provable reason for each step, until you arrive at whatever it is you are trying to prove. John

Equations/232141: i have 18=c+5 with aline under the c+5 and a 2 beneath it. how do i solve those problems?? 1 solutions Answer 171639 by solver91311(16877)   on 2009-10-27 18:18:28 (Show Source): You can put this solution on YOUR website! I think you mean: In which case, multiply both sides by 2, then add -5 to both sides. John

test/232140: how do you subtractfractions 1 solutions Answer 171634 by solver91311(16877)   on 2009-10-27 18:14:12 (Show Source): You can put this solution on YOUR website! The same way you add them. Find and apply a common denominator and then, in the case of subtraction, find the difference of the resulting numerators. John

Systems-of-equations/232127: solve by substituion, 6m +n= 28 m-7n=62 what is the solution set. I came upt with (3,4) am I close 1 solutions Answer 171625 by solver91311(16877)   on 2009-10-27 18:01:10 (Show Source): You can put this solution on YOUR website! The answer to the question posed would certainly depend on what you mean by "close." On the other hand, the concept of "close" doesn't apply here. An answer that differs from the correct answer by 1 is just as wrong as one that differs by 500. Now, if you would care to write back and show the work you did, perhaps I can find where you made your error. John

Quadratic_Equations/232134: 9/x- 2= 5/x^2 1 solutions Answer 171620 by solver91311(16877)   on 2009-10-27 17:48:17 (Show Source): You can put this solution on YOUR website! What is your question? John

Polynomials-and-rational-expressions/232019: This problem I have needs to be divided but I not finding that I am able too. Divide this algebraic expression (2x^3-x^2+3x-1)/(x+2) 1 solutions Answer 171565 by solver91311(16877)   on 2009-10-27 13:50:16 (Show Source): You can put this solution on YOUR website! You need to do polynomial long division. Too difficult and time-consuming to render on this site, so the best thing is for you to look at either wikipedia or purplemath to learn the process for yourself. http://en.wikipedia.org/wiki/Polynomial_long_division http://www.purplemath.com/modules/polydiv2.htm The following site has a calculator that will take you through your specific problem step-by-step. http://www.mathcelebrity.com/algmaster.php John

Equations/232018: Show That The Lines Are Parallel By Showing That Their Slopes Are Equal: 1. f(x)=4x+1 And g(x)=4x 2. f(x)=(1/3)x+5 and g(x)= (1/3)x-2 1 solutions Answer 171564 by solver91311(16877)   on 2009-10-27 13:45:13 (Show Source): You can put this solution on YOUR website! 1. Both functions are in slope-intercept form. (the intercept for g(x) is zero) That means that the coefficient on x is the value of the slope. 2. Same thing. John

Surface-area/232021: The circumference of a circular garden is 628 feet. Find the area of the garden. ok I know to get area we use pie r squared however, I have no clue how to get the radius? I have so far got this: 628/3.14 200=r squared? 1 solutions Answer 171557 by solver91311(16877)   on 2009-10-27 13:18:44 (Show Source): You can put this solution on YOUR website! So: The area is Then by substitution Turn on your calculator and have fun... By the way, unless otherwise specified (such as your instructor giving you special instructions) the results of a calculation involving measurements should be no more precise than the least precise given measurement. Your circumference was given to the nearest foot, so your area should be expressed to the nearest square foot -- round off the calculator result to the nearest whole number. John

Equations/231878: In class we had to figure out how to solve problems bu using solving the sub-problem of that problem. Which is basically just steps to get to figuring out the big picture. In the following problem I wasn't quite sure where to start with that. Here is the problem: "In right triangle RED, angle R is the right angle. Point O is on segment ER and point A is on segment ED. Segment OA is perpendicular to segment ED. EA = 6, AD = 14, and ER = 16. Find the area of quadrilateral ROAD." So with the picture you draw with that, do I have to cut the right triangle in half and then solve? I was so confused nor do I know where to start with finding the sub problems. If anyone has a suggestion it would be very helpful. Much appreciated in advance! 1 solutions Answer 171494 by solver91311(16877)   on 2009-10-27 01:27:15 (Show Source): You can put this solution on YOUR website! Notice a few things right off: 1. EA = 6 and AD = 14 means that ED = 20. 2. OA perpendicular to RE means OA parallel to RD, hence: * Triangle OEA similar to triangle RED * Quadrilateral ROAD is a trapeziod 3. 20 is 4 times 5 and 16 is 4 times 4, hence RD has to be 12: 4 times 3 -- 3-4-5 right triangle. (verify by using Pythagoras and calculating if you want) The hypotenuse of OEA is 6, so because of similar triangles. Hence OE = 4.8 and OA = 3.6. Verification left as an exercise for the student. Since OE = 4.8, RO = 16 - 4.8 = 11.2. And because of right angle R, RO is an altitude of the trapezoid The formula for the area of a trapezoid is: Plug in the values: You can do your own arithmetic. John

Inequalities/231838: Solve the following compound inequalities. Graph the solution set. 1. -5<7-2x<15 ***i got totally lost trying to do this homework problem. please help me!!!!*** 1 solutions Answer 171484 by solver91311(16877)   on 2009-10-26 22:36:22 (Show Source): You can put this solution on YOUR website! Add -7 Multiply by remembering to switch the sense of the inequality because of multiplying by a negative. Draw a number line. Put a little circle at -4. Put a little circle at 6. Make a fat line that connects the two little circles. Make sure your little circles are open circles -- not filled in like the picture. John

Triangles/231834: the perimeter of the equilateral triangle is 7 inches less than twice the perimeter of the square..what does that mean? 1 solutions Answer 171479 by solver91311(16877)   on 2009-10-26 21:56:24 (Show Source): You can put this solution on YOUR website! The perimeter of any plane figure is the distance all the way around it. For an equilateral triangle, it is 3 times the measure of one of the sides. For a square it is 4 times the measure of one of the sides. Measure one side of your square. Multiply by 4. Then multiply by 2. Then subtract 7. You will now have the perimeter of the triangle. John

Polynomials-and-rational-expressions/231761: for what values of x is the rational expression below undefined? (x+2)(x-1)/x(x+3) 1 solutions Answer 171441 by solver91311(16877)   on 2009-10-26 19:39:13 (Show Source): You can put this solution on YOUR website! For what values of would the denominator be zero? Same thing. John

Polynomials-and-rational-expressions/231754: reduce to lowest terms: 9-x/5x-45 I got x/5x-5 is that correct? 1 solutions Answer 171440 by solver91311(16877)   on 2009-10-26 19:37:53 (Show Source): You can put this solution on YOUR website! Sorry. Not even close. But , so John

Equations/231712: evaluate: int(x^4 + 3x^2,dx) 1 solutions Answer 171439 by solver91311(16877)   on 2009-10-26 19:30:26 (Show Source): You can put this solution on YOUR website! so: Power Rule: Also: so: Check: John

Linear_Equations_And_Systems_Word_Problems/231711: #1. The sum of two numbers is 54, and their difference is nine more than the smaller number. find the numbers 1 solutions Answer 171437 by solver91311(16877)   on 2009-10-26 19:23:56 (Show Source): You can put this solution on YOUR website! Let represent the smaller number. Let represent the larger number. Then: Substitute: Now just solve for . Then subtract from 54 to get . John

Exponents-negative-and-fractional/231719: how can we simplify this: 2L*C/(c^2 - v^2) = ? 1 solutions Answer 171435 by solver91311(16877)   on 2009-10-26 19:19:00 (Show Source): You can put this solution on YOUR website! You can factor the difference of two squares in the denominator, but that's about it. John

Polynomials-and-rational-expressions/231720: Perform the operations indicated: 1. (7x- 2) + (6x+ 4) 2. (3x - 3.5) - (x + 1.8) 3. [7x^2 - 2/3)x]- [(4/9)X - 5] 4. (-5x^2 + 12x - 4) - (-2x^2 + 6) 5. -3x(-4x^2 + 7x - 9) 6. (8 - 3x)(2 + 4x) 7. (2x + 8)^2 8. (2x + 5)(x^2 + 3x + 2) 9. 6x^2+8x-7/ -x 10.3x^2+22x-8 / x+2 1 solutions Answer 171433 by solver91311(16877)   on 2009-10-26 19:17:20 (Show Source): You can put this solution on YOUR website! Sorry. Not doing your entire homework assignment for you -- no matter how many times you submit. John

Equations/231699: find the value of cos 105 degrees without using a calculator.retain radical notation. 1 solutions Answer 171429 by solver91311(16877)   on 2009-10-26 19:13:50 (Show Source): You can put this solution on YOUR website! Simplification of this expression is left as an exercise for the student. Sanity check: Notice that the left hand term is smaller than the right hand term. That means that cos(105) < 0, which makes sense for a Quadrant II angle. John

Equations/231686: find: int((x^3 + 1),dx) 1 solutions Answer 171411 by solver91311(16877)   on 2009-10-26 18:36:49 (Show Source): You can put this solution on YOUR website! so: Power Rule: so: Check: John

Travel_Word_Problems/231680: a bicyle takes 1.5 hours to travel 22.5 km . What was the average speed 1 solutions Answer 171405 by solver91311(16877)   on 2009-10-26 18:24:34 (Show Source): You can put this solution on YOUR website! Divide 22.5 by 1.5 John

Graphs/231679: how do you find a solution,for example x + 11< 8? 1 solutions Answer 171404 by solver91311(16877)   on 2009-10-26 18:23:10 (Show Source): You can put this solution on YOUR website! Add -11 to both sides, then x is any value less than -3. John

Quadratic_Equations/231652: how would you put an equation that is like y=ax+bx+c into the format y=a(x-h)²+k? 1 solutions Answer 171401 by solver91311(16877)   on 2009-10-26 18:21:16 (Show Source): You can put this solution on YOUR website! I presume you mean First, factor an out of the first two terms on the right. Complete the square: Factor the square: Then, by inspection: and John

Miscellaneous_Word_Problems/231639: write an equation in standard form that you can solve by factoring and one that you cannot solve by factoring. 1 solutions Answer 171386 by solver91311(16877)   on 2009-10-26 17:35:11 (Show Source): You can put this solution on YOUR website! I'm going to go way out on a limb and presume that you mean a quadratic equation. In fact, there is no such thing as a quadratic equation that cannot be solved by factoring. Even if you have irrational or complex roots, you still have roots. And if you have roots, you have factors. Now, in many cases it may be very difficult to find the factors and you may have to resort to other means to solve the equation. For example, consider: which does not factor over the integers (doesn't factor over the rationals, either). The quadratic formula tells us that the roots are: Meaning that: Deucedly difficult to solve by factoring, but not entirely impossible. On the other hand, if you did not ask the ENTIRE question, that is, if the question was "...cannot solve by factoring over the real numbers (or rationals, or integers)" then you could give: : No real number factors as an example for the second half of your question. John

Points-lines-and-rays/231629: The measure of an angle is 10 less than 3 times the measure of its complement. Find the measure of both angles. I'm doing: x+y=90 x=3y-10 3y-10+y=90 4y-10=90 4y=80 y=20 x=3y-10 x=3(20)-10 x=60-10 x=50 It doesn't equal 90! Help! 1 solutions Answer 171381 by solver91311(16877)   on 2009-10-26 17:11:06 (Show Source): You can put this solution on YOUR website! Absolutely on the right track. But you have got to watch your signs. Perfect up to this point. But now you need to ADD 10 to both sides: John

Permutations/231623: How many four-digit numbers can you form from the numbers 1,2,3,4,5,6,7,8, and 9 (a) if you use each digit only once? (b) if you can repeat each digit. 1 solutions Answer 171380 by solver91311(16877)   on 2009-10-26 17:04:29 (Show Source): You can put this solution on YOUR website! a. 9 choose 4: b. 9 ways to choose the first number times 9 ways to choose the second number... In either case, you get to do your own arithmetic. John

Miscellaneous_Word_Problems/231627: one number is four more than another. Their product is 77. find the numbers. 1 solutions Answer 171379 by solver91311(16877)   on 2009-10-26 16:59:49 (Show Source): You can put this solution on YOUR website! Expand, put in standard form, and solve the quadratic. By the way, there are two sets of two numbers that solve this problem. John

Numbers_Word_Problems/231621: The sum of 3 numbers is 10. The first is twice the second. The sum of the second and third is 6. Find the numbers. 1 solutions Answer 171377 by solver91311(16877)   on 2009-10-26 16:56:48 (Show Source): You can put this solution on YOUR website! You should be able to do this one in your head. If the sum of the three is 10 and the sum of the last two is 6, then the first one has to be 4. Then if the first is twice the second, the second must be 2. And from that you get that the last one must be 6 minus 2 is 4. John