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Polynomials-and-rational-expressions/234574: A boat can travel 9 miles upstream in the same amount of time it takes to travel 11 miles downstream. if the current of the river is 3 miles per hour, complete the chart below and use it to find the speed of the boat in still water distance = rate * Time upstream 9 r-3 downstream 11 r+3 1 solutions Answer 172956 by solver91311(16877)   on 2009-11-03 12:08:24 (Show Source): You can put this solution on YOUR website! The time is the same for both the upstream and downstream trips ("in the same amount of time"), so just call it . Since we can also say So for the upstream trip: And for the downstream trip: But , so we can say: Just cross-multiply and solve for John

Numbers_Word_Problems/234564: How do write this out?: One third of the sum of a number and seven is seven 1 solutions Answer 172952 by solver91311(16877)   on 2009-11-03 11:59:28 (Show Source): You can put this solution on YOUR website! "sum" means add. "of" means multiply. "is" means equals. Let represent the number. Then the sum of the number and seven means . One third of the sum means one-third times the sum, so, . Finally, all of that is seven which means: So the number is 14. John

Mixture_Word_Problems/234550: If x ml of water are added to 200 ml of pure orange (concentrate) the result is a mixture that is 80% orange juice (concentrate) and the rest water, what equations could be used to solve for x? Please help me solve the problem too. 1 solutions Answer 172940 by solver91311(16877)   on 2009-11-03 11:43:41 (Show Source): You can put this solution on YOUR website! The total quantity of mixture at the end is the 200 ml of concentrate plus the amount of water added, , or . 80% of the mixture is pure concentrate, and the pure concentrate amount is 200 ml, so: Just solve for John

Graphs/234536: Fin the area of a triangle whose vertices have coordinates of (0,9), (0, - 4), (5, -4). 1 solutions Answer 172936 by solver91311(16877)   on 2009-11-03 11:28:30 (Show Source): You can put this solution on YOUR website! The first thing to do is plot the three points and draw the triangle so that you can see what you have to work with. You can tell from the fact that two of the points have identical -coordinates that one of the sides of the triangle is a vertical line segment. You can also see that two of the points have identical -coordinates, so another side of the triangle is a horizontal line segment. Having one side vertical and another side horizontal tells us that this is a right triangle. We can say the base is either one of these two sides and the height is the other. In order to compute the area, use the formula: where is the measure of the base and is the measure of the height. Now all we need are those measurements. Given the coordinates of two points you can find the distance between them using the distance formula: Where and are the coordinates of the two points. Let's call line segment BC the base. B has coordinates and C has coordinates . Substitute these values into the distance formula: hence the measure of the base is 5. Do the same process to calculate the measure of the height, that is line segment AB. Then use these values in the Area Formula to calculate your area. John

Linear-equations/234531: Graph the equation using the slope and y intercept. y=5/4x+6 so I think the slope is 5/4. I think the y intercept is 6. I need to know if these are correct and also how I graph it. I think I plot the point (0,6) and then go down 5 and over 4 to plot a second point and then draw a line. 1 solutions Answer 172932 by solver91311(16877)   on 2009-11-03 10:45:21 (Show Source): You can put this solution on YOUR website! Yes, yes, yes, and almost. The slope is positive 5 over positive 4, so you go UP 5 and RIGHT 4. Anytime you have a positive slope, the line will go up as you go from left to right. Negative slopes go down as you go from left to right. You don't need help with your math, you just need confidence. Go to http://www.padowan.dk/graph/ and download the free graphing program. Write back and I'll answer any questions you have about using it. John

percentage/234471: ONE PIECE OF THE PIE HAS THE SAME SHAPE AS WOULD BE FORMED BY THE HANDS OF A CLOCK WHEN IT IS EXACTLY THREE O'CLOCK.THIS PIECE WOULD REPRESENT _% OF THE WHOLE PIE. 1 solutions Answer 172880 by solver91311(16877)   on 2009-11-03 01:35:10 (Show Source): You can put this solution on YOUR website! Is there some reason that you feel the need to shout? Typing in ALL CAPS is the text communication equivalent of shouting. It is both annoying and rude. The answer to your question depends on whether you are considering the piece that goes from 12 to 3 clockwise, or from 12 to 3 counterclockwise. The 3 is at 90 degrees from 12, so the smaller piece is 90/360 or 1/4. The larger piece is then 3/4. Just convert 1/4 or 3/4, whichever you think it is, to percent. You can do that by dividing the denominator of the fraction into the numerator and then multiplying the result by 100. John

Coordinate-system/234467: IN A TWO-AXIS SYSTEM EACH POINT HAS- COORDINATES 1 solutions Answer 172879 by solver91311(16877)   on 2009-11-03 00:56:28 (Show Source): You can put this solution on YOUR website! Fascinating fact. Was there a question there somewhere? Also, why do you find it necessary to shout? Typing in ALL CAPS is the text communication equivalent of shouting. It is both annoying and rude.

Equations/234440: determine whether the equation defines y as a function of x 1 solutions Answer 172878 by solver91311(16877)   on 2009-11-03 00:54:44 (Show Source): You can put this solution on YOUR website! What equation?

logarithm/234463: log x^9=1/2 1 solutions Answer 172877 by solver91311(16877)   on 2009-11-03 00:48:56 (Show Source): You can put this solution on YOUR website! First use: So And Now use and the fact that if the base is not specified, base 10 is understood to write: But So That's the exact answer. Use your calculator if you need a numeric approximation. John

Quadratic_Equations/234430: 2 different rational solutions, 2 different irrational solutions,exactly one rational solution or 2 different imaginary solutions?? x^2 - 12x + 34 = 0 1 solutions Answer 172844 by solver91311(16877)   on 2009-11-02 22:41:32 (Show Source): You can put this solution on YOUR website! Calculate the discriminant: , where , , and are the lead, 1st degree, and constant coefficients of the quadratic equation in standard form. Then: Two real and unequal roots. If the discriminant is a perfect square, then the roots are rational, otherwise they ar e irrational. One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors. A conjugate pair of complex roots of the form where is the imaginary number defined by John

Quadratic_Equations/234381: What is a step-by-step way to solve a Quadratic Equation? 1 solutions Answer 172842 by solver91311(16877)   on 2009-11-02 22:32:18 (Show Source): You can put this solution on YOUR website! There are three methods to solve a quadratic equation. For purposes of this discussion we will presume that the equation to be solved is in standard form, that is: Factoring If you can find numbers , , , and such that , , and , then you can write: Then, using the Zero Product Rule, that is: or You can say: Or Completing The Square Step 1: Put the equation into standard form, that is: . Step 2: Multiply both sides of the equation by the reciprocal of the lead coefficient, that is: . becomes . Step 2: Add the additive inverse of the constant term to both sides, that is: becomes . Step 3: Divide the coefficient on the 1st degree term by 2 and then square the result, that is, calculate . Step 4: Add the results of step 3 to both sides of the equation, that is: becomes Step 5: Factor the perfect square on the left, that is: becomes . Step 6: Take the square root of both sides. Remember to consider both the positive and negative roots, that is: becomes . Step 7: Collect terms and simplify, that is: becomes . The Quadratic Formula The quadratic formula was derived by completing the square on the general quadratic -- just as was done in the discussion above on completing the square. Take the three coefficients, , , and and substitute them into the equation found in the last step of the completing the square discussion, namely: Note that the character of the two roots is indicated by the Discriminant, which is the expression under the radical in the quadratic formula, that is: Two real and unequal roots. If the discriminant is a perfect square, the roots are rational, otherwise they are irrational. One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors. A conjugate pair of complex roots of the form where is the imaginary number defined by John

Money_Word_Problems/234235: #4 EllEN WISHES TO MIX CANDY WORTH $1.92 PER POUND WITH CANDY WORTH $3.11 PER POUND TO FORM 36 POUNDS OF A MIXTURE WORTH $2.48 PER POUND. HOW MANY POUNDS OF THE MORE EXPENSIVE CANDY SHOULD SHE USE? 1 solutions Answer 172740 by solver91311(16877)   on 2009-11-02 17:24:01 (Show Source): You can put this solution on YOUR website! Is there some reason you feel the need to SHOUT? Typing in ALL CAPS is the electronic equivalent of shouting, and is therefore both annoying and rude. Please stop. Let represent the number of pounds of $3.11 per-pound candy. Since there are to be a total of 36 pounds in the final mixture, the number of pounds of $1.92 per-pound candy must be: . If there are pounds of candy that cost $3.11, then the total cost of that part of the mixture must be . Likewise the total cost of the less expensive part of the mixture must be . And finally, the total cost of the overall mixture must be $2.48 times 36. The sum of the costs of the two kinds of candy must be the total cost of the mixture, so: Just solve for . John

real-numbers/234234: Can you show me how to slove these problems?: 1 solutions Answer 172736 by solver91311(16877)   on 2009-11-02 17:14:10 (Show Source): You can put this solution on YOUR website! Yes. Which one would you like to be shown? John

Quadratic_Equations/234141: Consider the Quadratic formula f(x)=x^2-2x-35 What is the vertex? x-intercepts 1 solutions Answer 172734 by solver91311(16877)   on 2009-11-02 17:13:07 (Show Source): You can put this solution on YOUR website! I think you mean "quadratic function." That's because , is, in fact, a quadratic function. The Quadratic Formula is something else entirely. Given a quadratic function of the form: The -coordinate of the vertex is . The -coordinate of the vertex is the value of the function at that -value. So: , and . Hence the vertex is at John

Triangles/234222: a rectangle is 2 feet long and 1.5 feet wide,, what is the distance if you measure it diagonally? 1 solutions Answer 172729 by solver91311(16877)   on 2009-11-02 17:02:08 (Show Source): You can put this solution on YOUR website! Use Pythagoras: so Or in your case: You can do your own arithmetic. John

Square-cubic-other-roots/234208: I can't figure out the Square Root of 175. Please help. 1 solutions Answer 172725 by solver91311(16877)   on 2009-11-02 16:58:12 (Show Source): You can put this solution on YOUR website! It depends. Do you just want a numerical approximation or do you want the exact answer in simplest terms? For a numerical approximation, enter 175 into your calculator then press the square root key. Round to an appropriate level of precision. For an exact answer in simplest terms, first determine the prime factorization of your radicand. 175 is odd, therefore not divisible by 2: 1+7+5=13, 13 not divisible by 3, so 175 is not divisible by 3: 175 ends in 5, so 175 is divisible by 5. 175 divided by 5 = 35: 35 is 7 times 5, so the prime factorization of 175 is 5 times 5 times 7. There are a pair of 5s in the prime factorization. Take one five out of the radicand and toss the other one, leaving you with: John

Expressions-with-variables/234210: i have a test tomorrow and i'm so confused on questions like these: 3x+7-2x=4x+10 can you please help ASAP!!!!!!! 1 solutions Answer 172724 by solver91311(16877)   on 2009-11-02 16:48:00 (Show Source): You can put this solution on YOUR website! First simplify the left: because Add -7 to both sides: Add to both sides: Multiply both sides by Check: . Yep. John

Quadratic_Equations/234184: For this problem I need to complete the square, and find the roots of the quadratic equation x^2 + 16x = 0 1 solutions Answer 172720 by solver91311(16877)   on 2009-11-02 16:34:15 (Show Source): You can put this solution on YOUR website! Step 1: Put the equation into standard form, that is: . (This is already done for this problem) Step 2: Multiply both sides of the equation by the reciprocal of the lead coefficient, that is: . becomes . Since the lead coefficient in the given problem is 1, this step can be skipped. Step 3: Add the additive inverse of the constant term to both sides, that is: becomes . (This is already done for this problem) Step 4: Divide the coefficient on the 1st degree term by 2 and then square the result, that is, calculate . For this problem: 16 divided by 2 is 8, 8 squared is 64. Step 5: Add the results of step 3 to both sides of the equation, that is: becomes For this problem, . Step 6: Factor the perfect square on the left, that is: becomes . For this problem: . Step 7: Take the square root of both sides. Remember to consider both the positive and negative roots, that is: becomes . For this problem: Step 8: Collect terms and simplify, that is: becomes . For this problem: , so or . John

Quadratic_Equations/234186: I need to use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. (it is not necessary to find the roots; just determine the number and types of solutions) x^2 + 6x - 7 = 0 1 solutions Answer 172712 by solver91311(16877)   on 2009-11-02 15:54:56 (Show Source): You can put this solution on YOUR website! Given a quadratic equation in the form: The discriminant is found by: And is evaluated as follows: Two real and unequal roots. If the discriminant is a perfect square, the roots are rational, otherwise not. One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors. A conjugate pair of complex roots of the form where is the imaginary number defined by John

Percentage-and-ratio-word-problems/234193: After a 17% markdown, a coat is $494.68. What was the original price of the coat? 1 solutions Answer 172706 by solver91311(16877)   on 2009-11-02 15:46:16 (Show Source): You can put this solution on YOUR website! Let represent the original price. Then: Just solve for John

Exponents-negative-and-fractional/234194: how do i plot a negative fraction? 1 solutions Answer 172705 by solver91311(16877)   on 2009-11-02 15:44:09 (Show Source): You can put this solution on YOUR website! To the left of zero. John

Geometry_proofs/234187: Hi I'm currently doing home school and I have geometry. My question is how do you know if it's SSS, ASA or SAS in a proof? I've been doing good answering the problems, but I've only been guessing. I want to understand it better, I'm going to do state testing next couple of months. Thanks. 1 solutions Answer 172704 by solver91311(16877)   on 2009-11-02 15:43:03 (Show Source): You can put this solution on YOUR website! There are three ways to prove that two triangles are congruent. Either all three sides have equal measure (Side-Side-Side or SSS), two angles and the side between them all have equal measures (Angle-Side-Angle or ASA), or two sides and the angle between them have equal measures, (Side-Angle-Side or SAS). Depending on your proof, you choose the one that you are able to demonstrate. For some proofs, it is possible that it can be done more than one of the ways, and for others, there may only be one way -- and that is the problem: figuring out which of the three ways is going to work and then how you get there starting at the givens. Sometimes intuition works well, sometimes creativity helps, and sometimes you just have to use good old trial and error. Sorry, no magic formulas or bullets here. John

Geometry_Word_Problems/234189: If the area a of a triangle is 60 sq m and the base is 20 m what is the altitude 1 solutions Answer 172703 by solver91311(16877)   on 2009-11-02 15:35:28 (Show Source): You can put this solution on YOUR website! The area of a triangle can be found according to the formula: Where is the area, is the measure of the base, and is the measure of the height (or altitude). So, to find the altitude given the Area and the measure of the base: Plug in what you know and do the arithmetic. John

Graphs/234174: graph the solution set of each compound inequalitys. r < 6 or r > 6 1 solutions Answer 172698 by solver91311(16877)   on 2009-11-02 14:55:36 (Show Source): You can put this solution on YOUR website! A number line with a little circle on 6 and a fat arrow extending to the end of the line in both directions. You are trying to illustrate all numbers EXCEPT for 6. John

Sequences-and-series/234161: How do i solve this to get three variables? a+b+c=3 3b-c=4 2a-b-2c=-5 1 solutions Answer 172697 by solver91311(16877)   on 2009-11-02 14:52:17 (Show Source): You can put this solution on YOUR website! I don't know how you do it. But I would use the substitution method on this one. Solve the 2nd equation for : Substitute this expression for into the first equation: and then simplify: Solve this one for : Substitute this expression for and the previously derived expression for into the third equation: . And then solve for Substitute this value for the derived expression for and solve for . Substitute the values for and into the original first equation and solve for . The last couple of steps are left as an exercise for the student. John

Exponents/234149: Can someone explain to me if there is rule about when the exponents are 0? when adding like terms x^0 is cancelled? but when solving a problem 2^0 is 1? I feel like im missing something? 1 solutions Answer 172688 by solver91311(16877)   on 2009-11-02 13:25:43 (Show Source): You can put this solution on YOUR website! ℂ, Therefore if was "cancelled" when adding like terms, there must have been a -1 somewhere to cancel it. Now if is a factor (as opposed to a term), then it can just go away because ℂ, John

Miscellaneous_Word_Problems/233390: t the opening night of the phantom of the opera, two different types of souvenirs were sold. posters sold for $20 each and t-shirts sold for $25 each. onw thousand souvenirs were sold in all for a total cost of $22,000. how many posters and t-shirts were sold? 1 solutions Answer 172267 by solver91311(16877)   on 2009-10-31 02:04:17 (Show Source): You can put this solution on YOUR website! Let represent the number of posters. Let represent the number of t-shirts. Then the amount of money collected for posters would be dollars and the amount of money collected for t-shirts would be dollars. Using the data given: Solve the system. The values of and are the numbers of posters and t-shirts sold. John

real-numbers/233353: how can you tell when an equation has a solution of all real numbers? 1 solutions Answer 172266 by solver91311(16877)   on 2009-10-31 02:03:09 (Show Source): You can put this solution on YOUR website! Not sure what you are talking about. Do you mean a system of linear equations that is consistent and dependent? Or are you talking about a polynomial equation and asking if you can tell if all of the roots are real numbers? Or are you talking about an identity where any real number will satisfy the equation? John

Linear_Algebra/233393: Using long division of polynomials can you please solve this equation, and also explain the process(11x^4-12x^3+15x^2+13x+14)/ x^2-6. Thanks 1 solutions Answer 172265 by solver91311(16877)   on 2009-10-31 01:41:06 (Show Source): You can put this solution on YOUR website! The process of polynomial long division is way too difficult to render on this site. Your best bet is to look at either Wikipedia: http://en.wikipedia.org/wiki/Polynomial_long_division or PurpleMath: http://www.purplemath.com/modules/polydiv2.htm By the way, you don't have an equation. An equation has an equals sign in it. What you have is a rational expression. And yeah, it makes a difference. John

Angles/233391: Find the measueres of the angles. 5x+10 and 3x this is a complementary angle. 1 solutions Answer 172264 by solver91311(16877)   on 2009-10-31 01:03:18 (Show Source): You can put this solution on YOUR website! I presume you mean that the angle that measures and the angle that measures are complementary angles. To the extent that is true, you can say: because the sum of the measures of two complementary angles is 90 degrees. So just solve for and substitute that value back into the given expressions for the measures of the two angles. John

Money_Word_Problems/233367: Can someone help me how to slove this problem step by step. "John took out two loans totaling $6,000 to help pay for college expenses. One loan was at 8% simple interest, and the other was at 10%. After one year, the student owed $740 in interest. Find the amount of the loan at 10%. 1 solutions Answer 172263 by solver91311(16877)   on 2009-10-31 00:58:29 (Show Source): You can put this solution on YOUR website! Let represent the amount at 10%. Then must be the amount at 8%. The amount of interest attributable to the 10% loan would then be and the amount of interest attributable to the 8% loan would be . The sum of these two interest amounts is $740, so: Just solve for John