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 Pythagorean-theorem/316018: find the length of the hypotenuse of the right triangle, side a=25, side b=121 solutions Answer 226062 by jim_thompson5910(28476)   on 2010-06-20 19:08:23 (Show Source): You can put this solution on YOUR website! We basically have this triangle set up: To find the unknown length, we need to use the Pythagorean Theorem. Remember, the Pythagorean Theorem is where "a" and "b" are the legs of a triangle and "c" is the hypotenuse. Since the legs are and this means that and Also, since the hypotenuse is , this means that . Start with the Pythagorean theorem. Plug in , , Square to get . Square to get . Combine like terms. Rearrange the equation. Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense). ================================================================ Answer: So the solution is which approximates to .
 Graphs/316017: You are selling cups of coffee at a sporting event. Your sales records show that when the coffee is priced at $3 per cup, you sell 650 cups. When the coffee is prices at$2.50, you sell 930 cups. Using that information, write a linear equation for the relationship between price (p) and quantity (q) sold. Your starting point is: q = mx + b, which is the slope intercept form of an equation, and using the two ordered pairs you find m and b. Make sure your answer here is an equation. 1 solutions Answer 226061 by jim_thompson5910(28476)   on 2010-06-20 19:04:28 (Show Source): You can put this solution on YOUR website!Basically, we're looking for the equation that goes through the points and First let's find the slope of the line through the points and Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Divide So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Distribute Multiply Add 650 to both sides. Combine like terms. So the equation that goes through the points and is Now simply replace 'x' and 'y' with 'p' and 'q' to get
 Geometry_Word_Problems/316014: Determine the length and width of a rectangle with a perimeter of 82 inches and a diagonal of 29 inches.1 solutions Answer 226059 by jim_thompson5910(28476)   on 2010-06-20 18:50:44 (Show Source): You can put this solution on YOUR website!Hint: Let W = width and L = length. The perimeter of a rectangle is . Plug in to get . The diagonal 'd' can be obtained through the Pythagorean theorem, which means that . Plug in (the given diagonal length) to get . So at this point, you have two equations with two unknowns.
 Pythagorean-theorem/316009: what is the area of a triangle with a base of 15m and a height of 16m1 solutions Answer 226056 by jim_thompson5910(28476)   on 2010-06-20 18:35:11 (Show Source): You can put this solution on YOUR website!Area of triangle = (base * height)/2 So which means that the area of the triangle is 120 square meters.
 Exponents-negative-and-fractional/316010: What does 3 to the negative 2 power equal? Please show how to work this out and write as a fraction? Also, how do I work out 1.13x10 to the power of 1 + 9.1x10 to the power of -1?1 solutions Answer 226055 by jim_thompson5910(28476)   on 2010-06-20 18:33:51 (Show Source): You can put this solution on YOUR website! and
 Linear-equations/316011: wright the standard form of the equation for the line that passes through the points (8,1),(8,9)1 solutions Answer 226054 by jim_thompson5910(28476)   on 2010-06-20 18:31:44 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Remember, you cannot divide by zero. So this means that the slope is undefined. Since the slope is undefined, this means that the equation of the line through the points and is (since both points have the x coordinate of 8)
 Equations/316007: What is the solution of 5x - 2 + 3 = 32?1 solutions Answer 226052 by jim_thompson5910(28476)   on 2010-06-20 18:02:37 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is
 Equations/316000: If y varies inversly with x & y=5 when x=7 what is the value of y when x=4 I got 8.751 solutions Answer 226044 by jim_thompson5910(28476)   on 2010-06-20 17:27:35 (Show Source): You can put this solution on YOUR website!"If y varies inversly with x" means that where 'k' is some constant number. So if "y=5 when x=7" means that . Solve for 'k' to get . So we get the equation . Finally, plug in x=4 to get . So you have the correct answer. Good job.
 Equations/315998: The length of a rectangle is 5 ft more than its width and its area is 84 square feet. Find its width and length. Let x represent the width of the rectangle and translate the problem into an equation. Don't solve.1 solutions Answer 226041 by jim_thompson5910(28476)   on 2010-06-20 17:18:13 (Show Source): You can put this solution on YOUR website!"The length of a rectangle is 5 ft more than its width" means that the length is units. Since "its area is 84 square feet", we know that . Since we don't have to solve this, I'll leave it like this. If you wanted to solve, distribute and then get everything to one side. Once you have a simplified quadratic, use the quadratic formula to solve.
 Quadratic_Equations/315994: Write a problem in which the quadratic equation x(x + 3)=108 must be solved in order to solve the problem.1 solutions Answer 226039 by jim_thompson5910(28476)   on 2010-06-20 17:10:07 (Show Source): You can put this solution on YOUR website!A rectangle in which has a length 3 units longer than its width has an area of 108 units.
 Polynomials-and-rational-expressions/315972: solve r/14-r/35=1/141 solutions Answer 226038 by jim_thompson5910(28476)   on 2010-06-20 17:08:48 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Combine like terms on the left side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is which approximates to .
 Polynomials-and-rational-expressions/315993: Explain how (p+q)^2 differs from p^2+q^2 by expanding (p+q)^21 solutions Answer 226037 by jim_thompson5910(28476)   on 2010-06-20 17:07:46 (Show Source): You can put this solution on YOUR website!FOIL out to get
 Equations/315912: y=3y+11 solutions Answer 226028 by jim_thompson5910(28476)   on 2010-06-20 16:53:45 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Miscellaneous_Word_Problems/315873: A student is solving the equation s^2=9^2 and has determined that s=9. He or she has looked up the answer in the back of the book and finds that s=-9 is also a solution. The student feels this is a misprint. How would you advise the student?1 solutions Answer 225974 by jim_thompson5910(28476)   on 2010-06-20 04:30:13 (Show Source): You can put this solution on YOUR website!Simply show him/her that and which can only mean that
 Angles/315856: does a 113 degrees has a complement? 1 solutions Answer 225968 by jim_thompson5910(28476)   on 2010-06-20 01:33:18 (Show Source): You can put this solution on YOUR website!No a 113 degree angle doesn't have a complement angle, but it does have a supplement. Is that what you're referring to?
 Rational-functions/315855: 2x-y=41 solutions Answer 225967 by jim_thompson5910(28476)   on 2010-06-20 01:00:11 (Show Source): You can put this solution on YOUR website!What do you want to do here?
 Polynomials-and-rational-expressions/315837: List all numbers for which the rational expression is undefined 4/b+7 I am not sure but I think 7 is the anwser. Could you please show me how to do this problem.1 solutions Answer 225953 by jim_thompson5910(28476)   on 2010-06-19 22:33:43 (Show Source): You can put this solution on YOUR website!If the rational expression is , then... First take the denominator and set it equal to zero to get . We're doing this because we want to find the values of 'b' that make the denominator zero (remember, we can't divide by zero). Solve to get . So the value makes the rational expression undefined.
 Polynomials-and-rational-expressions/315806: 1 solutions Answer 225952 by jim_thompson5910(28476)   on 2010-06-19 22:30:29 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor the last inner denominator. Take note that the inner LCD is Multiply EVERY term by the inner LCD to clear out all the inner fractions. Multiply and simplify Rearrange the terms. Distribute. Combine like terms. So
 Expressions-with-variables/315801: (t^2) / (t-3) - (8t-15) / (t-3)1 solutions Answer 225928 by jim_thompson5910(28476)   on 2010-06-19 19:36:14 (Show Source): You can put this solution on YOUR website! So where
 Rational-functions/315800: 9 5x+7 Find all numbers for which the rational expression is underfined.1 solutions Answer 225926 by jim_thompson5910(28476)   on 2010-06-19 19:34:14 (Show Source): You can put this solution on YOUR website!Hint: The rational expression is undefined when the denominator is equal to zero. So simply solve to find the value(s) of 'x' that make the rational expression undefined.
 Exponents/315791: just wondering how to solve this without a calculator? (9^8)(4^3)/ (9^7)(4^2)=1 solutions Answer 225924 by jim_thompson5910(28476)   on 2010-06-19 18:26:26 (Show Source): You can put this solution on YOUR website!Hint: . Use this idea to calculate
 Age_Word_Problems/315785: The ages of two brothers are 11 and 8 years. In how many years' time will the product of their ages be 208?1 solutions Answer 225923 by jim_thompson5910(28476)   on 2010-06-19 17:58:20 (Show Source): You can put this solution on YOUR website!Hint: Add 'x' years to both ages to get and years. Multiply them and set them equal to 208 to get . From here, FOIL out the left side and subtract 208 from both sides to get everything to one side. After combining like terms and simplifying, use the quadratic formula to solve for 'x' (note: ignore any negative solutions)
 logarithm/315732: Given f(x) = "log base a of x" please describe the restrictions on a and the restrictions on x1 solutions Answer 225922 by jim_thompson5910(28476)   on 2010-06-19 17:39:36 (Show Source): You can put this solution on YOUR website!Since , this means that the restrictions on 'a' are very similar to the restrictions on 'x'. However, we must make sure that . So this means that For 'x', we can plug in any positive number (since we cannot take the log of 0 or any negative number). So this means that . Because the conditions on 'a' are similar, this means that as well but we must add that Let me know if this makes sense to you.
 Money_Word_Problems/315783: if 300 jellybeans cost you x dollars. How many jellybeans can you purchase for 50 cents at the same rate? A. 150/x B. 150x C. 6x D. 1500/x E. 600x Please select answer, show work and explain1 solutions Answer 225918 by jim_thompson5910(28476)   on 2010-06-19 17:30:57 (Show Source): You can put this solution on YOUR website!Hint: Set up the ratio where 'y' is the amount of jelly beans you can purchase for 50 cents. Once you've set up the equation, simply solve for 'y'.
 Equations/315782: one number is 4 less than twice another number. if their sum is 11, what are the 2 number?1 solutions Answer 225917 by jim_thompson5910(28476)   on 2010-06-19 17:18:45 (Show Source): You can put this solution on YOUR website!Hint: "one number is 4 less than twice another number" means that and "their sum is 11" tells us that . From here, plug in to get .
 Complex_Numbers/315735: Perform the indicated operation -Imaginary numbers 1). (9-5i) + (4+7i) 2). (1+3i) - (2+ 8i) 3). (11i)(5i) 4). (12-5i)(2+3i)1 solutions Answer 225915 by jim_thompson5910(28476)   on 2010-06-19 17:04:53 (Show Source): You can put this solution on YOUR website!Only post one problem at a time please. 1)
 Linear-equations/315771: Write an equation of the line which passes through these points (0, -4) and (0, 8)1 solutions Answer 225914 by jim_thompson5910(28476)   on 2010-06-19 17:03:13 (Show Source): You can put this solution on YOUR website!Since the 'x' coordinate is zero for both points, this means that a vertical line of the form goes through these points. In this case, because the x coordinate is zero. So the equation of the line that goes through the points (0, -4) and (0, 8) is
 Quadratic_Equations/315637: how can i solve this problem using quadratic formula 12x(squared)+3x+27=01 solutions Answer 225827 by jim_thompson5910(28476)   on 2010-06-18 20:58:18 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "x": Start with the quadratic formula Plug in , , and Square to get . Multiply to get Subtract from to get Multiply and to get . Simplify the square root (note: If you need help with simplifying square roots, check out this solver) or Break up the expression. or Reduce. So the solutions are or
 Quadratic_Equations/315590: Can someone please help me out with this. Thanks in advance t(9+t)=4(2t+5)1 solutions Answer 225806 by jim_thompson5910(28476)   on 2010-06-18 17:59:00 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Get every term to the left side. Combine like terms. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "t": Start with the quadratic formula Plug in , , and Square to get . Multiply to get Rewrite as Add to to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the solutions are or
 Inequalities/315600: Solve -3x + 14 - x < 56 + 3x 1 solutions Answer 225804 by jim_thompson5910(28476)   on 2010-06-18 17:56:49 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Combine like terms on the left side. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Finance/315602: Find an equation of the line containing the points (-3, 1) and (-1, 3).1 solutions Answer 225803 by jim_thompson5910(28476)   on 2010-06-18 17:56:04 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Rewrite as Distribute Multiply Add 1 to both sides. Combine like terms. Simplify So the equation that goes through the points and is Notice how the graph of goes through the points and . So this visually verifies our answer. Graph of through the points and