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# Recent problems solved by 'richard1234'

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 percentage/391802: barney baked 100 pastries for a school picnic. of these 100 pastries 65 were doughnt and the rest were croissants what percent of barney's pastries were croissants1 solutions Answer 278016 by richard1234(5390)   on 2011-01-07 20:26:56 (Show Source): You can put this solution on YOUR website!This means that 35 pastries were croissants, so the percentage is 35/100 = 35%.
 Graphs/391851: Hi, My teacher gave me some make up work and I don't remember how it was done. There are boxes for missing symbols, I guess, but I will demonstrate this with []. I am not sure what to do: 1. [] (x/3) > [] (-1) 2. 3m > 6 ___ ___ [] [] 3. -4t< -16 -4t [] -16 ___ ____ [] [] thanks, any help would be appreciated. _ 31 solutions Answer 278015 by richard1234(5390)   on 2011-01-07 20:24:06 (Show Source): You can put this solution on YOUR website!Can you describe the symbol more in depth? Is it a letter denoting a function, or a Greek letter, or absolute value, or a matrix, etc...
 Linear-systems/391852: I need help solving these equations using the elimination method. x + 8y = 28 -x + 5y = 11 5x + 2y = -13 7x - 3y = 11 0.3x - 0.2y = 4 0.2x + 0.3y = 29/19 8x - 9y = 32.5 7y - 2x = -10.5 0.05x + 0.25y = 11 0.15x + 0.05y = 12 1 solutions Answer 278014 by richard1234(5390)   on 2011-01-07 20:19:57 (Show Source): You can put this solution on YOUR website!The first pair of equations is quite simple, just add them to get 13y = 39, y = 3 --> x = 4 Do the others the same way. You might have to multiply one or both equations by a constant to cancel a variable out. For example, the next set of equations, you could multiply the first equation by 3 and the second equation by 2, then adding them to cancel y.
 Travel_Word_Problems/391837: If I traveled 25 miles at 99 cents a mile how much would that be?1 solutions Answer 278012 by richard1234(5390)   on 2011-01-07 20:12:24 (Show Source): You can put this solution on YOUR website!(25 mi)*(\$.99/mi) = \$24.75
 Functions/391842: y= x -2x²-8 Determine the zeros of your function. Give an algebraic reason for the existence or non-existence of real-valued zeros of your quadratic function.1 solutions Answer 278011 by richard1234(5390)   on 2011-01-07 20:04:17 (Show Source): You can put this solution on YOUR website!Reorder the terms to produce . By the quadratic formula, . Since the roots have an imaginary part not equal to zero, the zeros of the function are complex.
 Linear_Equations_And_Systems_Word_Problems/391801: Given a right triangle with a hypotenuse of 16 and a leg of 8, find the length of the other leg to three decimal places.1 solutions Answer 278010 by richard1234(5390)   on 2011-01-07 20:00:16 (Show Source): You can put this solution on YOUR website!If you recall the right triangle with sides x, , and 2x, then if x = 8, the missing side is , or 13.856.
 Numbers_Word_Problems/391697: the difference between two number is 3. One number is t. What are the possible values for the other number?1 solutions Answer 278009 by richard1234(5390)   on 2011-01-07 19:58:06 (Show Source): You can put this solution on YOUR website!t+3, t-3
 Rational-functions/391783: can u teach me verything about pre algebra plz i dont understyand it1 solutions Answer 278007 by richard1234(5390)   on 2011-01-07 19:54:30 (Show Source): You can put this solution on YOUR website!There's quite a bit to teach, as pre-algebra, algebra, and algebra (as a whole) are very broad subjects. I suggest you read your pre-algebra book or go to a library and find a pre- or algebra book.
 Linear-systems/391841: Use the substitution method to solve the linear system. y=3x x=3y1 solutions Answer 278003 by richard1234(5390)   on 2011-01-07 19:46:26 (Show Source): You can put this solution on YOUR website!Replace y with 3x in the equation x = 3y to get x = 3(3x) = 9x x = 0 Since y = 3x = 3(0), y = 0.
 logarithm/391340: Solve each equation using logarithms. If an answer is not exact give the answer to four decimal places 3x+3 + 3x = 84 (hint: 3 x+3 = 3x 33) Solve each equation using logarithms. If an answer is not exact give the answer to four decimal places 7x = 12 Determine whether the statement is true or false 3 logb 3√a = logba Assume that x, y, z and b are positive numbers. Use the properties of logarithms to write each expression in terms of the logarithms of x, y, z LogbX1/2Y3 Assume that x, y, z and b are positive numbers. Use the properties of logarithms to write each expression in terms of the logarithms of x, y, and z. Logb 3xz Assume that x, y, z and b are positive numbers. Use the properties of logarithms to write each expression as the logarithm of one quantity 3 logb 3√a = logb a Assume that x, y, z and b are positive numbers. Use the properties of logarithms to write each expression in terms of the logarithms of x, y, and z Logbx1/2y3 Assume that x, y, z and b are positive numbers. Use the properties of logarithms to write each expression in terms of the logarithms of x, y, and z Logb3xz find each value to four decimel places ln 12/7 1 solutions Answer 277649 by richard1234(5390)   on 2011-01-06 09:30:44 (Show Source): You can put this solution on YOUR website!I would advise not to put your entire homework into one question. For nearly all the problems, you can solve them by using the identities and (regardless of the base). A couple of the problems will require you to use .
 Quadratic_Equations/391285: what is the quadratic formula? what is the origin of the quadratic formula?1 solutions Answer 277571 by richard1234(5390)   on 2011-01-05 23:41:03 (Show Source): You can put this solution on YOUR website!The quadratic formula says that the two roots of any second degree polynomial {{ax^2 + bx + c}}} are . It is possible to derive the quadratic formula by completing the square. This Wikipedia article lists multiple ways to derive the formula: http://en.wikipedia.org/wiki/Quadratic_equation
 Expressions-with-variables/391254: I am trying to figure out how to solve a problem. Its a word problem. It is--- The difference of the squares of two consecutive odd positive integers is 40. find the integers. I have tried X^2-(X^2+2)=40 but cant get it right. Am i even close?1 solutions Answer 277544 by richard1234(5390)   on 2011-01-05 21:54:59 (Show Source): You can put this solution on YOUR website!The equation you have becomes -2 = 40, by cancelling the x^2. Instead, it should look something like By difference of two squares this is equivalent to , therefore the two integers are 11 and 9. It is easy to check that
 Distributive-associative-commutative-properties/391226: Could someone help me with this one, please? 4x-9x+2y=-5x+2y ... and the just says to simplfy, but I keep getting the same1 solutions Answer 277535 by richard1234(5390)   on 2011-01-05 21:41:20 (Show Source): You can put this solution on YOUR website!-5x + 2y is the simplest form.
 Linear_Equations_And_Systems_Word_Problems/391234: The perimeter of a rectangle is 18 inches. The length is twice the width. Please find the length and the width. (I worked at this thing but I got no where because I can only make one equation x+x+y+y=18 but in order to graph it on my worksheet I need another equation but I don't see another one.)1 solutions Answer 277534 by richard1234(5390)   on 2011-01-05 21:39:25 (Show Source): You can put this solution on YOUR website!If x is the length, then the width y must be equal to 2x. So, y = 2x and we can substitute y to obtain x + x + 2x + 2x = 18 6x = 18 x = 3 --> y = 2(3) = 6.
 Trigonometry-basics/391229: Solve the following equation for x: cos x = -1, for the interval 0 < x < 2 pi1 solutions Answer 277527 by richard1234(5390)   on 2011-01-05 21:36:24 (Show Source): You can put this solution on YOUR website!Look at a unit circle. For any point on the unit circle, the x-coordinate represents and the y-coordinate represents . Since cos x = -1, the x-coordinate must be -1, and the y-coordinate must be 0 (due to the Pythagorean identity). This only occurs when .
 Linear-equations/391197: How do I go about solving this: "equation of vertical line that contains (-4, 8) its would also be great if you could tell me the general linear form. I have no idea how to begin solving this because I do not have the formula. Please and thank you very much.1 solutions Answer 277519 by richard1234(5390)   on 2011-01-05 21:32:41 (Show Source): You can put this solution on YOUR website!If a linear equation is vertical, then its slope is undefined. The only way for (the expression for slope) to be undefined is if there is some such that . This means that for some change in y, x is held constant. Since the line goes through (-4, 8), then x is held constant at -4. Therefore the equation is x = -4.
 Travel_Word_Problems/391218: susan rode her bike to and from the store at a rate of 5mph.If it took her 0.5 hours for her to make the trip how far is the store from her house? i think you have to use time=dis/rate1 solutions Answer 277511 by richard1234(5390)   on 2011-01-05 21:25:04 (Show Source): You can put this solution on YOUR website!Yes. Except, use an alternate form, distance = rate*time. D = (5 mi/hr)(.5 hr) = 2.5 mi
 Trigonometry-basics/391220: Determine the value of y for the following equation: y =sec (pi) 1 solutions Answer 277493 by richard1234(5390)   on 2011-01-05 21:03:29 (Show Source): You can put this solution on YOUR website! Since , --> y = -1
 Trigonometry-basics/391208: Verify that tanx cscx/secx=1 is an identity. Write your proof below. Thank you so much for all of your help!!!!! God Bless!!!!!!1 solutions Answer 277491 by richard1234(5390)   on 2011-01-05 21:02:00 (Show Source): You can put this solution on YOUR website!We want to show that . Rewriting everything in terms of sin and cos, Cancel out sin(x) to obtain which is true for all x that makes the values defined.
 Inverses/391211: im trying to help my niece and we don't understand this problem F(x) = x-71 solutions Answer 277490 by richard1234(5390)   on 2011-01-05 20:59:31 (Show Source): You can put this solution on YOUR website!It simply means that f(x) defines a function for a value x. It's similar to an input-output method. The function f(x) is linear, so the graph looks like this:
 Linear-equations/391217: graph the equation of the line that is perpendicular to the graph of each equation and passes through the given point1 solutions Answer 277489 by richard1234(5390)   on 2011-01-05 20:57:38 (Show Source): You can put this solution on YOUR website!I don't know what the original equation or point is.
 Evaluation_Word_Problems/391199: 1x-6x=?1 solutions Answer 277484 by richard1234(5390)   on 2011-01-05 20:13:49 (Show Source): You can put this solution on YOUR website!-5x
 Polynomials-and-rational-expressions/391195: Solve. (x - 3)^2 + (x + 2)^2 = 17 I am not sure what to do after I distribute the square root through out the problem... This is what I have so far: (or is that wrong??) (x^2 + 9) + (x^2 + 4) = 17 x^2 + x^2 + 13 = 171 solutions Answer 277483 by richard1234(5390)   on 2011-01-05 20:09:19 (Show Source): You can put this solution on YOUR website!You forgot the x terms in the expansion. It should look like: After that, you can collect like terms and solve via the quadratic formula.
 Rectangles/391158: what is the maximum area of a rectangle with a perimeter of 100 feet1 solutions Answer 277475 by richard1234(5390)   on 2011-01-05 19:54:28 (Show Source): You can put this solution on YOUR website!Many different ways to solve this. Solution 1 ---------- If the sides of the rectangle are x and 50-x (so that the perimeter is 100), the area is , which is a parabola in terms of x. The vertex occurs at , or x = 25. It points downward, so x = 25 maximizes the area, so the area is 625. Solution 2 ---------- Another way is finding the extrema of . We have which is equal to zero when x = 25 (this is actually where the -b/2a rule comes from). Solution 3 ---------- Yet another way comes from an unusual theorem: AM-GM inequality. Suppose we have two terms and . Then by AM-GM, Since , , The AM-GM inequality says the equality occurs if and only if all the 's are equal, that is, , and the optimal area is 625. It's pretty rare you'll see a solution like the last one. However AM-GM can be used to prove many similar theorems, i.e. proving that the rectangular solid of fixed surface area that has maximum volume is a cube.
 Systems-of-equations/391152: 2x+y-z=7 2x-y+3z=13 3x+2y-z=171 solutions Answer 277454 by richard1234(5390)   on 2011-01-05 19:32:11 (Show Source): You can put this solution on YOUR website!Add the first two equations (this clears out the y-term) to get 4x + 2z = 20 --> 2x + z = 10 Multiply the second equation by 2, so we can add the second and third equations and also clear the y-terms. This results in another equation in terms of x and z that is not equivalent to the one we already obtained. 4x - 2y + 6z = 26 3x + 2y - z = 17 -------------------- 7x + 5z = 43 We can rewrite this as 5(2x + z) - 3x = 43 --> 5(10) - 3x = 43 --> x = 7/3, z = 16/3. Substituting x and z into any of the equations, we get y = 23/3. Therefore the solution (x,y,z) is (7/3, 23/3, 16/3).
 Triangles/391153: in equilateral triangle one angle measures 3x+y the other 2x+40 and the third 2y. what is x and what is y 1 solutions Answer 277445 by richard1234(5390)   on 2011-01-05 19:15:45 (Show Source): You can put this solution on YOUR website!Each angle must measure 60 degrees. Therefore, 2y = 60 --> y = 30. Now use the first angle 3x + y, replace y with 30. It is equal to 60, so x is 10. The remaining angle, 2x+40, is already equal to 60 since if we replace x with 10, we get 60. So, x = 10, y = 30.