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# Recent problems solved by 'funmath'

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 Graphs/64955: can i see graphing of equations1 solutions Answer 45444 by funmath(2925)   on 2006-12-13 10:37:44 (Show Source): You can put this solution on YOUR website!You didn't specify the kind of equation you wanted to graph, here's something I did for someone else: Solve by graphing E1: y=2x+3 E2: x+y=3 : For E1: (I'm graphing this line by plotting points.) Let x=0 and solve for y: y=2(0)+3 y=0+3 y=3 Plot (0,3) Now let x=2 and solve for y (Pick any point within reason.) y=2(2)+3 y=4+3 y=7 Plot (2,7) Connect the points and you should have this line: For E2: (I'm graphing this line by the intercept method.) Let x=0 and solve for y: 0+y=3 y=3 Plot (0,3) Notice that both lines have the same y-intercept. This is the solution to the system. (We're not supposed to know that yet, and most of the time we won't, so let's keep graphing.) Let y=0 and solve for x: x+0=3 x=3 Plot (3,0) Connect the points and you have a second line: The lines intersect at the solution: (0,3) Happy Calculating!!!!
 Linear-equations/64949: find an equation of the line satisfying the given conditions. parallel to the line 2x+y=3 and through (-2,3)1 solutions Answer 45439 by funmath(2925)   on 2006-12-13 09:49:19 (Show Source): You can put this solution on YOUR website!find an equation of the line satisfying the given conditions. parallel to the line 2x+y=3 and through (-2,3) The equation of any line parallel to this one would have the same slope as this one. We need to find out what that is by putting this equation into slope intercept form:, m=slope and b=y-intercept. the slope, m=-2 Now that we have a slope and a point, we can use the point slope formula to find the equation of the line: m=-2 and (x1,y1)=(-2,3) Happy Calculating!!!
 expressions/64950: Please help me with this equation: b2-2bc+c21 solutions Answer 45426 by funmath(2925)   on 2006-12-13 08:55:31 (Show Source): You can put this solution on YOUR website!If you're supposed to factor: You'll eventually want to memorize this: This is a perfect square trinomial. Happy Calculating!!!
 logarithm/64943: Solve, and express your answer in exact form: 3^x = 4^(l-x)1 solutions Answer 45423 by funmath(2925)   on 2006-12-13 07:25:55 (Show Source): You can put this solution on YOUR website!Solve, and express your answer in exact form: Happy Calculating!!!!
 Graphs/64944: Sketch using transformations: f(x) = -2|x+2|. Start with the basic graph and show all stages. I know that there are supposed to be four graphs, but otherwise I'm stuck. Help!1 solutions Answer 45421 by funmath(2925)   on 2006-12-13 07:19:27 (Show Source): You can put this solution on YOUR website!Sketch using transformations: f(x) = -2|x+2|. Start with the basic graph and show all stages. f(x)=|x| looks like: f(x)=|x+2| causes a horizontal shift left two units: f(x)=2|x+2| causes a vertical stretch of a factor of 2: f(x)=-2|x+2| causes a reflection about the x-axis: Happy Calculating!!!
 Linear-equations/64947: write in slope-intercept form 1.a slope -4 and y intercept of 3/4 2.a line passing through (-3,-6) with slope 9/5 3.line that passes through (5,2) and 9/5 1 solutions Answer 45418 by funmath(2925)   on 2006-12-13 07:13:27 (Show Source): You can put this solution on YOUR website! write in slope-intercept form : 1.a slope -4 and y intercept of 3/4 The slope intercept form of a line is: , where m=slope and b=y-intercept. In this case, m=-4 and b=3/4, so the equation is: : 2.a line passing through (-3,-6) with slope 9/5 When given a point and a slope, we can find the equation of the line with the point-slope formula: , where m=slope and (x1,y1)=given point In this case, m=9/5 and (x1,y1)=(-3,-6) : 3.line that passes through (5,2) and m=9/5 You have a point and a slope, use the point slope formula that we used for the last one: m=9/5 and (x1,y1)=(5,2) : Happy Calculating!!!
 Exponents-negative-and-fractional/64848: This question is from textbook An Incremental Development simplify 1 / -27^-2/31 solutions Answer 45336 by funmath(2925)   on 2006-12-12 15:07:34 (Show Source): You can put this solution on YOUR website!simplify Happy Calulating!!!!
 Functions/64824: FOR THE FUNCTION DEFINED BY ,, USE A SKETCH TO HELP FIND A FORMULA FOR f^-1(x).1 solutions Answer 45334 by funmath(2925)   on 2006-12-12 15:04:18 (Show Source): You can put this solution on YOUR website!FOR THE FUNCTION DEFINED BY ,, USE A SKETCH TO HELP FIND A FORMULA FOR f^-1(x). Is graphed below. Ignore the left side of the graph because the domain includes only positive values. I have also graphed the line y=x, because inverse functions are reflected about that line. Notice that the graph has a y-intercept of (0,2), therefore the inverse will have an x-intercept of (2,0). Notice also that the graph goes toward -infinity as x goes towards +infinity, therefore its inverse will have x's that go to -infinity as y goes to positive infinity. The parent f(x)=x^2, therefore the parent f^-1(x)=sqrt(x), it has a horizontal reflection so f^-1(x)=sqrt(-x). It also has a horizontal shift right 2 units, so the inverse function is: f^-1(x)= The graph of the inverse is below: If you aren't being taught about reflections and shifts, plot the points for f(x) and then reverse the x's and y's and you'll have the inverse. Happy Calculating!!!
 logarithm/64825: SOLVE THE EQUATION In(x+5)-In(3)=In(x-3).1 solutions Answer 45332 by funmath(2925)   on 2006-12-12 14:48:04 (Show Source): You can put this solution on YOUR website!SOLVE THE EQUATION In(x+5)-In(3)=In(x-3). Check for extraneous solutions: The solution x=7 is valid. Happy Calculating!!!
 Functions/64829: IF f(x)=x^2+5,FIND f(a+h)-f(a)1 solutions Answer 45328 by funmath(2925)   on 2006-12-12 14:38:53 (Show Source): You can put this solution on YOUR website!IF f(x)=x^2+5,FIND f(a+h)-f(a) ---> --->---> Therefore Happy Calculating!!!!
 Polynomials-and-rational-expressions/64830: I can not figure out this question. 5. Simplify by (multiplying out) or by (factoring and then dividing): a. (14x to the 3rd y to the 4th z)/(7x to the 4th y to the 2nd z to the 4th) b. 2xy(3x to the 2nd y - 5x to the 2nd y + 6) c. (2x + y - 3)(3x - 2y) d. (2x to the 3rd + 7x to the 2nd - x - 2)/(2x + 1)1 solutions Answer 45327 by funmath(2925)   on 2006-12-12 14:33:30 (Show Source): You can put this solution on YOUR website!5. Simplify by (multiplying out) or by (factoring and then dividing): a. : b. : c. : d. I had to use long division for this one, which is all but impossible to show you on this. The answer is . If you have Word, I have mathtype and can send you an attachment to show you how to get this.
 Functions/64831: GIVEN f(x)=5x+7 AND g(x)=x^2+7, FIND (g o f)(x).1 solutions Answer 45324 by funmath(2925)   on 2006-12-12 14:14:12 (Show Source): You can put this solution on YOUR website!GIVEN f(x)=5x+7 AND g(x)=x^2+7, FIND (g o f)(x). = Substitute the f function into the g function for x. Happy Calculating!!!!
 Polynomials-and-rational-expressions/64411: If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm^2. What were the dimensions of the original square?1 solutions Answer 45040 by funmath(2925)   on 2006-12-09 07:53:07 (Show Source): You can put this solution on YOUR website!If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm^2. What were the dimensions of the original square? Let the original side be: x Then the area is:x^2 Then if we decreased it by 3 the new sides would be: x-3 The area of the original decreased by 81 is: x^2-81 The area of the new square is:(x-3)^2 The original sides were 15 cm. Sanity Check: If the original sides were 15 cm, the area would be 15^2=225. If the new sides were 15-3=12 cm, the area would be 12^2=144 If we subtract the two areas we get: 225-144=81 Happy Calculating!!!
 Probability-and-statistics/64412: If in an hypothesis test the null hypothesis is rejected, then do I reject the alternative or motivated hypothesis as well?1 solutions Answer 45039 by funmath(2925)   on 2006-12-09 07:41:58 (Show Source): You can put this solution on YOUR website!If in an hypothesis test the null hypothesis is rejected, then do I reject the alternative or motivated hypothesis as well? Your null hypothesis always contains an =, your alternative never contains an =. They are opposites. If you reject the null, you are not finding evidence that rejects the alternative. In our book, we don't use the term, "motivated hypothesis." If that means the same thing as our "claim" does then, sometimes your claim is your null and sometimes its the alternative. If your claim is this=that, then your null is your claim and when you reject your null, you reject your claim. If your claim is this Different teachers and books are real specific about the way you need to word your conclusions. The book used at our college has a flow chart that tells you what to conclude based on your claim and rejection or failure to reject your null. If yours doesn't and this hasn't cleared things up for you, let me know and I will type a chart based on our flow chart. Happy Calculating!!!
 Exponents/64413: Simplify. Write your answer with only positive exponents. b^7b^–10 1 solutions Answer 45038 by funmath(2925)   on 2006-12-09 07:26:44 (Show Source): You can put this solution on YOUR website!The two rules we're going to use are: Simplify. Write your answer with only positive exponents. Happy Calculating!!!!
 Rational-functions/64186: This question is from textbook Algebra & Trigonometry I dont understand how to answer this problem because: 1)i dont get how you find the domain 2)i dont understand how i graph the equation1 solutions Answer 44973 by funmath(2925)   on 2006-12-08 12:08:18 (Show Source): You can put this solution on YOUR website!I don't have your book, what is the problem and directions? funmath
 Systems-of-equations/64260: This question is from textbook Algebra 1 Page 385 problem #3 y=3x y=x squared - 41 solutions Answer 44972 by funmath(2925)   on 2006-12-08 12:05:06 (Show Source): You can put this solution on YOUR website!I don't have your book, what are your directions. Is this a system of equations that you need to solve?
 Exponential-and-logarithmic-functions/64331: This question is from textbook college algebra 2^x=50 This is my problem... I know that it is an exponential equation, but how would you solve the problem I need so much help I feel so stupid when it comes to math could you please help me thank you.1 solutions Answer 44971 by funmath(2925)   on 2006-12-08 11:42:38 (Show Source): You can put this solution on YOUR website!Don't feel stupid, nobody was born knowing how to do this. Everyone has to learn it. take the log or ln of both sides of the equation. Plug this into your calculator and you get: x=5.64385619 Happy Calculating!!!!
 Linear-equations/64330: What is the slope of the equation: 5x-6y= -181 solutions Answer 44970 by funmath(2925)   on 2006-12-08 11:35:27 (Show Source): You can put this solution on YOUR website!The slope intercept form of a line is , where m=slope and b=y-intercept. What is the slope of the equation: 5x-6y= -18 -5x+5x-6y=-5x-18 0-6y=-5x-18 -6y=-5x-18 -6y/-6=(-5/-6)x-18/-6 y=(5/6)x+3 The slope is the coefficient of x, : You didn't ask, but we also know that the y-intercept is b=3 Happy Calculating!!!
 Linear-systems/64309: Is x=2,y=9 a parallel line, perpendicular line, or neither of these two lines. thanks for your help. Hockeyk41@aol.com1 solutions Answer 44946 by funmath(2925)   on 2006-12-08 07:09:42 (Show Source): You can put this solution on YOUR website!Is x=2,y=9 a parallel line, perpendicular line, or neither of these two lines. thanks for your help. x=2 is a vertical line going through the x-axis at 2 with an undefined slope. y=9 is a horizontal line going through the y-axis at 9 with a slope of 0. horizontal and vertical lines hit each other at a 90 degree angle and are therefore perpendicular. Happy Calculating!!!
 Divisibility_and_Prime_Numbers/64277: Find the prime factorization of 401 solutions Answer 44945 by funmath(2925)   on 2006-12-08 07:06:10 (Show Source): You can put this solution on YOUR website!Most people use factor trees to do this these days. That's real difficult to do in this program, so what I'm going to do is divide by the smallest numbers I know that will go evenly into 40, then the reamianders. The left column will be the prime factors. Find the prime factorization of 40 2 * 20 2 * 10 2 * 5 5 * 1 The prime factors are 2*2*2*5 or Happy Calculating!!!
 Signed-numbers/64276: Simplify: –(–10)1 solutions Answer 44943 by funmath(2925)   on 2006-12-08 07:00:54 (Show Source): You can put this solution on YOUR website!Simplify: –(–10) -(-10) means "the opposite of -10" or "-1 times -10" (when the signs are the same, multiply as usual and the answer is positive. +10 or 10 Happy Calculating!!!!
 Functions/64279: find the constant of variation k. m varies directly with n; m - 144 when n = 8.1 solutions Answer 44941 by funmath(2925)   on 2006-12-08 06:56:40 (Show Source): You can put this solution on YOUR website!You have a type-o for m's value. find the constant of variation k. m varies directly with n; m - 144 when n = 8. m=kn <---m varies directly with n is written this way. -144=k(8) <---substitute your values in for m and n and solve for k. -144/8=8k/8 -18=k If you meant m=144 instead of m=-144, just remove all the negatives. k=18. Happy Calculating!!!
 Equations/64293: 1.) 2(y-6)=3y+12-y 2.) 6-2y=7y+13 3.) 3x-5(x-6)=2(10-x)+10 4.) 5n+7=7(n+1)-2n 5.) -4(p+2)+8=2(p-1)-7p+151 solutions Answer 44939 by funmath(2925)   on 2006-12-08 06:49:30 (Show Source): You can put this solution on YOUR website!1.) 2(y-6)=3y+12-y 2y+2(-6)=3y-y+12 2y-12=2y+12 -2y+2y-12=-2y+2y+12 0-12=0+12 -12=12 No solution, this is inconsistent. : 2.) 6-2y=7y+13 6-2y+2y=7y+2y+13 6-0=9y+13 6=9y+13 6-13=9y+13-13 -7=9y+0 -7=9y -7/9=9y/9 -7/9=y : 3.) 3x-5(x-6)=2(10-x)+10 3x-5(x)-5(-6)=2(10)+2(-x)+10 3x-5x+30=20-2x+10 2x+30=-2x+30 2x+2x+30=-2x+2x+30 4x+30=30 4x+30-30=30-30 4x+0=0 4x=0 4x/4=0/4 x=0 : 4.) 5n+7=7(n+1)-2n 5n+7=7(n)+7(1)-2n 5n+7=7n+7-2n 5n+7=7n-2n+7 5n+7=5n+7 This is an identity, there are infinitly many solutions. : 5.) -4(p+2)+8=2(p-1)-7p+15 -4(p)-4(2)+8=2(p)+2(-1)-7p+15 -4p-8+8=2p-2-7p+15 -4p+0=2p-7p-2+15 -4p=-5p+13 -4p+5p=-5p+5p+13 p=0+13 p=13 Happy Calculating!!!
 Square-cubic-other-roots/64286: Solve for the variable: (square root of)(2x + 1) = -1 a) 0 b) 1 c) -1 d) -2 e) none of these1 solutions Answer 44938 by funmath(2925)   on 2006-12-08 06:34:42 (Show Source): You can put this solution on YOUR website!Solve for the variable: (square root of)(2x + 1) = -1 a) 0 b) 1 c) -1 d) -2 none of these You can't take the square root of anything and get a negative number, so you can look at this and know that this has no solution, however, if you didn't notice that, you would try to solve it this way. But when you check x=0, you will find that it's extraneous. Not true, so 0 is extraneous and there is no solution. Happy Calculating!!!
 Quadratic_Equations/64292: 1.) If g(x)= 2-2x^2/3x^3+10x+3, find g(o) 2. If f(x)=-3x+5 then f(x+h)-f(x)/h = ? 3. If y=3x^2-6x+5, determine the vertex and the parabola 4. Find the midpoint between the two points (8,6) and (4,8)1 solutions Answer 44937 by funmath(2925)   on 2006-12-08 06:25:24 (Show Source): You can put this solution on YOUR website!I'm not sure where your fractions begin and end without parentheses. If I misinterpretted your questions, let me know. 1.) If , find g(o) : 2. If f(x)=-3x+5 then (f(x+h)-f(x))/h = ? : 3. If y=3x^2-6x+5, determine the vertex and the parabola There are two ways to do this, if your class is putting the equation in vertex form to do this, let me know and I'll redo this. When a quadratic equation is in this form I use this formula to find the x value of the vertex. a=3, b=-6 and c=5 Now plug that in for x in the equation to find y. The vertex is (1,2) : 4. Find the midpoint between the two points (8,6) and (4,8) The midpoint formula is (,) (x1,y1)=(8,6) and (x2,y2)=(4,8) (,) (12/2,14/2) (6,7) Happy Calculating!!!
 Linear-equations/64295: My question is: How do I write the steps to writing an equation in standard form starting with a linear equation( in general all linear equations ) step by step? Thank you very much tutor, Steven Honolulu, Hawaii1 solutions Answer 44936 by funmath(2925)   on 2006-12-08 06:03:56 (Show Source): You can put this solution on YOUR website!Aloha Steven, The standard form of a linear equation is , where A,B, and C are intergers. Some books also require that A be positive. If we had a linear equation in slope intercept form like this: and we were asked to put it in standard form, the first thing that I would notice is that the x term is in the wrong place, so I would move it. Now I would notice that the coefficient of x is both negative and a fraction. To change that I would multiply everything by the -denominator, -4. (If your book doesn't require that A be positive, you can multiply by 4.) I hope that clarifies things. Let me know if you don't understand something that I showed you. Happy Calculating!!!
 Reduction-of-unit-multipliers/64301: Divide. Write the answer in scientific notation. 5.2 x 10^-12 ____________ 7.5 x 10^-71 solutions Answer 44935 by funmath(2925)   on 2006-12-08 05:46:16 (Show Source): You can put this solution on YOUR website!Divide. Write the answer in scientific notation. 5.2 x 10^-12 ____________ 7.5 x 10^-7 Happy Calculating!!!
 Exponential-and-logarithmic-functions/64308: Hello I am struggling with this question in my college course work any help would be appreciated... (e^x)^4 e^5 ____________= 3 e^2x1 solutions Answer 44934 by funmath(2925)   on 2006-12-08 05:38:23 (Show Source): You can put this solution on YOUR website! Put this in your calculator. x~-1.950693856 Round off to whatever your asked for. Happy Calculating!!!
 Human-and-algebraic-language/64281: Write the following phrase using symbols. 10 times the sum of t and z 1 solutions Answer 44916 by funmath(2925)   on 2006-12-07 20:59:04 (Show Source): You can put this solution on YOUR website!Write the following phrase using symbols. 10 times the sum of t and z times means multiply * sum means add + 10*(t+z) or 10(t+z) Happy Calculating!!!