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# Recent problems solved by 'ewatrrr'

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 Quadratic_Equations/440914: Find the center and radius of the circle. y^2=25-x^21 solutions Answer 304639 by ewatrrr(10682)   on 2011-04-27 13:25:52 (Show Source): You can put this solution on YOUR website! ``` Hi Finding the center and radius of the circle: y^2=25-x^2 Standard Form of an Equation of a Circle is where Pt(h,k) is the center and r is the radius y^2=25-x^2 x^2 + y^2 = 25 Center (0,0) aand r = 5 ```
 Quadratic_Equations/441028: Which quadratic equation has solutions of 5 and 7?1 solutions Answer 304638 by ewatrrr(10682)   on 2011-04-27 13:23:50 (Show Source): You can put this solution on YOUR website! ``` Hi Which quadratic equation has solutions of 5 and 7? The factor theorem states that a polynomial f(x) has a factor (x − k) if and only if f(k) = 0 (x-5)(x-7) = x^2 - 12x + 35 ```
 Quadratic_Equations/441078: we are doing conics in algebra and we have to put these equation into the standard form for the conic and i am having trouble with these equations. 1) parabola: x^2-2x+8y+9=0 2)parabola: x^2-2x+8y+17=0 3)parabola: y^2-4y-4x=0 4)hyperbola; 12x^2-20y^2-12x+40y-37=0 is there any way you can help?1 solutions Answer 304637 by ewatrrr(10682)   on 2011-04-27 13:21:09 (Show Source): You can put this solution on YOUR website! ``` Hi putting equations into the standard form for the conic completing the squares 1) parabola: x^2-2x+8y+9=0 (x-1)^2 = -8y - 8 (x-1)^2 = -8(y+1) 2)parabola: x^2-2x+8y+17=0 (x-1)^2 = -8y-16 (x-1)2 = -8(y+2) 3)parabola: y^2-4y-4x=0 (y-2)^2 = 4x + 4 (y-2)^2 = 4(x+1) 4)hyperbola; 12x^2-20y^2-12x+40y-37=0 12[(x-.5)^2 - .25] - 20[(y+1)^2-1] - 37 = 0 12(x-.5)^2 -3 - 20(y+1)^2 + 20 - 37 = 0 12(x-.5)^2 - 20(y+1)^2 = 20 (x-.5)^2/20/12 - (y+1)^2 = 1 ```
 Quadratic_Equations/441277: Nature of solutions, y^2=4/7y+5/31 solutions Answer 304633 by ewatrrr(10682)   on 2011-04-27 13:09:34 (Show Source): You can put this solution on YOUR website! ``` Hi Nature of solutions: y^2= 4/7y+5/3 y^2 -4/7y - 5/3 = 0 There are NO real solutions: discriminant is a negative number ```
 Quadratic_Equations/441280: x^2+6x+9=25, give exact and approximate within 3 decimal places.1 solutions Answer 304627 by ewatrrr(10682)   on 2011-04-27 13:00:09 (Show Source): You can put this solution on YOUR website! ``` Hi x^2+6x+9=25 factoring left side (x+3)^2 = 25 x+3 = ± 5 |taking the square root of both sides of the EQ x = -3 ± 5 x = -8 and x = 2 ```
 Quadratic_Equations/441281: (x+2)^2=36, give exact and approximate to 3 decimal places. 1 solutions Answer 304626 by ewatrrr(10682)   on 2011-04-27 12:57:43 (Show Source): You can put this solution on YOUR website! ``` Hi (x+2)^2 = 36 x+2 = ± 6 x = - 2 ± 6 x = -8 and x = 4 ```
 Polynomials-and-rational-expressions/441326: 3x^2+4x=0 My answer I got was x= negative two thirds (I do not know how to type the answer in correct form, sorry.) Is this right? If not where did I go wrong. Thank you!! 1 solutions Answer 304625 by ewatrrr(10682)   on 2011-04-27 12:53:29 (Show Source): You can put this solution on YOUR website! ``` Hi 3x^2+4x = 0 x(3x+4) = 0 zero-product property x = 0 (3x+4) = 0 x = -4/3 ```
 test/441279: If f(x)={x+2/(3)},then the value of f(0)equals___________________ I need this answer asap 1 solutions Answer 304619 by ewatrrr(10682)   on 2011-04-27 12:23:29 (Show Source): You can put this solution on YOUR website! ``` Hi f(x)=(x+2)/3 f(0) = (0+2)/3 = 2/3 f(0) = 2/3 ```
 Number-Line/441295: −3 + 8x + 4 + (−10x) combine like terms1 solutions Answer 304617 by ewatrrr(10682)   on 2011-04-27 12:13:29 (Show Source): You can put this solution on YOUR website! ``` Hi combining like terms -3 + 8x + 4 + (-10x) 8x + (-10x) + 4 -3 -2x + 1 OR 1-2x ```
 Matrices-and-determiminant/441304: Use Cramer's rule to solve the system of equations: x-2y+z=3 3x+2y+z=-3 2x-3y-3z=-51 solutions Answer 304615 by ewatrrr(10682)   on 2011-04-27 12:07:50 (Show Source): You can put this solution on YOUR website! ``` Hi Using Cramer's rule to solve the system of equations: x-2y+z= 3 3x+2y+z=-3 2x-3y-3z=-5 x = -1 , y = -1 and z = 2 See below Solved by pluggable solver: Using Cramer's Rule to Solve Systems with 3 variables First let . This is the matrix formed by the coefficients of the given system of equations. Take note that the right hand values of the system are , , and and they are highlighted here: These values are important as they will be used to replace the columns of the matrix A. Now let's calculate the the determinant of the matrix A to get . To save space, I'm not showing the calculations for the determinant. However, if you need help with calculating the determinant of the matrix A, check out this solver. Notation note: denotes the determinant of the matrix A. --------------------------------------------------------- Now replace the first column of A (that corresponds to the variable 'x') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'x' column so to speak). Now compute the determinant of to get . Again, as a space saver, I didn't include the calculations of the determinant. Check out this solver to see how to find this determinant. To find the first solution, simply divide the determinant of by the determinant of to get: So the first solution is --------------------------------------------------------- We'll follow the same basic idea to find the other two solutions. Let's reset by letting again (this is the coefficient matrix). Now replace the second column of A (that corresponds to the variable 'y') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'y' column in a way). Now compute the determinant of to get . To find the second solution, divide the determinant of by the determinant of to get: So the second solution is --------------------------------------------------------- Let's reset again by letting which is the coefficient matrix. Replace the third column of A (that corresponds to the variable 'z') with the values that form the right hand side of the system of equations. We will denote this new matrix Now compute the determinant of to get . To find the third solution, divide the determinant of by the determinant of to get: So the third solution is ==================================================================================== Final Answer: So the three solutions are , , and giving the ordered triple (-1, -1, 2) Note: there is a lot of work that is hidden in finding the determinants. Take a look at this 3x3 Determinant Solver to see how to get each determinant. ```
 Probability-and-statistics/441291: A sample of 106 golfers showed that their average score on a particular golf course was 87.98 with a standard deviation of 5.39. Answer each of the following show all work with the final answer to at least two decimal places: A) Find the 90% confidence interval of the mean score for all 106 golfers. B) Find the 90% confidence interval of the mean score for all golfers if this is a sample of 130 golfers instead of 106. C) Which confidence interval is larger and why?1 solutions Answer 304614 by ewatrrr(10682)   on 2011-04-27 11:59:14 (Show Source): You can put this solution on YOUR website! ``` Hi sample of 106 golfers showed that their average score on a particular golf course was 87.98 with a standard deviation of 5.39. A) Find the 90% confidence interval of the mean score for all 106 golfers. ME = 1.645[5.39/sqrt(106)] = .8612 CI: 87.98-.8612 < u < 87.98+.8612 CI: 86.9988 < u < 88.8412 B) Find the 90% confidence interval of the mean score for all golfers if this is a sample of 130 golfers instead of 106. ME = 1.645[5.39/sqrt(130)] = .7776 CI: 87.2024 < u < 88.7576 C) Which confidence interval is larger and why? confidence interval is larger for the smaller sample size of 106 due to the fact the ME is larger Summary of z values for various confidence intervals a a/2 crtical regions 90% 0.1 5% z <-1.645 z >+1.645 95% 0.05 2.50% z <-1.96 z >+1.96 98% 0.02 1% z <-2.33 z >+2.33 99% 0.01 0.50% z<-2.575 z >+2.575 ```
 Probability-and-statistics/441252: Mary has 14 hats. She has 4 green, 2 blue and 8 red. If she selects two hats what is the probability that both hats are different colors? Round your answer to two decimal places.1 solutions Answer 304595 by ewatrrr(10682)   on 2011-04-27 10:19:31 (Show Source): You can put this solution on YOUR website! ``` Hi, Previously posted Mary has 30 hats. She has 5 green, 7 blue, 12 red, and 6 brown. selects two hats at random P(they are different colors) = 1 - P(both are the same color) P(both are the same color) = 5/30*4/29 + 7/30*6/29 + 12/30*11/29 + 6/30*5*29 = (20 + 42 + 132 + 30)/30*29 = 224/30*29 = .2575 P(they are different colors) = 1 -.2575 = .7425 ```
 Probability-and-statistics/441255: Mary has 30 hats. She has 5 green, 7 blue, 12 red, and 6 brown. If she selects two hats at random, what is the probability that both hats are different colors? Round your answer to two decimal places. 1 solutions Answer 304594 by ewatrrr(10682)   on 2011-04-27 10:17:37 (Show Source): You can put this solution on YOUR website! ``` Hi Mary has 30 hats. She has 5 green, 7 blue, 12 red, and 6 brown. selects two hats at random P(they are different colors) = 1 - P(both are the same color) P(both are the same color) = 5/30*4/29 + 7/30*6/29 + 12/30*11/29 + 6/30*5*29 = (20 + 42 + 132 + 30)/30*29 = 224/30*29 = .2575 P(they are different colors) = 1 -.2575 = .7425 ```
 Radicals/441237: wat si the formula to make a chart for this quadratic equation y=x2+4x=61 solutions Answer 304589 by ewatrrr(10682)   on 2011-04-27 10:06:05 (Show Source): You can put this solution on YOUR website! ``` Hi chart for this quadratic equation y=x^2+4x+6 ```
 Rate-of-work-word-problems/441244: Painters A and B can paint a wall in 10 hours when working at the sametime. Painter B works twice as fast as A. How long would it take to each of them to paint if they worked alone?1 solutions Answer 304583 by ewatrrr(10682)   on 2011-04-27 09:56:53 (Show Source): You can put this solution on YOUR website! ``` Hi Painter B works twice as fast as A. Let x and 2x represent time(in hours)it takes solo for B and A Question states***Per hour the equalizer 1/x + 1/2x = 1/10 |Multiplying thru by 10x so as all denominators = 1 10 + 5 = x x = 15hr, time solo for B. time solo for A is 30hr CHECKING our Answer*** 1/15 + 1/30 = 2/30 + 1/30 = 3/30 = 1/10 ```
 Quadratic_Equations/441239: I need help solving this quadratic equation - -3w^2-6w+3=0 thanks for your help1 solutions Answer 304582 by ewatrrr(10682)   on 2011-04-27 09:48:31 (Show Source): You can put this solution on YOUR website! ``` Hi solving the quadratic equation -3w^2-6w+3=0 factoriing -3(w^2+2w-1)= 0 ```
 Exponents/441213: i hope you can solve the following for me: 1. x2m+n (2m+n being the exponent) ------ xm+3n (m+3n being the exponent) 2. 22m+2 (2m+2 being the exponent) ----- 2(2m-1)2 ( (2m-1)2 being the exponent) 3. (x+1)3n-2 (3n-2 being the exponent) --------- (x+1)2-3n (2-3n being the exponent) THANK YOU1 solutions Answer 304581 by ewatrrr(10682)   on 2011-04-27 09:42:53 (Show Source): You can put this solution on YOUR website! ``` Hi, Note the use of ^ (uppercase 6) Refer to the Laws governing exponents: ** **** 1. 2. 3. ```
 Quadratic_Equations/441177: How do you complete the squares in this equation: x^2-2x+y^2-15=0?1 solutions Answer 304574 by ewatrrr(10682)   on 2011-04-27 08:56:46 (Show Source): You can put this solution on YOUR website! ``` Hi x^2-2x+y^2-15=0 |Only one square to complete (x-1)^2 -1 + y^2 -15 = 0 (x-1)^2 + y^2 = 16 1) Circle with Center(1,0) and radius of 4 Standard Form of an Equation of a Circle is where Pt(h,k) is the center and r is the radius ```
 Quadratic-relations-and-conic-sections/440689: a. Find the co-ordinates of the vertex and the focus of the parabola x^2=4(x+y). Find the foci and vertices of the hyperbola 9 x^2 - y^2 - 36x +8y - 5 = 0 .1 solutions Answer 304422 by ewatrrr(10682)   on 2011-04-26 14:08:31 (Show Source): You can put this solution on YOUR website! ``` Hi a. Find the co-ordinates of the vertex and the focus of the parabola x2=4(x+y) x^2 - 4x = 4y (x-2)^2 - 4 = 4y OR (x-2)^2 = 4(y+1) Using the vertex form of a parabola, where(h,k) is the vertex 1/4(x-2)^2 - 1 = y Vertex (2,-1) The standard form is , where the focus is (h,k + p) (x-2)^2 = 4(y+1) 4p = 4 , p = 1 focus(2,0) ```
 Quadratic-relations-and-conic-sections/440664: find the foci of the ellipse with the equation: x^2\16 + y^2/36=11 solutions Answer 304415 by ewatrrr(10682)   on 2011-04-26 13:45:08 (Show Source): You can put this solution on YOUR website! ``` Hi Standard Form of an Equation of an Ellipse is where Pt(h,k) is the center and a and b are the respective vertices distances from center. find the foci of the ellipse with the equation: | Center(0,0) a = 4 and b = 6 f = sqrt(36-16) = sqrt(20) = ±2sqrt(5) ellipse with foci (0, ±2sqrt(5)) ```
 Quadratic-relations-and-conic-sections/440669: write an equation of the ellipse with foci (0, plus of minus 2) and co-vertices at (plus or minus 1, 0). a) x^2/25 +y^2 =1 b) x^2 + y^2/25 =1 c) x^2 + y^2/5 =1 d)x^2/5 +y^2 =11 solutions Answer 304413 by ewatrrr(10682)   on 2011-04-26 13:39:29 (Show Source): You can put this solution on YOUR website! ``` Hi Standard Form of an Equation of an Ellipse is where Pt(h,k) is the center and a and b are the respective vertices distances from center. ellipse with foci (0, ± 2) and co-vertices at (± 1, 0). f = a^2 = 5 ```
 Quadratic-relations-and-conic-sections/440657: Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the function. f(x)=-4(x+1)^2+41 solutions Answer 304412 by ewatrrr(10682)   on 2011-04-26 13:31:42 (Show Source): You can put this solution on YOUR website! ``` Hi Using the vertex form of a parabola, where(h,k) is the vertex y = -4(x+1)^2 +4 1) parabola opens downward a = -4 < 0 Vertex Pt(-1,4) is a maximum pt 2) Line of symetry is the x = -1 3) relative to the the translation from the origin: to the left 1 and up 4 ```
 Quadratic-relations-and-conic-sections/440789: please help me solve y=-3x^2-4..also need to give the minimum and maximum point , the equation of the parabola from the origin, then state whether the parabola opens upward or downward1 solutions Answer 304411 by ewatrrr(10682)   on 2011-04-26 13:26:38 (Show Source): You can put this solution on YOUR website! ``` Hi Using the vertex form of a parabola, where(h,k) is the vertex y = -3x^2 -4 1) parabola opens downward a = -3 < 0 Vertex Pt(0,-4) is a maximum pt 2) Line of symetry is the y-axis 3) relative to the the translation form the origin: down 4 ```
 Quadratic-relations-and-conic-sections/440799: please help me answer....y=(x-4)^2+6...also need to know minimum and maximum points, the equation of the line of symmetry, the distance and direction of the transition of the parabola as well as whether the parabola opens upward and downward1 solutions Answer 304410 by ewatrrr(10682)   on 2011-04-26 13:23:43 (Show Source): You can put this solution on YOUR website! ``` Hi Using the vertex form of a parabola, where(h,k) is the vertex y = (x-4)^2+6 1) parabola opens upward a = 1 > 0 Vertex Pt(4,6) is a minumum pt 2) Line of symetry is the x = 4 3) relative to the the translation form the origin: to the right 4 & up 6 ```
 Quadratic-relations-and-conic-sections/440801: please help me solve this: f(x)=1/2x^2-6....also need to know the minimum and maximum point as well as the equation of the line of symmetry and the distance and direction of the translation of the parabola from the origin, then state whether the parabola opens upward or downward1 solutions Answer 304409 by ewatrrr(10682)   on 2011-04-26 13:18:08 (Show Source): You can put this solution on YOUR website! ``` Hi Using the vertex form of a parabola, where(h,k) is the vertex f(x)=1/2x^2-6 1) parabola opens upward a = 1/2 > 0 Vertex Pt(0,-6) is a minumum pt 2) Line of symetry is the y -axis 3) relative to the the translation from the origin: down 6. ```
 percentage/440810: How would I set up an equation for the following problem? It took 85 hours to complete 75% of the work...How long will it take to complete 100% of the work?1 solutions Answer 304398 by ewatrrr(10682)   on 2011-04-26 12:30:34 (Show Source): You can put this solution on YOUR website! ``` Hi Let x represent the time to complete 100% of the work Question sets up the Proportion*** 75%/100% = 85hr/x Cross Multiplying 75x = 85*100 x = 85*100/75 x = 113 1/3 hr, the time to complete 100% of the work ```
 Rate-of-work-word-problems/440803: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together? 1 solutions Answer 304396 by ewatrrr(10682)   on 2011-04-26 12:23:43 (Show Source): You can put this solution on YOUR website! ``` Hi Sally can paint a house in 4 hours, and John can paint the same house in 6 hour Let x represent the time for both of them to paint the house together Question states*** Per hour the equalizer 1/4 + 1/6 = 1/x 3x + 2x = 12 |multiplying thru by 12x so as all denominators=1 5x = 12 x = 12/5 or 2.4hr Or 2 hour and 24 min ```
 Functions/440804: find the domain of the function f(x)= 3/(3x-24)1 solutions Answer 304394 by ewatrrr(10682)   on 2011-04-26 12:19:18 (Show Source): You can put this solution on YOUR website! ``` Hi Note: The Domain is the allowable values for x find the domain of the function f(x)= 3/(3x-24) |CANNOT divide by zero Denominator = 0 when x = 8 Domain: {x| x ≠ 8} Which says x is all Real numbers with the exception of 8. ```
 Polynomials-and-rational-expressions/440677: y varies directly with the square of x and inversely with z. If y = 16 when x=2 and z=3, find k, the constant of proportionality, and find y when x=5 and z=41 solutions Answer 304393 by ewatrrr(10682)   on 2011-04-26 12:13:42 (Show Source): You can put this solution on YOUR website! ``` Hi y varies directly with the square of x and inversely with z: y = kx^2/z 16 = k 2^2/3 | y = 16 when x=2 and z=3 12 = k find y when x=5 and z=4 y = 12*5^2/4 y = 75 ```
 Polynomials-and-rational-expressions/440679: I need help with the following problems: 1) 2/x^2-x-12 - 6/x+4 = 2/x-3 2) x-1/3 + x+2/4 = 1/6 3) 5/3x - 1/9 = 1/x 4) 3/3x-2 = 4/2x+1 I need to solve these "Equations with Rational Expressions" and i am having trouble figuring out how to find the LCD for some of them and others i just don't know how to go about solving them at all. Please help. ~ Thank you.1 solutions Answer 304392 by ewatrrr(10682)   on 2011-04-26 12:09:49 (Show Source): You can put this solution on YOUR website! ``` Hi If I am understqanding Your question(s) properly: 2) OR 4(x-1) + 3(x-2) = 2 |Multiplying thru with 12 so as all denominators = 1 7x = 12 x = 12/7 3) |Multiplying thru with 9x so as all denominators = 1 3*5 - x = 9 6 = x 4) | Cross Multiplying 4(3x-2) = 3(2x+1) 6x = 11 x = 11/6 1) Check Your sign: should this be? then 2 - 6(x-3) = 2(x+4) |Multiplying thru with (x+4)(x-3): 2 - 6x + 18 = 2x+4 16 = 8x x = 2 ```
 Polynomials-and-rational-expressions/440754: -21x3+15x2-30x=1 solutions Answer 304388 by ewatrrr(10682)   on 2011-04-26 11:54:25 (Show Source): You can put this solution on YOUR website! ``` Hi -21x3+15x2-30x = -3x(7x^2-5x+10) ```