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# Recent problems solved by 'ewatrrr'

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 Exponents/669489: 2^5/2 - 2^3/21 solutions Answer 416420 by ewatrrr(10682)   on 2012-10-21 11:25:24 (Show Source): You can put this solution on YOUR website! ``` Hi, 2^5/2 - 2^3/2 = ```
 Trigonometry-basics/669520: Using Cramer's rule solve 2x - y = 4 3x + y - z = 10 y + z = 3 Thanks1 solutions Answer 416419 by ewatrrr(10682)   on 2012-10-21 11:19:06 (Show Source): You can put this solution on YOUR website! ``` Hi, 2x - y = 4 3x + y - z = 10 y + z = 3 3x + 2y = 13 3x + 2(2x-4) = 13 7x = 21, x = 3 and y= 2 and z = 1 Using Cramer's rule 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 (3, 2, 1) 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. ```
 Functions/669504: f(x)=8x+9, g(x)=x^2+7x find (fg)(2)1 solutions Answer 416416 by ewatrrr(10682)   on 2012-10-21 11:13:10 (Show Source): You can put this solution on YOUR website! ``` Hi, f(x)=8x+9, g(x)=x^2+7x (fg)(x) = (8x+9)(x^2+7x) (fg)(2) = ```
 Equations/669025: Use synthetic division to find P(–2) for P(x) = x4 + 9x3 - 9x + 2 . A. –2 B. 0 C. –36 D. 68 1 solutions Answer 416022 by ewatrrr(10682)   on 2012-10-19 15:50:14 (Show Source): You can put this solution on YOUR website! ``` Hi, P(x) = x4 + 9x3 - 9x + 2 P(-2) = 16 -72 +18 + 2 = -36 ```
 Polynomials-and-rational-expressions/669013: What polynomial has a graph that passes through the given points? (-2, 2) (-1, -1) (1, 5) (3, 67) A. y = -x3 + 4x2 + 2x - 2 B. y = x3 + 4x2 + 2x - 2 C. y = x4 + 4x3 + 2x2 - 2x D. y = x3 - 4x2 - 2x - 21 solutions Answer 416021 by ewatrrr(10682)   on 2012-10-19 15:43:32 (Show Source): You can put this solution on YOUR website! ``` Hi, B Might recommend downloading the FREE graph software at: http://www.padowan.dk.com ```
 Equations/669022: Find the roots of the polynomial equation. -x3 + 5x2 - 11x + 55 = 0 A) i√11, -1√11,-5 B) √11,-√11,5 C) i√11,-5 D) i√11,-i√11,51 solutions Answer 416018 by ewatrrr(10682)   on 2012-10-19 15:20:37 (Show Source): You can put this solution on YOUR website! ``` Hi, y = -x3 + 5x2 - 11x + 55 ||x = 5 one root -125 + 125 - 55 + 55 = 0 using Synthetic Divsion 5 -1 5 -11 55 -5 0 -55 -1 0 -11 0 results in: -x^2 - 11 = 0 x^2 + 11 = 0 x^2 = -11 x = ± i√11 roots are: i√11,-i√11,5 ```
 Graphs/669018: Find the real solutions of the equation by graphing. x2 + 2x + 2 = 01 solutions Answer 416015 by ewatrrr(10682)   on 2012-10-19 15:14:59 (Show Source): You can put this solution on YOUR website! ``` Hi, y = x^2 + 2x + 2 Pt(0,2) on the curve y = x^2 + 2x +1 -1 + 2 y = (x + 1)^2 + 1 parabola, V(-1,1) line of symmetry x = -1 Graph, NO real solutions ```
 Permutations/669001: A college math club consists of 16 men and 20 women. a. in how many different ways can a committee of 5 members be chosen? b. in how many different ways can a committee of 5 be chosen and have it consist of 2 men and 3 women? c. it the 5 committee members are randomly selected, what is the probability that the committee will consist of 2 men and 3 women1 solutions Answer 416005 by ewatrrr(10682)   on 2012-10-19 14:47:23 (Show Source): You can put this solution on YOUR website! ``` Hi, college math club consists of 16 men and 20 women. total a. in how many different ways can a committee of 5 members be chosen? b. in how many different ways can a committee of 5 be chosen and have it consist of 2 men and 3 women? c. it the 5 committee members are randomly selected, what is the probability that the committee will consist of 2 men and 3 women ```
 Numeric_Fractions/668990: Could you please explain the difference between 2 3/4 and 2 (3/4)?1 solutions Answer 416002 by ewatrrr(10682)   on 2012-10-19 14:44:07 (Show Source): You can put this solution on YOUR website! ``` Hi, 2 3/4 this is a mixed fraction, 11/4 as an improper fraction 2(3/4) the parenthesis indicates multiplication ```
 expressions/668999: Simplify the expression. (3 + i) - (2 - 2i) A. 1 + 3i B. 5 - i C. 4i D. -1 - 3i 1 solutions Answer 415999 by ewatrrr(10682)   on 2012-10-19 14:40:21 (Show Source): You can put this solution on YOUR website! ``` Hi, (3 + i) - (2 - 2i) = 3-2 + i + 2i = 1 + 3i ```
 Travel_Word_Problems/668974: if your traveling 6 mph how long will it take you to go 197 feet?1 solutions Answer 415994 by ewatrrr(10682)   on 2012-10-19 14:29:23 (Show Source): You can put this solution on YOUR website! ``` Hi, if your traveling 6 mph how long will it take you to go 197 feet? ||| Cross Multiplying to solve x = 197/31680 = .006 hr ```
 Equations/668991: Use the Quadratic Formula to solve the equation. -2x2 - 5x + 5 = 0 A) -5/2 [+ or -] √65/2 B) -4/5 [+ or -] √130/4 C) -5/4 [+ or -] √32/2 D) -5/4 [+ or -] √65/41 solutions Answer 415991 by ewatrrr(10682)   on 2012-10-19 14:23:31 (Show Source): You can put this solution on YOUR website! ``` Hi, -2x2 - 5x + 5 = 0 ||Standard form: ax^2 + bx + c = 0 ```
 Linear-equations/668931: can you create your own quadratic equation and show how it would be solved by graphing, factoring, the quadratic formula, and by completing the square. 1 solutions Answer 415990 by ewatrrr(10682)   on 2012-10-19 14:19:01 (Show Source): You can put this solution on YOUR website! ``` Hi, This was an example today y = x^2 +2x - 8 ||factoring (x+4)(x-2) = 0 , x = -4 0r x = 2 are the solutions , x = -1 ± 3 y = x^2 +2x +1 - 1 - 8 Completing the Square y = (x+1)^2 - 9 V(-1,-9) and line of symmetry is x = -1 and when y = 0 ⇒ (x+1)^2 = 9, x = -1 ± 3, Pt(2,0) & (-4,0) are the x-intercepts ```
 Graphs/668960: Solve by graphing. x2 +2x - 8 = 01 solutions Answer 415986 by ewatrrr(10682)   on 2012-10-19 14:09:28 (Show Source): You can put this solution on YOUR website! ``` Hi, Previously Posted y = x^2 +2x - 8 y = x^2 +2x +1 - 1 - 8 y = (x+1)^2 - 9 V(-1,-9) and line of symmetry is x = -1 and when y = 0 ⇒ (x+1)^2 = 9, x = -1 ± 3, Pt(2,0) & (-4,0) are the x-intercepts ```
 Geometry_proofs/668985: In a geometric proof, how do you know what statement to say next, after you state the given? I kind of understand proofs when the teacher gives me each statement, but when i am by myself i am blank!1 solutions Answer 415985 by ewatrrr(10682)   on 2012-10-19 14:07:44 (Show Source): You can put this solution on YOUR website! ``` Hi, In a geometric proof, statements following the given are a means to the end Ask yourself, starting with the givens, how do I reach the final conclusion.. (final conclusion being... what is being 'proved' to be true) What steps must be taken (what statements used...) ```
 Numbers_Word_Problems/668984: what are four consecutive even whole numbers whose sum is less than 35. 1 solutions Answer 415984 by ewatrrr(10682)   on 2012-10-19 14:01:48 (Show Source): You can put this solution on YOUR website! ``` Hi, what are four consecutive even whole numbers whose sum is less than 35. x + (x+2) + (x+4) + (x+6) < 35 4x < 23 x < 5.75 4, 6, 8, 10 and.. 4 + 6 + 8 + 10 = 28 < 35 ```
 Equations/668986: Solve this by graphing: x2 +2x - 8 = 0 I had tried to graph this for several hours, but I still can't figure it out. Please help !1 solutions Answer 415983 by ewatrrr(10682)   on 2012-10-19 13:56:40 (Show Source): You can put this solution on YOUR website! ``` Hi, Previously Posted y = x^2 +2x - 8 y = x^2 +2x +1 - 1 - 8 y = (x+1)^2 - 9 V(-1,-9) and line of symmetry is x = -1 and when y = 0 ⇒ (x+1)^2 = 9, x = -1 ± 3, Pt(2,0) & (-4,0) are the x-intercepts ```
 Graphs/668975: Solve this by graphing: x^2 +2x - 8 = 0 I had tried to graph this for several hours, but I still can't figure it out.1 solutions Answer 415981 by ewatrrr(10682)   on 2012-10-19 13:55:34 (Show Source): You can put this solution on YOUR website! ``` Hi, y = x^2 +2x - 8 y = x^2 +2x +1 - 1 - 8 y = (x+1)^2 - 9 V(-1,-9) and line of symmetry is x = -1 and when y = 0 ⇒ (x+1)^2 = 9, x = -1 ± 3, Pt(2,0) & (-4,0) are the x-intercepts ```
 Word_Problems_With_Coins/668972: An example of my practice word problem for Algebra - I have worked it out and can not get the answer. Susan has been saving money in a vacation fund. She has a jar filled with quarters and dollar coins. So far, she has saved \$76.50. The number of quarters is 5 more than 3 times the amount of dollar coins she has saved. How many of each coin does she have? D = Dollar Q = 3D + 5 3d + d + 5 = 76.50 4d + 5 = 76.50 4d = 76.50 - 5 4d = 71.50/4 d = 17.875 AGH I can not get the answer- plase help! Thank you!!1 solutions Answer 415976 by ewatrrr(10682)   on 2012-10-19 13:15:46 (Show Source): You can put this solution on YOUR website! ``` Hi, Number of Dollars: D Number of quarters: 3D + 5 CENTS makes sense 100D + 25(3D + 5) = 7650¢ 175D = 7650 - 125 175D = 7525 D = 43, the number of dollar coins. There are 134 quarters. and.. ```
 logarithm/668961: A standard measurement of the speed at which a radioactive substance decays is its half life. The half life of a radioactive substance is the time that it takes for one-half of the substance to decaay. The equation which describes radioactive decay is given below. If the half life of radioactive substance is 10,000 years, then at what rate is it decaying? A = Aoe^rt where: A = amount remaining after "t" years; Ao = initial amount present; R = annual rate of decay. Any help would be appreciated - I don't know where to start. 1 solutions Answer 415975 by ewatrrr(10682)   on 2012-10-19 13:06:07 (Show Source): You can put this solution on YOUR website! ``` Hi, half life of radioactive substance is 10,000 years ln(.5)/10,000 = r = -.000069 , the rate of decay ```
 Expressions-with-variables/668962: Can anyone help me simplify this expression? I am unsure of the proper steps. Thank you! 2j+6 ----------- j^2 - 6 - 271 solutions Answer 415973 by ewatrrr(10682)   on 2012-10-19 12:57:28 (Show Source): You can put this solution on YOUR website! ``` Hi, factoring the numerator and denominator... ```
 Angles/668968: two angles are complementary. one of the angles is 8 degrees more than half the other. find the two angles1 solutions Answer 415972 by ewatrrr(10682)   on 2012-10-19 12:53:33 (Show Source): You can put this solution on YOUR website! ``` Hi, two angles and are complementary. one of the angles is 8 degrees more than half the other. Translate into an equation: |||Multiplying thru by 2 so as all denominators = 1 2x = (90°-x) + 16 3x = 106 x = 35 1/3° and it complement is 54 2/3 ° and... ```
 Money_Word_Problems/668966: A store decreased its price on a computer by \$112 to \$478. What was the original price?1 solutions Answer 415971 by ewatrrr(10682)   on 2012-10-19 12:46:23 (Show Source): You can put this solution on YOUR website! ``` Hi, A store decreased its price on a computer by \$112 to \$478. What was the original price? \$478 + \$112 = \$590 ```
 Probability-and-statistics/668965: There are three boxes. Two of the boxes have something special in them, while the third one is empty. You are to select two boxes out of three(you don't know which one is empty). You win if you select the two boxes which have something special in them, and lose otherwise. How do you maximize the probability of winning, and what is that probability.1 solutions Answer 415969 by ewatrrr(10682)   on 2012-10-19 12:42:20 (Show Source): You can put this solution on YOUR website! ``` Hi, Two of the boxes have something special in them, while the third one is empty. select two boxes ... P(selecting boxes/prizes) = How do you maximize the probability of winning...leave that up to you :) ```
 Travel_Word_Problems/668964: a vehicle traveling at the posted speed of 25 mph will take no less than 20 seconds to move from point a to point b, Where are points a and b?1 solutions Answer 415968 by ewatrrr(10682)   on 2012-10-19 12:38:00 (Show Source): You can put this solution on YOUR website! ``` Hi, a vehicle traveling at the posted speed of 25 mph 0r will take no less than 20 seconds to move from point a to point b, = .14mi a nd b are .14mi apart. (rounded to the nearest tenth) ```
 Rational-functions/668949: Annual profit in thousands of dollars is given by the function, P(x) = -.1x2 + 50x - 300, where x is the number of items sold, x ≥ 0. I am suppose to explain -300? I believe it has to do with the final costs, is this correct?1 solutions Answer 415966 by ewatrrr(10682)   on 2012-10-19 12:29:25 (Show Source): You can put this solution on YOUR website! ``` Hi, Annual profit in thousands of dollars is given by the function, P(x) = -.1x2 + 50x - 300, where x is the number of items sold, x ≥ 0. the -300 would be the adjustments to the annual profits due to 'fixed cost' that is to say if NO items were sold..there would be a loss of \$300,000 and...solving -1x^2 + 50x - 300 = 0 would tell us how many need to be sold to break even. ```
 Graphs/668945: http://postimage.org/image/cyx9jb9vd/ I can't find a way to put the graph on here to the website. I had put the problem on the image website.1 solutions Answer 415961 by ewatrrr(10682)   on 2012-10-19 12:14:41 (Show Source): You can put this solution on YOUR website! ``` Hi, -3y ≥ 6x - 3 y ≤ -3x + 1 1st graph y = -3x + 1 (0,1) and (1,-2) on this line, plot pts, connect with a line 2nd Shaded area 'BELOW' (and including the line) is the graph of y ≤ -3x + 1 will let you do that shading ```
 Graphs/668946: http://postimage.org/image/gnmyisjw9/ I can't find a way to put the graph on here to the website. I had put the problem on the image website.1 solutions Answer 415958 by ewatrrr(10682)   on 2012-10-19 12:07:09 (Show Source): You can put this solution on YOUR website! ``` Hi, y = 2|x| (0,0), (1,2) and (-1,2) on this graph ```
 Linear_Equations_And_Systems_Word_Problems/668876: a plane made a trip of 2280 miles in 4 hours flying with a tail wind. The return trip took 4 hours and 45 minutes flying with the same head wind. Find the wind speed and speed of the plane in still air1 solutions Answer 415926 by ewatrrr(10682)   on 2012-10-19 08:50:55 (Show Source): You can put this solution on YOUR website! ``` Hi, s + w = 2280mi/4hr = 570mph s - w = 2280mi/4.75hr = 480mph 2s = 1050mph s = 525mph, speed of the plane in still air. w = 45mph ```
 test/668889: 2 5/2 - 2 3/21 solutions Answer 415922 by ewatrrr(10682)   on 2012-10-19 08:39:08 (Show Source): You can put this solution on YOUR website! ``` Hi, ```
 Equations/668887: What is the equation of the given line in standard form? Use integer coefficients. y=5/7x-12 A) -5x+7y=-12 B) -5x-7y=-84 C) -5x+7y=-84 D) 5x+7y=-841 solutions Answer 415921 by ewatrrr(10682)   on 2012-10-19 08:37:29 (Show Source): You can put this solution on YOUR website! ``` Hi, Line: y=5/7x-12 |||Multiplying thru by 7 so as all denominators = 1 7y = 5x - 84 5x - 7y = 84 ||The Line in standard form ```