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# Recent problems solved by 'fractalier'

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 Equations/44242: 1 over 2x-7 + 3 over 7-2x show work isn't the bottom denominators the same?1 solutions Answer 29275 by fractalier(2101)   on 2006-06-29 16:26:27 (Show Source): You can put this solution on YOUR website!No they are not, but close, because 2x-7 / 7-2x = -1 I posted this solution about an hour ago...
 Trigonometry-basics/44196: Find the exact value of cot(-π/6). Thanks1 solutions Answer 29274 by fractalier(2101)   on 2006-06-29 16:25:13 (Show Source): You can put this solution on YOUR website!cot(-pi/6) = cos(-pi/6) / sin(-pi/6) = sqrt(3)/2 / (-1/2) = -sqrt(3)
 Quadratic_Equations/44343: Carlos scored 15 more points than John in the basketball game. If the product of the two point totals is 154, how many points did each boy score?1 solutions Answer 29273 by fractalier(2101)   on 2006-06-29 16:23:07 (Show Source): You can put this solution on YOUR website!Let their totals be C and J. Then C = J + 15 and CJ = 154 Now substituting we get J(J + 15) = 154 J^2 + 15J = 154 J^2 + 15J - 154 = 0 (J + 22)(J - 7) = 0 J = -22 or J = 7 but since you can't score negative points, J = 7 and C = 22
 Trigonometry-basics/44341: What are the possible answers? sin(x) - sin(3x) = 01 solutions Answer 29272 by fractalier(2101)   on 2006-06-29 16:20:28 (Show Source): You can put this solution on YOUR website!This will take a while...please follow along...from sin x - sin 3x = 0 we get sin x - sin (x + 2x) = 0 sin x - (sin x cos 2x - sin 2x cos x) = 0 sin x - (sin x * (cos^2 x - sin^2 x) - 2 sin x cos * cos x) = 0 sin x - (sin x * (cos^2 x - sin^2 x) - 2 sin x cos^2 x) = 0 how factor out sin x sin x(1 - cos^2 x + sin^2 + 2 cos^2 x) = 0 sin x(1 + cos^2 x + sin^2) = 0 2 sin x = 0 sin x = 0 x = 0, pi
 Probability-and-statistics/44279: An African hospital is treating patients who have Lhassa Fever. Seventy percent of patients with this disease die, and each patient lives or dies independently of other patients. Suppose over along period, the hosptial expects to treat 100 patients. What is the mean number of deaths expected during this period? My answer is 100 x .70 = 70 patients. The 2nd part of that is suppose over a long period, the hospital expects to treat 100 patients. What is the standard deviation of the number of deaths expected during this period? (I am not sure how to begin finding this answer)1 solutions Answer 29269 by fractalier(2101)   on 2006-06-29 16:03:33 (Show Source): You can put this solution on YOUR website!Your expected mean of 70 is correct. I believe that sigma is found by sigma = sqrt(np(1-p)) but it has been a while since I did this kind of stat problem, but if this is a binomial setting, then this is correct...and if so sigma = sqrt(100*.7*.3) sigma = sqrt(21) or about 4.58
 Equations/44319: This question is from textbook INTERMEDIATE ALGEBRA Write each equation in quadratic form and solve it by factoring. x(3x + 22/5)= 11 solutions Answer 29268 by fractalier(2101)   on 2006-06-29 15:57:14 (Show Source): You can put this solution on YOUR website!From x(3x + 22/5)= 1, we get 3x^2 + (22/5)x = 1 now multiply five and bring everything to the left...then factor... 15x^2 + 22x = 5 15x^2 + 22x - 5 = 0 (5x - 1)(3x + 5) = 0 so that 5x - 1 = 0 and 3x + 5 = 0 which leads to x = 1/5 and x = -5/3
 Equations/44328: 1 over 2x-7 + 3 over 7-2x1 solutions Answer 29258 by fractalier(2101)   on 2006-06-29 15:01:09 (Show Source): You can put this solution on YOUR website!The key to doing this one is to realize that 2x-7 / 7-2x = -1 A surprising result but true...so that 1 / 2x-7 + 3 / 7-2x = 1 / 2x-7 - 3 / 2x-7 = -2 / 2x-7 or 2 / 7-2x
 Graphs/44220: use substitution to find the solution of each system y=2x y=-x+12 also y=x-2 y=-x+61 solutions Answer 29256 by fractalier(2101)   on 2006-06-29 14:20:03 (Show Source): You can put this solution on YOUR website!For y=2x y=-x+12 we have 2x = -x+12 3x = 12 x = 4 and then y = 8 For y=x-2 y=-x+6 we have x-2 = -x+6 2x = 8 x = 4 and then y = 2
 Linear-equations/44193: This question is from textbook INTERMEDIATE ALGEBRA Solve by factoring: x2 – 5x = 61 solutions Answer 29255 by fractalier(2101)   on 2006-06-29 14:17:14 (Show Source): You can put this solution on YOUR website!Okay from x^2 – 5x = 6 we get x^2 - 5x - 6 = 0 (x - 6)(x + 1) = 0 x = 6 and x = -1
 Equations/44231: a^2-8a over (a+2)(a-8) please help set this up show work1 solutions Answer 29254 by fractalier(2101)   on 2006-06-29 14:15:37 (Show Source): You can put this solution on YOUR website!Okay, we factor and cancel...we get a^2-8a / (a+2)(a-8) = a(a-8) / (a+2)(a-8) = a / a+2
 Equations/44331: 1 + 1 over x = 72 over x^21 solutions Answer 29253 by fractalier(2101)   on 2006-06-29 14:13:23 (Show Source): You can put this solution on YOUR website!1 + (1/x) = 72/x^2 multiply all terms by x^2 and get x^2 + x = 72 x^2 + x - 72 = 0 (x+9)(x-8) = 0 x = -9 and x = 8
 Radicals/44333: Reduce each expression to the lowest terms. Show steps and solution. This is written in fraction form: 4x^2/2x^91 solutions Answer 29252 by fractalier(2101)   on 2006-06-29 14:11:39 (Show Source): You can put this solution on YOUR website!4x^2 / 2x^9 becomes 2x^2 / x^9 = 2 / x^7
 Expressions-with-variables/44336: 3+(6*2)1 solutions Answer 29251 by fractalier(2101)   on 2006-06-29 14:09:32 (Show Source): You can put this solution on YOUR website!Order of operations states that we multiply before adding, so we get 3 + (6*2) = 3 + 12 = 15
 Equations/44335: find the least common denominator of 8a+32, a^2+4a1 solutions Answer 29250 by fractalier(2101)   on 2006-06-29 14:08:35 (Show Source): You can put this solution on YOUR website!Since 8a+32 = 8(a + 4) and a^2+4a = a(a + 4), the LCD is 8a(a + 4).
 Complex_Numbers/44334: solve log(2x+3) = log(4x)+ 2, for x giving your answer correct to 3 significant figures1 solutions Answer 29249 by fractalier(2101)   on 2006-06-29 14:04:26 (Show Source): You can put this solution on YOUR website!Provided the problem is correctly stated we have log(2x+3) = log(4x) + 2 log(2x+3) - log(4x) = 2 log [(2x+3) / 4x] = 2 so that when we exponentiate we get (2x+3) / 4x = 10^2 = 100 2x + 3 = 400x 3 = 398x x = 3/398 or about .00754
 Polynomials-and-rational-expressions/44332: Factor each Trinomial using the “ac” method. Showing work and solution. 15x² - 7x – 21 solutions Answer 29248 by fractalier(2101)   on 2006-06-29 13:59:51 (Show Source): You can put this solution on YOUR website!From 15x² - 7x – 2, we factor by looking at the product of a times c, here that is 15 times 2...or 30...then we ask, what are the factors of 30 that have a difference of 7...that would be 10 and 3 and than adjust our binomial factors to reflect such products...so we get 15x² - 7x – 2 = (5x + 1)(3x - 1)
 Polynomials-and-rational-expressions/44329: Factor each polynomial - show work and solution: 9a² - 64b²1 solutions Answer 29247 by fractalier(2101)   on 2006-06-29 13:56:15 (Show Source): You can put this solution on YOUR website!Here we have the difference of squares, so it factors out like this... 9a² - 64b² = (3a + 8b)(3a - 8b)
 Equations/44327: k^2+10k+24 over k^2+11k+30 * k^2+5k over k^2-2k-24 help1 solutions Answer 29246 by fractalier(2101)   on 2006-06-29 13:53:24 (Show Source): You can put this solution on YOUR website!We always factor and cancel in problems like these...so we get k^2+10k+24 / k^2+11k+30 * k^2+5k / k^2-2k-24 = (k+6)(k+4) / (k+6)(k+5) * k(k+5) / (k-6)(k+4) = Now the k+6, k+5, and k+4's cancel, leaving k / k-6
 Polynomials-and-rational-expressions/44313: I need your help in finding the solutions to x^2-sqrt(5)x+ 5/4=0. What I have so far inside the square root is -5-(4)(1)(5/4).1 solutions Answer 29245 by fractalier(2101)   on 2006-06-29 13:50:54 (Show Source): You can put this solution on YOUR website!For x^2 - sqrt(5)x + 5/4 = 0, we have x = (sqrt(5) ± sqrt(5 - 5)) / 2 x = sqrt(5) / 2 a double root...
 Polynomials-and-rational-expressions/44314: I need help in finding the solutions to x^2+2(pie)=0.1 solutions Answer 29244 by fractalier(2101)   on 2006-06-29 13:46:33 (Show Source): You can put this solution on YOUR website!Okay, subtract the 2(pi) first and get x^2 + 2(pi) = 0 x^2 = -2(pi) now take the root and get imaginary solutions x = ± sqrt(-2(pi)) x = ± i*sqrt(2(pi))
 Polynomials-and-rational-expressions/44316: Hi, I have the solutions to a problem but I don't know if they are correct. The problem is x^3-x=0. The solutions I got are x=-3/2 and-1/2. If they are not correct, can you show me how to do them? Thanks. 1 solutions Answer 29243 by fractalier(2101)   on 2006-06-29 13:43:56 (Show Source): You can put this solution on YOUR website!Okay, from x^3 - x = 0 we factor out x first and then factor what is left... x(x^2 - 1) = 0 x(x + 1)(x - 1) = 0 so that x = 0, x = 1, and x = -1
 Expressions-with-variables/44317: will you please help me with this: what is (12a+6/5a^2)(6/a+1)(5a+5/2a+1)1 solutions Answer 29242 by fractalier(2101)   on 2006-06-29 13:42:08 (Show Source): You can put this solution on YOUR website!In this type of problem, we FACTOR and CANCEL, so we get (12a+6/5a^2)*(6/a+1)*(5a+5/2a+1) = 6(2a+1)/5a^2)*(6/a+1)*(5(a+1)/2a+1) = Now the 2a+1 cancels, as do the a+1...that leaves 6/5a^2 * 6 * 5 = now 5's cancel...leaving 36/a^2
 Inequalities/44321: This question is from textbook Intermediate Algebra Use the quadratic formula to solve each equation. x^2 + 3x + 2 = 01 solutions Answer 29241 by fractalier(2101)   on 2006-06-29 13:38:22 (Show Source): You can put this solution on YOUR website!From x^2 + 3x + 2 = 0, we have x = (-3 ± sqrt(9 - 8)) / 2 x = (-3 ± sqrt(1)) / 2 x = (-3 ± 1) / 2 x = -2 or x = -1
 Triangles/44324: Find an expression that represents the perimeter of the triangle. Thank You!!!1 solutions Answer 29240 by fractalier(2101)   on 2006-06-29 13:36:26 (Show Source): You can put this solution on YOUR website!Perimeter means you add the sides together and get 3/4x + 1/x^2 + 5/x^2 = 3x/4x^2 + 4/4x^2 + 20/4x^2 = (3x+24) / 4x^2 or 3(x+8) / 4x^2
 Linear-equations/44194: This question is from textbook INTERMEDIATE ALGEBRA Solve using the square root property: 2x2 = 401 solutions Answer 29237 by fractalier(2101)   on 2006-06-29 12:29:29 (Show Source): You can put this solution on YOUR website!From 2x^2 = 40 divide both sides by two first and get x^2 = 20 now take the square root and get x = ± sqrt(20) x = ± 2*sqrt(5)
 Systems-of-equations/44228: find the solutions of each system 3x+2y=5 4x+3y=51 solutions Answer 29236 by fractalier(2101)   on 2006-06-29 12:25:24 (Show Source): You can put this solution on YOUR website!Let us multiply the top one by 4 and the bottom one by 3 and subtract them...we get 3x + 2y = 5 4x + 3y = 5 which becomes 12x + 8y = 20 -(12x + 9y = 15) and thus -y = 5 and y = -5 so that when we substitute this into the first equation we get 3x + 2(-5) = 5 3x - 10 = 5 3x = 15 x = 5 Our solution is (5, -5)
 Radicals/44246: Find the time required for an ojbect to fall to ground from the building is 1400 Ft high. t=1/4 square root is s.1 solutions Answer 29235 by fractalier(2101)   on 2006-06-29 12:20:48 (Show Source): You can put this solution on YOUR website!What I think you mean is t = (1/4) * sqrt(s) where t is time and s is the distance....thus if we plug in 1400 feet for s we get t = (1/4) * sqrt(1400) t = 9.35 seconds
 Quadratic_Equations/44286: Find the roots of the equadratic equations by the method of completing the square. Express the roots, if they are not rational, in simplest radical form. 3x2 - 2x - 5 = 01 solutions Answer 29234 by fractalier(2101)   on 2006-06-29 12:15:37 (Show Source): You can put this solution on YOUR website!From 3x^2 - 2x - 5 = 0 divide by 3 first and get x^2 - (2/3)x - 5/3 = 0 Now half of 2/3 squared is 1/9, so x^2 - (2/3)x + 1/9 - 5/3 = 0 + 1/9 x^2 - (2/3)x + 1/9 = 5/3 + 1/9 = 15/9 + 1/9 (x - (1/3))^2 = 16/9 Now take the square root of both sides x - (1/3) = ± 4/3 x = 1/3 ± 4/3 so that x = 5/3 or -1
 Expressions-with-variables/44297: if x=-1 and y=2,what is the value of the expression 2x^3-3xy?1 solutions Answer 29227 by fractalier(2101)   on 2006-06-29 11:35:55 (Show Source): You can put this solution on YOUR website!To evaluate this, we merely plug in the values into 2x^3 - 3xy and get 2(-1)^3 - 3(-1)(2) = -2 + 6 = 4
 Graphs/44200: Find the slope and the y-intercept of the line. 6x - 9y = -18 1 solutions Answer 29218 by fractalier(2101)   on 2006-06-29 11:05:37 (Show Source): You can put this solution on YOUR website!If we solve 6x - 9y = -18 for y, it will be in slope-intercept form, y = mx + b, so we have 6x - 9y = -18 -9y = -6x - 18 y = (2/3)x + 2 so that the slope is 2/3 and the y-intercept is 2
 Equations/44229: rational expressions y^2+4y-21 over y^2+13+42 show work1 solutions Answer 29217 by fractalier(2101)   on 2006-06-29 11:00:37 (Show Source): You can put this solution on YOUR website!Here the technique is always FACTOR and CANCEL, so we have y^2+4y-21 / y^2+13+42 = (y+7)(y-3) / (y+7)(y+6) = (y-3) / (y+6)