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# Recent problems solved by 'fractalier'

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 real-numbers/44160: solve. approximate irrational roots to the nearest tenth. Together Anna and Carla can spray- paint a van in 8 hours. Alone it takes Anna 2 hours less than Carla. Find the time it takes each of them to paint the van alone. Give your answers to the nearest tenth of an hour. (units optional)1 solutions Answer 29097 by fractalier(2101)   on 2006-06-28 15:44:33 (Show Source): You can put this solution on YOUR website!Let Carla's individual time be c. So Anna's time is c-2. We set this one up like this t/A + t/B = 1 8/c + 8/(c-2) = 1 now multiply by the LCD, c(c-2), and get 8(c-2) + 8c = c(c-2) 8c - 16 + 8c = c^2 - 2c now collect like terms and solve... c^2 - 18c + 16 = 0 This cannot be factored so let's try completing the square... c^2 - 18c + 81 + 16 = 81 c^2 - 18c + 81 = 65 (c - 9)^2 = 65 c - 9 = ± √65 c = 9 ± √65 The negative root does not work since that would make Anna's time negative so Carla's time is c = 9 + √65 or about 17.1 hours Anna can do it in c-2 or about 15.1 hours
 Polynomials-and-rational-expressions/44139: Write each expression in simplest form 4r2 - 25s2 / 2r2 + 3rs - 20s2 Thank you!!!1 solutions Answer 29094 by fractalier(2101)   on 2006-06-28 15:36:42 (Show Source): You can put this solution on YOUR website!The key technique in rational expressions is to FACTOR and CANCEL...that's what we do here...so from 4r^2 - 25s^2 / 2r^2 + 3rs - 20s^2 = (2r+5s)(2r-5s) / (2r-5s)(r+4s) = (2r+5s) / (r+4s)
 real-numbers/44157: solve. approximate irrational roots to the nearest tenth. The difference of the square of a number and the number is 12. find the number.1 solutions Answer 29093 by fractalier(2101)   on 2006-06-28 15:33:51 (Show Source): You can put this solution on YOUR website!Let the number be x...then we have x^2 - x = 12 x^2 - x - 12 = 0 (x - 4)(x + 3) = 0 x = 4 or x = -3
 real-numbers/44150: solve by any method you prefer. u^2 - 15u = -11 solutions Answer 29092 by fractalier(2101)   on 2006-06-28 15:32:38 (Show Source): You can put this solution on YOUR website!Let's use the quadratic this time...so from u^2 - 15u = -1 u^2 - 15u + 1 = 0 u = (15 ± sqrt(225 - 4)) / 2 u = (15 ± √221) / 2
 real-numbers/44152: solve by any method you prefer. x^2 + 8x + 1 = 01 solutions Answer 29091 by fractalier(2101)   on 2006-06-28 15:30:43 (Show Source): You can put this solution on YOUR website!Let complete the square on this one...thus from x^2 + 8x + 1 = 0 we add 15 to both sides x^2 + 8x + 16 = 15 (x + 4)^2 = 15 x + 4 = ± √15 x = -4 ± √15
 real-numbers/44151: solve by any method you prefer. 3w^2 - 16 = 01 solutions Answer 29089 by fractalier(2101)   on 2006-06-28 15:28:42 (Show Source): You can put this solution on YOUR website!From 3w^2 - 16 = 0 add 16, divide by three and take the root and get 3w^2 = 16 w^2 = 16/3 w = ± sqrt(16/3) now rationalize w = ± 4√3 / 3
 Numeric_Fractions/44137: Benny is traveling at a speed of 60 mi./h. What is his speed in feet per second.1 solutions Answer 29075 by fractalier(2101)   on 2006-06-28 12:51:47 (Show Source): You can put this solution on YOUR website!The direct conversion is 60 mi/hr = 88 ft/sec but you would find that by multiplying 60 mi/hr by 5280 ft / 1 mi and then 1 hr / 3600 sec...
 Expressions-with-variables/44135: can someone please help me with i have tried it but i dont seem to be able to come up with an answer. thanks! solve the equation and check your solutions: sqaure root of 4x^2+5 = 3x1 solutions Answer 29071 by fractalier(2101)   on 2006-06-28 12:37:13 (Show Source): You can put this solution on YOUR website!√(4x^2 + 5) = 3x we square both sides to begin and get 4x^2 + 5 = 9x^2 5 = 5x^2 x^2 = 1 x = ±1 Now check... only positive one checks out...
 Polynomials-and-rational-expressions/43813: This question is from textbook Algebra and trigonometry with analytic geometry The polynomial f(x)divided x-3 results in a quotient of x^2+3x-5 with a remainder of 2. Find f(3). my answer is -2, could that be right. thanks again.1 solutions Answer 29064 by fractalier(2101)   on 2006-06-28 12:13:32 (Show Source): You can put this solution on YOUR website!To find the original f(x) we need to multiply (x^2 + 3x - 5) by (x - 3) and then adding 2...we get f(x) = x^3 - 14x + 15 + 2 f(x) = x^3 - 14x + 17 so that f(3) = 3^3 - 14(3) + 17 f(3) = 27 - 42 + 17 f(3) = 2 Close, but I get positive 2, not -2.
 Polynomials-and-rational-expressions/44109: simplify the following expression. write your answers with positive exponents only. (x^2)^-3(x^-2)/(x^2)^-41 solutions Answer 29063 by fractalier(2101)   on 2006-06-28 12:08:52 (Show Source): You can put this solution on YOUR website!Assuming the problem is correct as written, we get [(x^2)^-3 * (x^-2)] / (x^2)^-4 = [(x^-6)(x^-2)] / x^-8 = x^-8 / x^-8 = 1
 Divisibility_and_Prime_Numbers/44113: How would I determine the maximum and minimum values of the following set of numbers: 3, -36/7, -1, -2/3, 5/4, 26/91 solutions Answer 29062 by fractalier(2101)   on 2006-06-28 12:05:43 (Show Source): You can put this solution on YOUR website!We can express these as decimals (approximately)...that's one way...so we get 3, -36/7, -1, -2/3, 5/4, 26/9 becoming 3, -5.143, -1, -.667, 1.25, 2.889 From this list you can see which is the greatest negative, that is, the minimum value ==> -36/7 and then the maximum value ==> 26/9
 Money_Word_Problems/44108: Can someone explain this to me? The cost in dollars of manufacturing (w) wing nuts is given by the expression 0.07w + 13.3. Find the cost when 375 wing nuts are made. What is the average cost to manufacture one wing nut?1 solutions Answer 29061 by fractalier(2101)   on 2006-06-28 12:03:10 (Show Source): You can put this solution on YOUR website!Posted this one a few days ago, here goes again... Let us call the cost function c(w) = .07w + 13.3 Now if the number of wing nuts, w, is 375, we substitute that in for w and get c(375) = .07(375) + 13.3 c(375) = 26.25 + 13.3 c(375) = \$39.55 To find the average cost, we divide that total cost by 375 wing nuts and get \$39.55 / 375 = \$.1055 or 10.55 cents each
 real-numbers/44127: Give an example of a number that is a real number, but not a rational number.1 solutions Answer 29060 by fractalier(2101)   on 2006-06-28 11:59:29 (Show Source): You can put this solution on YOUR website!√2 or square root of two is an example. It cannot be expressed as a fraction of two integers and so is not rational.
 real-numbers/44128: Give an example of a number that is a rational number, but not an integer.1 solutions Answer 29059 by fractalier(2101)   on 2006-06-28 11:58:27 (Show Source): You can put this solution on YOUR website!3/5 is an example.
 Polynomials-and-rational-expressions/44107: I am so confused with these problems.... What expression raised to the fouth power is 81x (12 to the power)y (8 to the power) z (16 to the power). All number except the 81 are exponents.1 solutions Answer 29058 by fractalier(2101)   on 2006-06-28 11:57:54 (Show Source): You can put this solution on YOUR website!Let us write it this way...looking for n such that n^4 = 81(x^12)(y^8)(z^16) well we need to raise both sides to the 1/4 power, so that n = ±3(x^3)(y^2)(z^4)
 Polynomials-and-rational-expressions/44110: perform the indicated calculation. write your result in scientific notation. (6*10^12)(3.2*10^8)/(1.6*10^7(3*10^2)1 solutions Answer 29057 by fractalier(2101)   on 2006-06-28 11:55:10 (Show Source): You can put this solution on YOUR website!Okay from (6*10^12)(3.2*10^8) / (1.6*10^7)(3*10^2) 19.2 x 10^20 / 4.8 x 10^9 = 4 x 10^11
 Divisibility_and_Prime_Numbers/44112: How do I write 116 2/3% as a fraction or mixed number.1 solutions Answer 29055 by fractalier(2101)   on 2006-06-28 11:53:35 (Show Source): You can put this solution on YOUR website!Posted this solution about an hour ago...7/6
 Linear-equations/44117: 4 - (2x-9) = -191 solutions Answer 29054 by fractalier(2101)   on 2006-06-28 11:52:38 (Show Source): You can put this solution on YOUR website!Let us distribute the negative sign, collect terms and solve...we get 4 - (2x-9) = -19 4 - 2x + 9 = -19 -2x + 13 = -19 -2x = -32 x = 16
 Polynomials-and-rational-expressions/44120: add using the vertical method 5x^2+2x-4 x^2-2x-3 and 2x^2-4x-31 solutions Answer 29053 by fractalier(2101)   on 2006-06-28 11:50:56 (Show Source): You can put this solution on YOUR website!5x^2 + 2x - 4 + x^2 - 2x - 3 + 2x^2 - 4x - 3 _____________ 8x^2 - 4x - 10
 Numeric_Fractions/44122: How do you find the remainder from division for the numerator when converting improper fractions into proper fractions?1 solutions Answer 29052 by fractalier(2101)   on 2006-06-28 11:49:37 (Show Source): You can put this solution on YOUR website!Let me show you by example... Let's say we wish to convert 35/8 to a mixed number... So we divide 8 into 35 and get 4 with a remainder of 3... We then state our answer as 4 3/8 Notice that the divisor (8) remains the denominator and our remainder from the division becomes our numerator...
 Polynomials-and-rational-expressions/44121: Subract usin gthe vertical method 7x^2+6x from 9x^2-31 solutions Answer 29048 by fractalier(2101)   on 2006-06-28 11:36:16 (Show Source): You can put this solution on YOUR website!Okay, vertically 9x^2 - 3 -(7x^2 + 6x) _____________ 2x^2 - 6x - 3
 Polynomials-and-rational-expressions/44065: I am not sure of this problem, can someone help me with this one? Use the five properties of exponents to simplify each of the following expressions. (y5)3(y3)2 _____________________ (y4)4 (all the numbers are suppose to be exponents) 1 solutions Answer 29042 by fractalier(2101)   on 2006-06-28 10:38:38 (Show Source): You can put this solution on YOUR website![(y^5)^3 * (y^3)^2] / (y^4)^4 = [(y^15) * (y^6)] / (y^16) = (y^21) / (y^16) = y^5
 Linear-equations/38919: 4. Find values for m and b in the following system so that the solution to the system is (-3,4). 5x + 7y = b mx + y = 22 1 solutions Answer 29041 by fractalier(2101)   on 2006-06-28 10:36:42 (Show Source): You can put this solution on YOUR website!We have to plug in -3 for x and 4 for y...we get 5(-3) + 7(4) = -15 + 28 = 13 = b and then -3m + 4 = 22 -3m = 18 m = -6
 Miscellaneous_Word_Problems/44034: Columbian Earthquake of 1906 At 8.6 on the richter scale, the Colombian earthquake of January 31, 1906, was one of the strongest earthquakes on record. Use the formula log(I)-log(Io) to write I as a mulitple of Io for this earthquake.1 solutions Answer 29040 by fractalier(2101)   on 2006-06-28 10:31:53 (Show Source): You can put this solution on YOUR website!We have log(I) - log(Io) = 8.6 and then by the laws of logarithms we have log (I/Io) = 8.6 I/Io = 10^8.6 I = (Io)(10^8.6) or about 400000000 * Io
 Equations/44041: graph the inequality y is less than or equal to -41 solutions Answer 29039 by fractalier(2101)   on 2006-06-28 10:28:37 (Show Source): You can put this solution on YOUR website!Draw a solid horizontal line thru the point (0, -4) and then shade the half-plane below the line (since it is less than or equal to -4)
 logarithm/44101: Solve log a (8x+5)=log a (4x+29). Thank you for any help you can provide.1 solutions Answer 29038 by fractalier(2101)   on 2006-06-28 10:26:09 (Show Source): You can put this solution on YOUR website!Well if logarithmic expressions are equal, their arguments are too, so that if log_a (8x+5) = log_a (4x+29) then 8x + 5 = 4x + 29 4x = 24 x = 6
 logarithm/44103: Write the expression log a(y+5)+2log a (x+1) as one logarithm. Thank you for your help on this:)1 solutions Answer 29037 by fractalier(2101)   on 2006-06-28 10:23:59 (Show Source): You can put this solution on YOUR website!The log of a product equals the sum of the logs...if we apply that and the power rule, we get log_a (y+5) + 2log_a (x+1) = log_a [(y+5)(x+1)^2]
 logarithm/44102: Given that log a (x)=3.58 and log a (y)=4.79, find log a (y/x). Thank you for any help.1 solutions Answer 29036 by fractalier(2101)   on 2006-06-28 10:21:41 (Show Source): You can put this solution on YOUR website!One of the basic laws of logarithms says that the log of a quotient is equal to the difference of the logs...so that log_a (y/x) = log_a (y) - log_a (x) = 4.79 - 3.58 = 1.21
 Equations/44053: Jill has \$3.50 in nickels and dimes. If she has 50 coins, how many of each type of coin does she have?1 solutions Answer 29035 by fractalier(2101)   on 2006-06-28 10:19:44 (Show Source): You can put this solution on YOUR website!Let N be the number of nickels and D be dimes, so that N + D = 50 Their values are 5N and 10D respectively, so that 5N + 10D = 350 Now let's multiply the first equation by 5 and subtract it from the second...we get 5N + 10D = 350 -(5N + 5D = 250) so we have 5D = 100 D = 20 N = 30
 Numeric_Fractions/44085: I need some help on this problem. I need to arrange the following numbers from smallest to largest: 3.07, 37/10, 3.0712, 3.078, 371/100, 3.0717, 3.072, 3.071 Thanks!1 solutions Answer 29034 by fractalier(2101)   on 2006-06-28 10:13:57 (Show Source): You can put this solution on YOUR website!In ascending order (smallest to largest) 3.07, 37/10, 3.0712, 3.078, 371/100, 3.0717, 3.072, 3.071 becomes 3.07, 3.071, 3.0712, 3.0717, 3.072, 3.078, 37/10, 371/100
 Numeric_Fractions/44084: Can someone help me on this? I need to add the following in the lowest terms: 2/7 + 2/7 + 6/7 Thanks, Lyn1 solutions Answer 29033 by fractalier(2101)   on 2006-06-28 10:11:11 (Show Source): You can put this solution on YOUR website!Since all of these are like denominators, we can add numerators directly and get 2/7 + 2/7 + 6/7 = 10/7 = 1 3/7