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# Recent problems solved by 'drk'

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 Rational-functions/269880: Given that f(x)=3x+1, g(x)=x^2-2x-6 and h(x)=x^3, find each: (f o g)(1/3)1 solutions Answer 197714 by drk(1908)   on 2010-02-15 15:54:38 (Show Source): You can put this solution on YOUR website!First, we find g(1/3) as g(1/3) = (1/3)^2 - 2(1/3) - 6 = 1/9 - 2/3 - 6 = 5 5/9 = 50/9 second (f of g)(1/3) = 3(50/9) + 1 = 50/3 + 1 = 17 2/3
 Rational-functions/269879: Given that f(x)=x^2-3 and g(x)=2x+1, find each of the following, it it exists (fg)(2)1 solutions Answer 197713 by drk(1908)   on 2010-02-15 15:52:34 (Show Source): You can put this solution on YOUR website!First we find g(2) as g(2) = 2(2) + 1 = 5 second, f(g(2)) = f(5) = 5^2-3 = 25 - 3 = 22
 Equations/269876: The table shows the current heights and average growth rates of two different species of trees. How long will it take for the two trees to be the same height? Tree Species | Current Height | Annual Growth A 38 Inches 4 inches B 45.5 Inches 2.5 Inches Define Variables, Write an equation. I would very much appreciate everyone's help!1 solutions Answer 197712 by drk(1908)   on 2010-02-15 15:51:17 (Show Source): You can put this solution on YOUR website!The equation we need is step 1 - subtract 38 to get step 2 - subtract 2.5x to get step 3 - divide by 1.5 to get in 5 years they will be the same height
 Quadratic-relations-and-conic-sections/269877: If a right circular cone intersects a plane that passes through one of its nappes, but the plane is neither parallel to the edge of the cone nor perpendicular to the cone's axis, the resulting curve will be a(n)1 solutions Answer 197711 by drk(1908)   on 2010-02-15 15:49:11 (Show Source): You can put this solution on YOUR website!The answer is ellipse
 Probability-and-statistics/269858: An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same colour is 0.44. Calculate the number of blue balls in the second urn.1 solutions Answer 197706 by drk(1908)   on 2010-02-15 15:32:26 (Show Source): You can put this solution on YOUR website!Probability same color means 2 red or 2 blue P(red from both) = (4/10) * 16/(16+b) P(blue from both) = (6/10) * b/(16+b) --- The sum of these = .44 so we can say (i) combining like terms, we get (ii) cross multiply to get (iii) distribute to get (iv) subtract 64 and then subtract 4.4b to get (v) divide to get
 Polynomials-and-rational-expressions/269865: I need help on finding the potential rational zeros of the polynomial function f(x) = -4x^4 + 3x^2 - 4x + 61 solutions Answer 197699 by drk(1908)   on 2010-02-15 15:07:14 (Show Source): You can put this solution on YOUR website!First we apply P - N - I to help us view sign changes and possible combinations. P . . . . N . . . . I 3 . . . . 1 . . . .0 1 . . . . 1 . . . .2 So we know that there must be 1 real negative root. ----------- next we apply P / Q as P: +-1, +-2, +-3, +-6 Q: +-1, +-2, +-4 we take all possible fractions and get: P/Q = +-1, +-1/2 +-1/4, +-2, +-3, +-3/2, +-3/4, +-6 This is our list of potential rational zeros
 Exponents/269864: I need help with an exponential function using data from a table. x values are 1,3,5 y values are 48,108,243 the questions are a. What is the growth factor? b. What is the percent of growth? c. Find the formula? d. What is the initial value? I know that the growth factor is 2.25 but I don't know where to go from there. You help would be greatly appreciatied.1 solutions Answer 197698 by drk(1908)   on 2010-02-15 15:01:40 (Show Source): You can put this solution on YOUR website!x values are 1,3,5 y values are 48,108,243 the questions are a. What is the growth factor? answer: the growth factor is or r = 1.5 --- b. What is the percent of growth? answer: The percent of growth is (1.5-1) x 100% = .5 x 100% = 50% --- c. Find the formula? answer: --- d. What is the initial value? answer: initial value is 48.
 Exponents/269861: what is 4^2 +(-3)-(-5)*2+201 solutions Answer 197697 by drk(1908)   on 2010-02-15 14:56:58 (Show Source): You can put this solution on YOUR website!we start with order of operations says to apply exponents, so we get next multiplication from left to right to get last add and subtract from left to right to get
 Polynomials-and-rational-expressions/269849: why is (4x+7)(x-5)(2x-9)(x-5) not in factored form1 solutions Answer 197696 by drk(1908)   on 2010-02-15 14:54:13 (Show Source): You can put this solution on YOUR website!This is not factored because you have 2 terms that are the same. To express in factored form, we say
 Surface-area/269860: how do you solve the surface area of a cone1 solutions Answer 197695 by drk(1908)   on 2010-02-15 14:51:50 (Show Source): You can put this solution on YOUR website!The formula for surface area of a cone is where l = slant height
 Rational-functions/269853: Hi. I am having trouble with the following problem. I understand everything except for the x-intercept part. I would greatly appreciate your help, Thanks in advance. Find an equation of a rational function f that satisfies the conditions: vertical asymptotes: x = - 2, x = 0 horizontal asymptote: y = 0 x-intercept: 5; f (6) = 1 1 solutions Answer 197693 by drk(1908)   on 2010-02-15 14:50:44 (Show Source): You can put this solution on YOUR website!Find an equation of a rational function f that satisfies the conditions: vertical asymptotes: x = - 2, x = 0 we can write a general form as (i) --- horizontal asymptote: y = 0 This means as x approaches infinity, then the function approaches zero. This happens when the degree of the numerator is less than the degree of the denominator we keep our function at (ii) --- x-intercept: 5 If y = 0 , then x = 5. From (ii) we get (iii) cross multiply to get 5a+b = 0 solving for a , we get (iv) --- f (6) = 1 means that if x = 6, then y = 1. From (i) and (iv) we get (vi) cross multiplying we get (vii) multiply by common denominator of 5, we get (viii) solving for b, we get (ix) This means that and our equation is
 Mixture_Word_Problems/269837: linda's cell phone bill is bill is \$30 per month plus 5 cents for every minute over 300 minutes. last month she paid \$31 for her cell phone usage. how many minutes did she use?1 solutions Answer 197691 by drk(1908)   on 2010-02-15 14:32:08 (Show Source): You can put this solution on YOUR website!The bill is b = 31 so we get distribute to get combine like terms to get subtract 15 to get divide to get She used 320 minutes
 Mixture_Word_Problems/269838: write an example of real number that is also an irrational number. explain how you know that the number is irrational.1 solutions Answer 197687 by drk(1908)   on 2010-02-15 14:07:14 (Show Source): You can put this solution on YOUR website!The sqrt(2) is a real that is not rational. You can't express the sqrt(2) as a fraction in any way.
 Mixture_Word_Problems/269840: identify an integer that is not a whole number.explain why the integer is not a whole number.1 solutions Answer 197685 by drk(1908)   on 2010-02-15 14:06:15 (Show Source): You can put this solution on YOUR website!-5 is an integer that is not a whole number. By definition, whole numbers are positive counting numbers including the number 0.
 Travel_Word_Problems/269831: A freight train and an express train leave towns 390km apart, traveling toward one another. The freight train travels 30km per hr slower than the express train. They pass one another 3 hr later. What are their speeds? 1 solutions Answer 197684 by drk(1908)   on 2010-02-15 14:04:55 (Show Source): You can put this solution on YOUR website!This is an RTD problem. Here is a table based on the given information trains . . . . . . . . .rate . . . . . . . . .time . . . . . . . . .distance freight. . . . . . . . r - 30 . . . . . . . . .3 . . . . . . . . . . 3r - 90 express. . . . . . . .r . . . . . . . . . . . . 3 . . . . . . . . . . . 3r totals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .390 Look at the last column, we get simplify to get add 90 to get divide to get express: freight:
 Quadratic_Equations/269830: Please help me solve the equation: .1 solutions Answer 197679 by drk(1908)   on 2010-02-15 13:40:17 (Show Source): You can put this solution on YOUR website!step 1 - expand to get combine like terms to get set = 0 to get factoring we get solving for f, we get f = 1/3 or f = -4/3
 Quadratic_Equations/269829: please help me solve the equation: . 1 solutions Answer 197677 by drk(1908)   on 2010-02-15 13:36:39 (Show Source): You can put this solution on YOUR website!step 1 - subtract 25 to get step 2 - divide by 9 to get step 3 - take a square root to get we need imaginary answers because we are taking the square root of a negative number.
 Rectangles/269821: What are the dimensions of a rectangle whose perimeter is 48 meters and whose area is 135 square meters?1 solutions Answer 197676 by drk(1908)   on 2010-02-15 13:34:52 (Show Source): You can put this solution on YOUR website!(i) P = 2L + 2W we know that P = 48, so we get (ii) 48 = 2L + 2W dividing by 2 we get (iii) 24 = L + W solving for L, we get (iv) L = 24 - W -------- (v) A = LW We know that A = 135, so we get (vi) 135 = LW substituting (iv) into (vi) we get (vii) 135 = (24-W)(W) expanding we get (viii) 135 = -W^2 + 24W setting = 0 we get (ix) W^2 - 24W + 135 = 0 factoring, we get (x) (W-15)(W-9) = 0 and then W = 15 or W = 9 ---- answer: W = 9, L = 15 ; W = 15, L = 9
 Miscellaneous_Word_Problems/269822: Please help me solve the following word problem: A picture frame measures 12 centimeters by 20 centimeters. 48 cm^2 of the picture shows inside the frame. Find the length and width of the inside of the frame.1 solutions Answer 197673 by drk(1908)   on 2010-02-15 13:30:01 (Show Source): You can put this solution on YOUR website!Assume that the 48 cm^2 is centered in the picture. We get (i) foil the left to get (ii) set = 0 and in descending order, we get (iii) factoring, we get (iv) solving for x, we get x = 4 or x = 12 the dimensions of the inside of the frame are: 4 x 12
 Sequences-and-series/269823: Using any mathematical operations or grouping symbols, arrange eight 8s to equal 1000. 1 solutions Answer 197671 by drk(1908)   on 2010-02-15 13:24:17 (Show Source): You can put this solution on YOUR website!The answer I have is 888 + 8(8+8) -8 -8 = 1000
 Quadratic_Equations/269820: Please help me solve this problem by completing the square: .1 solutions Answer 197670 by drk(1908)   on 2010-02-15 13:21:15 (Show Source): You can put this solution on YOUR website!step 1 - factor out 2 from the first and second term to get the blanks are waiting for certain numbers. step 2 - take (1/2) of the middl term and square it. Put that number in the first blank. step 3 - squaring it gives us 25/16, but we multiply this by 2 since there are 2 groups of these. We get 50/16. Now put this number into the other blank space to get step 4 - rewrite the trinomial as a binomial squared and simplify the right side to get step 5 - divide by 2 and reduce to get step 6 - take a square root to get step 7 - add 5/4 to get
 Travel_Word_Problems/269818: luke road his bike on a trail that formed a right triangle. One leg of the right triangle was 5 kilometers longer than the other leg. they hypotenuse of the right triangle was 25 kilometers long. How far did he ride all together?1 solutions Answer 197669 by drk(1908)   on 2010-02-15 13:14:37 (Show Source): You can put this solution on YOUR website!The three sides are: x, x+5, 25. By Pythagorean theorem we get (i) expanding, we get (ii) combine like terms to get (iii) set = 0 to get (iv) factor to get (v) So, x = 15 or x = -20 ---- The three sides are: 15, 20, and 25
 Problems-with-consecutive-odd-even-integers/269817: solve by quadratic equation. Find 3 positive consecutive integers such that the sum of their squares is 2451 solutions Answer 197668 by drk(1908)   on 2010-02-15 13:11:21 (Show Source): You can put this solution on YOUR website!Let x, x+1 and x + 2 be 3 positive consecutive integers. we get (i) expanding, we get (ii) combine like terms to get (iii) set = 0 to get (iv) factoring, we get (v) and solving for x, we get x = -10 or x = 8. The three numbers are 8, 9, and 10.
 Geometry_Word_Problems/269816: What could represent a cross section of a ball rolling along a flat surface? a.circle with a tangent line b.a circle with a secant line c. a circle with a chord d. an intercepted arc1 solutions Answer 197666 by drk(1908)   on 2010-02-15 13:07:09 (Show Source): You can put this solution on YOUR website!Looking at a ball rolling on a flat surface from the side we see a circle touching the ground at one point. Then answer is (A)
 Linear-equations/269813: bob has 60 coins consisting of quarters and dimes. The coins combined value is \$9.45. Find out are many are quarters and how many are dimes.1 solutions Answer 197665 by drk(1908)   on 2010-02-15 13:06:03 (Show Source): You can put this solution on YOUR website!(i) (ii) step 1 - multiply (i) by -10 to get (iii) step 2 - add (ii) and (iii) to get (Iv) step 3 - divide by 15 to get This means
 Numbers_Word_Problems/269624: The difference of the reciprocals of two consecutive integers is 1/42. Find the integers.1 solutions Answer 197602 by drk(1908)   on 2010-02-14 20:38:31 (Show Source): You can put this solution on YOUR website!we have (i) simplify the left side to get (ii) cross multiply to get (iii) set = 0 to get (iv) factoring, we get (v) So, x = -7 or x = 6 If x = -7 then x + 1 = -6 and we get -1/7 - (-1/6) = -1/7 + 1/6 = 1/42 If x = 6 then x + 1 = 7 and we get 1/6 - 1/7 = 1/42
 Miscellaneous_Word_Problems/269619: a cement walk of uniform width is built around a 20 foot by 40 foot rectangular pool an the area of the walk is 700 square feet. How wide will the walk be?1 solutions Answer 197598 by drk(1908)   on 2010-02-14 20:31:25 (Show Source): You can put this solution on YOUR website!The pool covers 800 square feet. The new cement walk plus pool will have dimensions (i) the area of the walkway - area of pool = 700, or (ii) distributing the left we get (iii) simplify the left to get (iv) subtract 700 and set = 0 to get (v) solving for x by the quadratic, we get x = -35 or x = 5. SInce we can use x = -35, we have x = 5 walkway = 5 feet wide
 Linear-equations/269620: input output change in output x y=2x-6 -2 2(-2)-6=-10 2 -1 ? -8=? 0 ? ? ? ? 1 ? ? ? ? 2 ? ? ? ? question is complete this table?1 solutions Answer 197595 by drk(1908)   on 2010-02-14 20:15:26 (Show Source): You can put this solution on YOUR website!here is the completed table: input . . . . . . . . output . . . . . . . . . . . . . . . . change in output x . . . . . . . . . . . y = 2x - 6 . . . . . . . . . . . . . . . .y = ? -2 . . . . . . . . . . 2(-2) - 6 =-10 . . . . . . . . . . . . . . -1 . . . . . . . . . . .2(-1) - 6 = -8 . . . . . . . . . . .(+2) 0 . . . . . . . . . . . 2(0) - 6 = -6 . . . . . . . . . . . .(+2) 1 . . . . . . . . . . . .2(1) - 6 = -4. . . . . . . . . . . . (+2) 2 . . . . . . . . . . . .2(2) - 6 = -2. . . . . . . . . . . . (+2)
 Inequalities/269622: 2(x-1)+3=x-3(x+1)what is x?1 solutions Answer 197593 by drk(1908)   on 2010-02-14 20:08:51 (Show Source): You can put this solution on YOUR website!here is the original problem (i) step 1 - distribute to get (ii) step 2 - simplify the left and right to get (iii) step 3 - add 2x to both sides to get (iv) step 4 - subtract 1 to get (v) divide by 4 to get (vi)
 percentage/269621: results of surveying 200 high school seniors to find out how many hours they worked per week at a job. pie charts: 42 (15 hours or less) 82(more than 15 hours) 76 (Didn't work0 a. find the ratio of students who work more than 15 hours a week to total students answers: 82/200=41/100 b. find the ratio of students who don't have a job to students who work more that 15 hours a week. answers: 76/200= 38=41 c. find the ratio of students with jobs to total students. d. find the ratio of students with jobs to students without jobs. I do not know how to solve problems c and d please help me.1 solutions Answer 197590 by drk(1908)   on 2010-02-14 20:06:15 (Show Source): You can put this solution on YOUR website!200 total students students with jobs = 42 + 82 = 124 students without jobs = 76 ---- c. find the ratio of students with jobs to total students. answer 124/200 = 62/100 = 31/50 ----- d. find the ratio of students with jobs to students without jobs. 124/76 = 31/19
 Percentage-and-ratio-word-problems/269557: Where Sondra lives, there is a 3% state sales tax, a 1½% county sales tax, and a 1% municipal sales tax. How much tax would Sondra pay if she bought a \$340 bicycle? PLEASE PLEASE HELP! I'M STUCK ON THIS PROBLEM1 solutions Answer 197588 by drk(1908)   on 2010-02-14 20:03:03 (Show Source): You can put this solution on YOUR website!She buys the bike for \$340 3% state sales tax = 340 * .03 = 10.20 1½% county sales tax = .015 * 340 = 5.10 1% municipal sales tax = .01 * 340 = 3.40 Bike + all taxes = 340 + 10.20 + 5.10 + 3.40 = \$358.70