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# Recent problems solved by 'drk'

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 Word_Problems_With_Coins/257726: How many ways can you make \$0.25 using pennies, nickels, dimes, and quarters 1 solutions Answer 189597 by drk(1908)   on 2010-01-17 15:07:39 (Show Source): You can put this solution on YOUR website!There appear to be 13 ways. Here they are in {p,n,d,q} form: {p,n,d,q} {0,0,0,1} (0,1,2,0} {5,0,2,0} {0,3,1,0} {5,2,1,0} {10,1,1,0} {15,0,1,0} {0,5,0,0} {5,4,0,0} {10,3,0,0} {15,2,0,0} {20,1,0,0} {25,0,0,0}
 Functions/257728: Find the function value. F(x) = x to the third power. F(-9) =1 solutions Answer 189596 by drk(1908)   on 2010-01-17 15:02:16 (Show Source): You can put this solution on YOUR website!F(x) = x^3 F(-9) = (-9)^3 = -9*-9*-9 = -729
 Linear-equations/257732: how do I solve k(x)=x+20 k (o)= k(-17)= k (-12)= k(14)= K (d+17)=1 solutions Answer 189595 by drk(1908)   on 2010-01-17 15:00:45 (Show Source): You can put this solution on YOUR website!To solve these, use the phrase "letter goes away and number comes to stay as follows: k(x)=x+20 k(0) = 0 + 20 = 20 k(-17) = -17 + 20 = 3 k (-12) = -12 + 20 = 8 k(14) = 14 + 20 = 34 K (d+17) = (d+17) + 20 = d + 37
 Geometry_proofs/257494: Given: Triangle ABC Prove: m<4= m<1 + m<2 Picture: A triangle with line, CD, connected to it. A is m<1, B is m<2, C is m<3, and m<4 are vertical angles to m<31 solutions Answer 189420 by drk(1908)   on 2010-01-16 13:33:29 (Show Source): You can put this solution on YOUR website!This is also called the exterior triangle theorem. With angle 4 vertical to angle 3, you cannot prove angle 4 = angle 1 + angle 2. For this to work, angle 4 must be supplementary to angle 3. Here is the proof for that. STATEMENT 1: triangle ABC REASON 1: given STATEMENT 2: angle 1 + angle 2 + angle 3 = 180 degrees REASON 2: definition of sum of angles of triangle STATEMENT 3: angle 3 + angle 4 = 180 REASON 3: definition of supplementary angles STATEMENT 4: angle 1 + angle 2 + angle 3 = angle 3 + angle 4 REASON 4: substitution [2,3] STATEMENT 5: angle 1 + angle 2 = angle 4 REASON 5: subtraction property of equality
 real-numbers/257495: Which set of numbers is not closed under multiplication? odd integers, even integers, prime numbers, or rational numbers.1 solutions Answer 189417 by drk(1908)   on 2010-01-16 13:21:29 (Show Source): You can put this solution on YOUR website!Primes are not closed under multiplication. -- Look at each separately: odd integers: odd x odd = odd [closed] even integers: even x even = even [closed] prime numbers: prime x prime = composite [NOT closed] rational numbers: fraction x fraction = fraction [closed]
 Geometry_proofs/257490: Given: AB and CD bisects each other at M Prove: AD is parallel to BC Picture: Two triangles connecting to get, kind of like a bow tie. 1 solutions Answer 189415 by drk(1908)   on 2010-01-16 13:14:27 (Show Source): You can put this solution on YOUR website!STATEMENT 1: AB bisects CD at M REASON 1:given STATEMENT 2: AM congruent BM REASON 2: definition of bisector STATEMENT 3: CM congruent DM REASON 3: definition of bisector STATEMENT 4: angle CMB congruent angle AMD REASON 4: definition of vertical angles STATEMENT 5:triangle CMB congruent triangle AMD REASON 5: SAS STATEMENT 6: CB congruent AD REASON 6: CPCTC STATEMENT 7: angle CBM congruent angle DAM REASON 7: CPCTC STATEMENT 8: CB is parallel to AD REASON 8: definition of parallel lines.
 Rectangles/257489: you have 80 feet of fencing to enclose a rectangular region. what is the maximum area?1 solutions Answer 189413 by drk(1908)   on 2010-01-16 13:09:36 (Show Source): You can put this solution on YOUR website!The perimeter is P = 2L + 2W or 80 = 2L + 2W dividing by 2 we get (i) 40 = L + W THe area is (ii) A = LW solving (i) for L, we get (iii) L = 40-W substituting that in (ii), we get (iv) A = (40-W)(W) using completing the square, we get A = -(W-20)^2 + 400 So, when W = 20, the max area is 400.
 Equations/257488: 3/7x+5/9y=27 and 1/9x+2/7y=71 solutions Answer 189411 by drk(1908)   on 2010-01-16 13:04:48 (Show Source): You can put this solution on YOUR website!The two equations are: (i) (ii) multiply both equations by 63 to get (iii) (iv) multiply (iii) by 7 and (iv) by -27 to get (v) (vi) adding down, we get y = 0. x = 63 {63,0)
 Linear-systems/257487: 12a^2 + 36b^2 -43ab=0 factorize it1 solutions Answer 189409 by drk(1908)   on 2010-01-16 12:59:14 (Show Source): You can put this solution on YOUR website!Our equation was step 1 - rewrite in descending order to get step 2 - factor to get step 3 - set each part = 0 and solve to get
 Percentage-and-ratio-word-problems/257474: Amy paid \$57.16 for a pair of shoes during a 35% off sale. What was the regular price? I am thinking that the original price was \$163.14 but not sure if I am right.1 solutions Answer 189408 by drk(1908)   on 2010-01-16 12:55:16 (Show Source): You can put this solution on YOUR website!If reduce a price by 35%, you still have 65% left. So, .65P = 57.16 dividing we get p ~ \$87.94. -- checking, 87.94*.35 ~ 30.78 87.94 - 30.78 ~ 57.16.
 Proportions/257482: the antecedent and consequent of a ratio differ by 40 and is equal to 2/7. find the ratio.1 solutions Answer 189407 by drk(1908)   on 2010-01-16 12:52:07 (Show Source): You can put this solution on YOUR website!We have a fraction of the following type N/D, where D NOT = 0. Based on the given information, D - N = 40 and N/D = 2/7. This is a reduced number. D = 40 + N by substitution, we get N / (40+N) = 2/7 cross multiply to get 7N = 80 + 2N solve for N to get 5N = 80 N = 16 Since N = 16, D = 56 Our fraction is 16/56.
 Proportions/257485: if a number of two digits is divided by th number obtained after reversing the digits, we get 2.08 , if the sum of the digit is 7, find the number.1 solutions Answer 189406 by drk(1908)   on 2010-01-16 12:47:38 (Show Source): You can put this solution on YOUR website!Let the original number be expressed as When you reverse the digits, you get Now the quotient = 2.08 as We also know that t + u = 7, so t = 7-u. We get This gives us cross multiplying, we get solving for u, we get original number is 52 reversed number is 25. quotient is 2.08
 Graphs/257483: I did this linear equation problem, but I want to make sure it is right. Graph a line using the "friendly numbers" -2, -1, 0, 1, 2 1. y = 2x + 3 This is the answer I put down: x / 2x+3 / y / (x,y) -2 / 2(-2)+3 / -1 / (-2,-1) -1 / 2(-1)+3 / 1 / (-1,1) 0 / 2(0)+3 / 3 / (0,3) 1 / 2(1)+3 / 5 / (1,5) 2 / 2(2)+3 / 7 / (2,7) I didn't know how to make columns on the computer for my answers. The above should be in columns, but I put slashes to indicate the columns. Now I am thinking about the answer because it states to a graph a line using the friendly numbers. Are my columns enough or do I have to graph a line? 1 solutions Answer 189405 by drk(1908)   on 2010-01-16 12:40:23 (Show Source): You can put this solution on YOUR website!Everything you have is correct. You have created the x,y coordinates. You still have to graph these.
 Proportions/257478: if y/x-z = y+x/z =x/y then find x:y:z1 solutions Answer 189404 by drk(1908)   on 2010-01-16 12:37:27 (Show Source): You can put this solution on YOUR website!A solution occurs when x = 4k, y = 2k, and z = 3k where K >=1. So, x:y:z = 4:2:3
 Equations/257415: a motorist drove a for 2 hours at one speed & then for 3 hours at another speed & one hour at the second speed, he would have covered 2444km. find the two speeds.1 solutions Answer 189403 by drk(1908)   on 2010-01-16 12:28:03 (Show Source): You can put this solution on YOUR website!This is an RTD problem. Here is a table base on given information: motorist . . . . . . . . .rate . . . . . . . . . .time . . . . . . . . . .distance . . . . . . . . . . . . . . .. R1 . . . . . . . . . . . .2 . . . . . . . . . .. . 2R1 . . . . . . . . . . . . . . . .R2 . . . . . . . . . . . .3 . . . . . . . . .. . .3R2 . . . . . . . . . . . . . . . R2 . . . . . . . . .. . . . 1 . . . . . . . . .. . .1R2 . . . . . .. . . . . . . . . . .. .. . . . . . . . . . .6 . . . . . .. . . . . . .2444 We see that (i) or dividing by 2, we get (ii) and that the average rate is avgR = 2444/6 = 407.33 This means that (iii) or (iv) substituting (iv) into (ii) we get (v) (vii) solving for R2, we get This makes R1 -- The rates appear to be the same.
 Triangles/257424: The equal sides of an isosceles triangle have lengths of (5x – 30) and (3x + 10). What is the greatest possible integer value of the third side?1 solutions Answer 189398 by drk(1908)   on 2010-01-16 12:10:22 (Show Source): You can put this solution on YOUR website!We set the two sides equal to each other as 5x – 30 = 3x + 10 Solving for x, we get Now, each side is worth 70. We have a 70, 70, and x sided triangle. Using the triangle inequality theorem, we get 70-70 < x < 70+70 or 0 < x < 140. The greatest integer < 140 is 139.
 Quadratic_Equations/257472: what is the axis of symmetry of this equation y=2x2+8x-2 1 solutions Answer 189396 by drk(1908)   on 2010-01-16 12:06:43 (Show Source): You can put this solution on YOUR website!To find axis of symmetry, we use -b/2a. So, -b/2a = -8/2(2) = -8/4 = -2 The axis of symmetry is X = -2.
 Problems-with-consecutive-odd-even-integers/257473: find three cosecutive odd integers such that the sum of the least and greatest is 781 solutions Answer 189395 by drk(1908)   on 2010-01-16 12:05:21 (Show Source): You can put this solution on YOUR website!Let x, x+2, x+4 b the 3 consecutive odd integers. From the given, we get x+ (x+4) = 78 2x + 4 = 78 2x = 74 x = 37 So, we get 37, 39, 41.