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# Recent problems solved by 'drk'

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 Numbers_Word_Problems/258042: Two numbers have the sum of -6 and a product of -16. Find the integers.1 solutions Answer 189886 by drk(1908)   on 2010-01-18 14:05:47 (Show Source): You can put this solution on YOUR website!Let x and Y be the numbers. From the given information, we get (i) (ii) step 1 - solve for X in (i) to get (iii) step 2 - substitute (iii) into (ii) to get (iv) expand (iv) to get (v) set = 0 to get (vi) divide by -1 and factor to get (vii) solve to get Y = 2, Y = -8. We have two answers in x,y form as (-8,2) and (2,-8)
 Permutations/258040: in how many ways can 3 cards from a deck of 52 by laid in a row face up?1 solutions Answer 189885 by drk(1908)   on 2010-01-18 14:01:36 (Show Source): You can put this solution on YOUR website!We have a combination problem. We want 3 face up , but also we want the rest, 49, face down, so we can say 52c3 = 22100
 Equations/258036: How would you write this in standard form using integers? y=2/3x-25/3. Thanks so much!1 solutions Answer 189884 by drk(1908)   on 2010-01-18 13:59:25 (Show Source): You can put this solution on YOUR website!We are given (i) standard form requires two things (1) no fractions (2) x and y on the same side -- step 1 - multiply (i) by 3 to get (ii) step 2 - subtract 2x to get at this point some teacher require positive x's, sop we could write
 Linear-equations/258033: slope and the vertical and horizontal intercept y=5x+2 can you show me the work so i know how to do this please thank you very much. 1 solutions Answer 189883 by drk(1908)   on 2010-01-18 13:57:01 (Show Source): You can put this solution on YOUR website!We start with (i) This is similar to (ii) matching up the 2 we get slope = m = 5. -- If we were to graph this, it would be a line. vertical intercept = do you mean x-intercept? horizontal intercept = do you mean y-intercept? -- X-intercept is when y = 0. If y = 0, then -- Y-intercept is when x = 0. If x = 0, then
 Linear_Equations_And_Systems_Word_Problems/258029: Janet invested \$27,000, part at 15% and part at 9%. If the total interest at the end of the year is \$3,390, how much did she invest at 15%? 1 solutions Answer 189879 by drk(1908)   on 2010-01-18 13:51:31 (Show Source): You can put this solution on YOUR website!This question is modeled after the I = prt question. IN this case however, we have two investments. So we can write I = prt + prt based on the given information, we get (i) simplifying (i) , we get (ii) and then (iii) subtracting, we get (iv) and dividing, we get x = \$11,777.78 @ 15% and 27000 - x = \$15,222.22 @ 9%.
 Distributive-associative-commutative-properties/258032: [9-2(5-4)]1 solutions Answer 189877 by drk(1908)   on 2010-01-18 13:46:35 (Show Source): You can put this solution on YOUR website!here is the question: step 1 - start from inner most ( ) 5-4 = 1, so we get step 2 - multiply 2x1 to get step 3 - subtract to get
 Exponents-negative-and-fractional/258031: how do you write 17,990,000 in scientific notation1 solutions Answer 189876 by drk(1908)   on 2010-01-18 13:44:35 (Show Source): You can put this solution on YOUR website!Notice there is no decimal - it is invisible all the way to the right of the number. We want a number of the form a*10^b, where 0 So, step 1 - from the given number move the decimal 7 jumps left. step 2 - since we started with a number bigger than 10, the exponent must be positive. step 3 - the answer is then 1.799 x 10^7
 Polynomials-and-rational-expressions/257813: what is: (3x-3 / (2x-5)^2) / (2x^2+3x-5 / 4x^2-25)1 solutions Answer 189708 by drk(1908)   on 2010-01-17 19:27:01 (Show Source): You can put this solution on YOUR website!The original problem is given as: step 1 - multiply by the reciprocal gets us step 2 - factor to get step 3 - cancel to get
 Rectangles/257815: The length of a rectangle is 2 ft more than four times the width. Express as an interger the maximum width of the rectangle when the perimeter is less than 34 ft ?1 solutions Answer 189707 by drk(1908)   on 2010-01-17 19:21:44 (Show Source): You can put this solution on YOUR website!Let length = L and width = W. from the given information, we get L = 4W + 2 P = 2L + 2W 34 > 2(4W+2) + 2W 34 > 10W + 4 30 > 10W 3 > W The maximum width is 2. If W = 2 L = 10 P = 24 < 34 -- If W = 3 L = 14 P = 34 this is NOT LESS than 34.
 Miscellaneous_Word_Problems/257783: Ricardo wants to replace the wooden door on his flat. The wooden door will be shaped like a rectangular solid and will measure 76 2/3 inches long and 44 1/4 inches wide; and will be 1 3/8 inch thick. How many cubic inches of wood will be needed for the door? Give solution exactly as a mixed number. 1 solutions Answer 189704 by drk(1908)   on 2010-01-17 19:17:30 (Show Source): You can put this solution on YOUR website!I would suggest turning all fractions into improper then multiply. 76 and 2/3 = 230/3 44 and 1/4 = 177/4 1 and 3/8 = 11/8 -- reduced becomes which is 4664 + 11/16 cubic inches
 Equations/257811: I'm trying to figure out the answer for 3m+4=19-2n I tried 3m+4-4=19-2n-4 3m=15-2n ? I get confused on these, thanks for your help1 solutions Answer 189703 by drk(1908)   on 2010-01-17 19:05:28 (Show Source): You can put this solution on YOUR website!Here is the original question (i) I notice you have two variables here. ALso M is next to the n on the keyboard, so it could be one variable. We have four options. Hopefully one of these will answer your question. -- option 1 - solve (i) for m subtract 4 from both sides to get divide by 3 to get -- option 2 - solve (i) for n subtract 19 from both sides to get divide by -2 to get -- option 3 - m=n solve (i) for m subtract 4 from both sides to get add 2m to both sides to get divide by 5 to get -- option 4 - m=n solve (i) for n subtract 4 from both sides to get add 2n to both sides to get divide by 5 to get
 Mixture_Word_Problems/257812: A mixture of acid and water is 35% acid. if the mixture contains a total of 40 Liters, how many liters of pure acid are in the mixture? How many liters of pure water are in the mixture?1 solutions Answer 189700 by drk(1908)   on 2010-01-17 18:58:01 (Show Source): You can put this solution on YOUR website!This is a mixture problem. Be careful here, as pure acid = 100% acid and water = 0% acid. As a matter of fact any time they give you water it is automatically 0 in the % column. WE have the following table based on given information: liquid . . . . . . . . . .% . . . . . . . . . . .L . . . . . . . . .%xL acid . . . . . .. . . . . 100 . . . . . . . . . x . . . . . . . . .100x water . . . . .. . . . . 0 . . . . . . . . . .. 40-x . . . .. . . . 0 mix . . . . .. . . . . . 35 . . . . . . . . . .40 . . . . . .. .. . 1400 From the third column, we get 100x = 1400 x = 14. So we have 14 Liters of pure acid 26 liters of pure water
 Polynomials-and-rational-expressions/257790: Can you plase help pme factor 4a^2+12ab+9b^2-25c^21 solutions Answer 189699 by drk(1908)   on 2010-01-17 18:53:50 (Show Source): You can put this solution on YOUR website!Here is the original problem: (i) look carefully, we really have this (ii) - which is the difference of two squares. Factoring (ii), we get - factoring as a difference of two squares, we get
 Matrices-and-determiminant/257807: Use the row echelon method to solve the system of three equations in three unknowns. x - y + 2z = -2 5x + z = 0 x + 2y+z = 41 solutions Answer 189697 by drk(1908)   on 2010-01-17 18:48:38 (Show Source): You can put this solution on YOUR website!We are given the following: x - y + 2z = -2 5x + z = 0 x + 2y+z = 4 -- in row echelon form, we have: 1 . . . . . (-1) . . . . . . .2 . . . . . . .(-2) 5 . . . . . .0 . . . . . . . .1 . . . . . . .0 1 . . . . . . 2 . . . . . . . 1 . . . . . .. 4 We need to get a diagonal matrix so take row 2 - 5 row 1 -> row 2; row 3 - row 1 -> row 3 -- 1 . . . . . (-1) . . . . . . .2 . . . . . . .(-2) 0 . . . .. . 5 . . . . . . . .(-9) . . .. . . 10 0 . . . .. . 3 . . . . . .. . . -1 . . . . . . . 6 (1/5) row 2 -> row 2 -- 1 . . . . . (-1) . . . . . . .2 . . . . . . .(-2) 0 . . . . . . 1 . . . . . . . .(-9/5) . . 2 0 . . . . . . 1 . . . . . . . .3 . . . . . . . 6 row 1 + row 2 -> row 1; row 3 - row 2 -> row 3 -- 1 . . . . . . 0. . . . . . . .(1/5) . . . . 0 0 . . . . . . 1 . . . . . . . .(-9/5) . . . 2 0 . . . . . . 0 . . . . . . . .(22/5) . . . .0 (5/24) row 3 -> row 3 -- 1 . . . . . . 0. . . . . . . .(1/5) . . . . 0 0 . . . . . . 1 . . . . . . . .(-9/5) . . . 2 0 . . . . . . 0 . . . . . . . .1 . . . . . . . 0 So, z = 0 y = 2 x = 0 {0, 2, 0}
 Travel_Word_Problems/257809: The distance from Melbourne to London is 10,500 miles. If a jet averages 500 mph between the two cities, What is its travel time in hours?1 solutions Answer 189690 by drk(1908)   on 2010-01-17 18:30:53 (Show Source): You can put this solution on YOUR website!This is: rate x time = distance. The rate = 500 and the distance = 10,500. we can use this formula to find the time as:
 Triangles/257796: Find the area of the triangle ABC having vertices A(7,-4) B(3,1) C(-10,-8)1 solutions Answer 189687 by drk(1908)   on 2010-01-17 18:29:12 (Show Source): You can put this solution on YOUR website!If you graph these out, you may notice that there are no right angles. This means we can use one of three formulas: (1) Hero's formula - approximate To use this we need the 3 distances. They are: sqrt(255), sqrt(61), sqrt(261) The semi perimeter, s, is about 12.79 A = sqrt(s*(s-a)(s-b)(s-c)) A = 50.5 (2) matrices Lets use matricies. If we apply matrices, we get 50.5 -- (3) 1/2absinC This requires trig calculations, which I don't know you have seen. -- So the area is 50.5.
 Inverses/257805: Inverse of y=4x-2 y=2x+4 y=1/4x + 1/2 y= 1/4x-1/2 y=4x +1/21 solutions Answer 189675 by drk(1908)   on 2010-01-17 18:10:36 (Show Source): You can put this solution on YOUR website!We stat with step 1 - reverse the x and y to get step 2 - solve for the new y to get separating our common denominator, we get So, the answer is y= 1/4x-1/2
 Linear-equations/257804: find the slope x+2y=41 solutions Answer 189674 by drk(1908)   on 2010-01-17 18:07:51 (Show Source): You can put this solution on YOUR website!Solving for y, we can get the slope subtract x to get divide by 2 to get The slope intercept form is matching these two equations, we see that slope = m = (-1/2)
 Matrices-and-determiminant/257803: A company makes 3 types of cable. Cable A requires 3 black wires, 3 white wires, and 2 red wires. Cable B requires 1 black, 2 white, and 1 red. Cable C requires 2 black, 1 white, and 2 red. If 95 black wires, 100 white wires, and 80 red wires were used, then how many of each cable were made? 1 solutions Answer 189673 by drk(1908)   on 2010-01-17 18:05:29 (Show Source): You can put this solution on YOUR website!Here we have a 3x3 system. Let the cables be A, B, and C. (i) 3A + 1B + 2C = 95 (ii) 3A + 2B + 1C = 100 (iii) 2A + 1B + 2C = 80 -- Lets eliminate the B's. Take (ii) - 2*(i) to get (iv) -3A -3C = -90 lets eliminate the B's. take (ii) - 2*(iii) to get (v) -1A -3C = -60 -- To eliminate C's, take (v) - (iv) to get (vi) 2A = 30 so A = 15 cables C = 15 cables B = 20 cables
 Graphs/257802: find the intercerpts and then use them to graph the equation 3y - 9 = 3x1 solutions Answer 189672 by drk(1908)   on 2010-01-17 17:59:02 (Show Source): You can put this solution on YOUR website!The x-intercept is when we let y = 0, and solve for x. We get (i) x = -3 The y-intercept is when we let x = 0, and solve for y. We get: (ii) y = 3 Now, we can graph these and create a line.
 Money_Word_Problems/257799: You want to have a \$90,000 college fund in 11 years. How much will you have to deposit now under the scenario below. Assume that you make no deposits into the account after the initial deposit. An APR of 5% compounded daily.1 solutions Answer 189671 by drk(1908)   on 2010-01-17 17:56:24 (Show Source): You can put this solution on YOUR website!We need the formula: (i) from the given information, we have (ii) so, (iii) dividing, we get (iv)
 Angles/257798: what angle is 5x's as large as its own complement1 solutions Answer 189670 by drk(1908)   on 2010-01-17 17:52:45 (Show Source): You can put this solution on YOUR website!Let x be an angle. Complementary angles add to 90. So, x = 5(90-x) x = 450 - 5x 6x = 450 x = 75
 Angles/257800: what angle is 10 degrees more than three times its own complement1 solutions Answer 189668 by drk(1908)   on 2010-01-17 17:50:56 (Show Source): You can put this solution on YOUR website!Let x be an angle. Complimentary angles add to 90 degrees, so x = 3(90-x)+10 x = 270 - 3x + 10 4x = 280 x = 70.
 Graphs/257801: What is the slope of y= -10x +61 solutions Answer 189667 by drk(1908)   on 2010-01-17 17:49:18 (Show Source): You can put this solution on YOUR website!The formula for slope is we are given matching the equations up, we get slope = m = -10.
 Distributive-associative-commutative-properties/257788: solve for x x(2x-1)=2x²+5x-121 solutions Answer 189666 by drk(1908)   on 2010-01-17 17:48:03 (Show Source): You can put this solution on YOUR website!step 1 - distributive property on the left to get (i) step 2 - simplify to get (ii) step 3 - solve for x to get (iii) checking, we get 2(2*2-1) = 2*2^2+5*2-12 2(3) = 16+10-12 6 = 6
 Distributive-associative-commutative-properties/257789: Solve for x 4x(x+1)=(2x-3)(2x+5)1 solutions Answer 189663 by drk(1908)   on 2010-01-17 17:33:15 (Show Source): You can put this solution on YOUR website!step 1 - distributive property on the left and foil on the right to get (i) (ii) simplifies to (iii) This is no solution
 Trigonometry-basics/257759: How to solve this problem and the steps w/five key points? y = Sin 4x? I'm a beginner can u help?1 solutions Answer 189653 by drk(1908)   on 2010-01-17 17:00:22 (Show Source): You can put this solution on YOUR website!This you really can't solve. You can simplify or graph. (i) -- Now 4x = 2x + 2x, so we get (ii) we have an identity: sin(A+B) = sinA cosB + sinB cosA or in our case (iii) But these are the same, so we can write (Iv) -- Now 2x = x + x, so we get (v) we have an identity: sin(A+B) = sinA cosB + sinB cosA or in our case (vi) But these are the same, so we can write (vii) From (iv) and (vii), we get
 Polynomials-and-rational-expressions/257734: (x-1)(x^2+10x+24=0...This one has me baffled..I can work 2nd set of parentheses but the (x-1) has got me confused.Is this a valid solvable problem?1 solutions Answer 189646 by drk(1908)   on 2010-01-17 16:53:22 (Show Source): You can put this solution on YOUR website!Here is the original question: step 1 - factor the second polynomial to get step 2 - set each pat = 0 and solve: x-1 = 0 x = 1 x + 4 = 0 x = -4 x + 6 = 0 x = -6 we have three answers {-6, -4, 1}
 Graphs/257736: Lorena borrowed \$100 from her father and plans to pay him back at a rate of \$10 per week. The graph shows the amount Lorena owes her father. Find the equation that represents this relationship. A. y= 10x - 100 B. y= 10x - 90 C. y= 100 - 10x D. y= -100 - 10x1 solutions Answer 189600 by drk(1908)   on 2010-01-17 15:10:44 (Show Source): You can put this solution on YOUR website!The answer is [C]. We owe 100 and eventually pay the loan down to zero.
 Graphs/257733: in direct variation if y varies directly with x: find the equation for the direct variation if y=20 when x= 3 find x when y=81 solutions Answer 189598 by drk(1908)   on 2010-01-17 15:09:38 (Show Source): You can put this solution on YOUR website!Step 1 write y = kx and find k using known x and y information. y = kx 20 = 3k k = 20/3 step 2 - rewrite the equation with your new K value as y = (20/3)x step 3 find x when y = 8 8 = (20/3)x 24/20 = x x = 6/5
 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}