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# Recent problems solved by 'drk'

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 Equations/252726: the perimeter of a rectangular lot is 156 meters. the length is twice the width. write the equation that describes the situation and find the length and width please :]1 solutions Answer 184786 by drk(1908)   on 2009-12-30 15:50:14 (Show Source): You can put this solution on YOUR website!Perimeter = 2L + 2W = 156. divide by 2 and we get L = 2W By substitution, we get W = 26 meters L = 52 meters
 Matrices-and-determiminant/252724: how do i use cramer's rule for three equations on this problem 5x-6y=7+7z 6x-4y+10z=-34 2x+4y=29+3z1 solutions Answer 184785 by drk(1908)   on 2009-12-30 15:47:55 (Show Source): You can put this solution on YOUR website!To use Cramers rule you need matricies. step #1 rewrite all equation so that variables are on one side and in order. 5x - 6y - 7Z = 7 6x - 4y + 10z = -34 2x + 4y -3Z = 29. -- step #2 - We need to find four determinants: (1) the determinant of the left side, D. D = -592 (2) the determinant of x, Dx, when you replace the x column with the answer column Dx = -1184 (3) the determinant of y, Dy, when you replace the y column with the answer column Dy = -2368 (4) the determinant of z, Dz, when you replace the z column with the answer column Dz = 1776 -- step #3 use fractions to find the answer: (1) Dx / D = x answer ; x = 2 (2) Dy / D = y answer ; y = 4 (3) Dz / D = z answer ; z = -3 I don't know an easier way to explain this. Hope this makes sense.
 Proportions/252723: A college student pays \$280 for a three hour course. How much would he have to pay for a class load of 16 hours? Round your answer to the nearest whole dollar1 solutions Answer 184784 by drk(1908)   on 2009-12-30 15:31:24 (Show Source): You can put this solution on YOUR website!This is proportions. 280/ 3 = X / 16 cross multiply to get 3X = 4480 X = 1493.33 To the nearest \$, X = \$1493.
 Problems-with-consecutive-odd-even-integers/252725: find three consecutive even integers so that the largest is 2 times more than the smallest1 solutions Answer 184783 by drk(1908)   on 2009-12-30 15:28:11 (Show Source): You can put this solution on YOUR website!We need three consecutive even integers. We don't know what they are. Some examples are: 2,4,6 ; 4,6,8 ; 6,8,10 and so on. -- Notice that the second number is 2 more than the first. Notice the third number is 4 more than the first. -- Since we don't know the first number, call is X. The second number is 2 more than this, it is X + 2. Third number is 4 more than this, it is X + 4. -- So, Three consecutive even integers can be expressed as: X, X+2, X+4. Two times the smallest is the largest means (i) 2X = X + 4, since the smallest was X and the largest was X + 4. subtract X from both sides to get X = 4. Now the first number was X. It is X = 4, the second number was X + 2, it is 4 + 2 = 6 the third number is X + 4, it is 4 + 4 = 8. The three numbers are 4 , 6, 8
 logarithm/252722: write the following expression as a single logarithm and state restrictions. 4log(x-1)+2log(x+5)-log(x-2) 1 solutions Answer 184782 by drk(1908)   on 2009-12-30 15:06:50 (Show Source): You can put this solution on YOUR website!Let's look at restrictions first: X can't = 1, 2, or -5 If X equals any of these the log wouldn't exist at log(0). -- step #1 - place all front numbers in exponents (power rule) -- step #2 - add of logs means multiply information and subtract means divide information. SO, log --- step #3 - simplify the numerator. This is not the fun step . . . log
 Numbers_Word_Problems/250722: Zeke's motor cycle traveled 270 miles at a certain speed. Had he gone 15 mph faster, the trip would have taken 3 hours less. Find the speed of the motorcycle.1 solutions Answer 184781 by drk(1908)   on 2009-12-30 14:54:34 (Show Source): You can put this solution on YOUR website!This is an RTD problem. Here is the table vehicle . . . . . . . rate . . . . . . . . time . . . . . . . .distance cycle . . . . . . . . . R . . . . . . .. . . 270/R . . . . . .. 270 cycle . . . . . . . . .R + 15 . .. . . . 270/R - 3 . . . .. 270 I let R = rate. The first time is D / R = 270 / R. All times are in hours, so the second time is (270/R - 3) hours. Look at the second line. (R + 15)(270/R - 3) = 270 By FOIL, we get 270 - 3R + 4050/R - 45 = 270 multiply both sides by R. we get 270R - 3R^2 + 4050 - 45R = 270R. Simplify to get 3R^2 + 45R - 4050 = 0 dividing by 3, we get R^2 + 15R - 1350 = 0 factoring, we get (R + 45)(R - 30) = 0 R = -45 or R = 30. we can use -45, so R = 30. The motorcycle was traveling at 30 mph.
 Surface-area/252721: A box is x inches high, (2x + 3) inches wide, and (2x + 5) inches long. In terms of x, what is the volume (V) of the box?1 solutions Answer 184780 by drk(1908)   on 2009-12-30 14:46:30 (Show Source): You can put this solution on YOUR website!Volume is V = LxWxH V = (X)(2x+3)(2x+5) V = 4x^3 + 16x^2 + 15X.
 Numbers_Word_Problems/250720: A chemist has one solution that is 20% saline and a second that is 65% saline. How many gallons of each should be mixed to get 120 gallons of a solution which is 50% saline?1 solutions Answer 184778 by drk(1908)   on 2009-12-30 14:45:11 (Show Source): You can put this solution on YOUR website!This is a mixture problem. Here is the table: SALINE . . . . . % . . . . . .gal . . . . . .%gal A . .. . . . . . .. 20 . . . .. . G . . . . . . . 20G B . . . . . . . . .. 65 . . . . .120-G . . . .7800 - 65G mix . . . . . . . 50 . . . . . .120 . . . . . .6000. -- I put in all information from the problem and then I had to use variables. I let G = gallons of A and 120-G be gallons of B. It is always total gallons - X. Now, 20G + 7800 - 65G = 6000 -45G = -1800 G = 40. I need 40 gallons of the 20% saline solution and 80 gallons of 65% saline solution.
 Miscellaneous_Word_Problems/250718: a Reactangle is twice as long as it is wide. If its length and width are both dimentions are increased by 4 m, its area is increased by 88m^2. Make a sketch and find the original dimentions of the rectangle1 solutions Answer 184777 by drk(1908)   on 2009-12-30 14:40:06 (Show Source): You can put this solution on YOUR website!First rectangle. a Rectangle is twice as long as it is wide translates to (i) L = 2W If its length and width are both dimentions are increased by 4 m is translated to L+4, W + 4. its area is increased by 88m^2 means that new area - original area = 88m^2. -- original area from (i) A = LW = (2W)(W) = 2W^2 -- new area after + 4 to both L and W. A = LW = (2W+4)(W+4) = 2W^2 + 12W + 16. -- new area - old area = 88 is 2W^2 + 12W + 16 - 2W^2 = 88 12W + 16 = 88 12W = 72 W = 6 L = 12. I am hoping from this you can make the sketch.
 Linear_Equations_And_Systems_Word_Problems/250687: what are the possible types of solutions for a linear system of two equations?1 solutions Answer 184776 by drk(1908)   on 2009-12-30 14:34:26 (Show Source): You can put this solution on YOUR website!Two equations with two unknowns have the possible type of solutions: (1) no solution - parallel lines (2) 1 solution - lines cross at one point. (3) infinite solutions - the lines are the same but in disguise.
 Travel_Word_Problems/250688: A bird can fly 35 mph in still air, 30 mph with the wind and 5 mph against the wind. What speed is the wind?1 solutions Answer 184775 by drk(1908)   on 2009-12-30 14:32:48 (Show Source): You can put this solution on YOUR website! bird . . . .35 = r bird . . . 65 = r + c bird . . . 5 = r -c substitute r with 35. 65 = 35 + c c = 30. check 5 = 35 - 30 [check] the speed of the wind is 30 mph
 percentage/252715: what is the total cost in dollars of a \$45 shirt with 5% sales tax?1 solutions Answer 184770 by drk(1908)   on 2009-12-30 14:22:36 (Show Source): You can put this solution on YOUR website!Price of shirt = P. total cost including tax is P (1 + tax rate). So, 45(1 + .05) 45*(1.05) \$47.25
 Quadratic_Equations/252708: convert y=3x^2+18x+30 to vertex form by completing the square convert y= -2x^2+28x-7 to vertex form by completing the square trying to figure this out.1 solutions Answer 184769 by drk(1908)   on 2009-12-30 14:20:46 (Show Source): You can put this solution on YOUR website!Let's start with the first equation and then repeat process for second: (i) STEP #1: factor out the 3 from the first two terms to get (ii) -- STEP #2: take 1/2 middle term number and square it. Multiply it by 3 and put that answer in the blanks. We get (iii) -- STEP #3: write the left side as a quantity squared and equalling the right. (iv) This is vertex form. -- -- (v) y= -2x^2+28x-7 STEP #1: factor out -2 from the first two terms to get (ii) -- STEP #2: take 1/2 middle term number and square it. Multiply it by -2 and put that answer in the blanks. Sometimes it's easier to say [middle number/2]. Don't forget your signs. We get (iii) -- STEP #3: write the left side as a quantity squared and equalling the right. (iv) This is vertex form.
 Length-and-distance/252712: i need to Find the length of the segment rounded to the nearest tenth. Then Find the coordinates of the midpoint of the segment. A) (-3,3)and B(1,-8) Yurboikev12@aol.com1 solutions Answer 184764 by drk(1908)   on 2009-12-30 14:05:35 (Show Source): You can put this solution on YOUR website!We have the coordinates A (-3,3) and B(1,-8) to find midpoint, we need the following formula: , putting in our numbers, we get (-3 + 1)/2 , (3 + -8)/2 - -> (-1, -5/2) To find length, we need distance formula, which is again putting your numbers in, we get d ~ 11.70 ~ 11.7
 Linear-systems/252709: Trying to develop a linear equation for: Gas used: 5, 8, 12, 15, 18, 20, 22, 25 Miles driven, 80, 100, 180, 225, 280, 290, 320, 3751 solutions Answer 184762 by drk(1908)   on 2009-12-30 13:58:30 (Show Source): You can put this solution on YOUR website!We have the following table: Gas used: 5, 8, 12, 15, 18, 20, 22, 25 Miles driven, 80, 100, 180, 225, 280, 290, 320, 375. To create a linear model, we want to apply some rule to x and then get y. Notice 5*15 = 75 + 5 = 80 8*15 = 120 - 20 = 100 12*15 = 180 15*15 = 225 18*15 = 270 + 10 = 280 20*15 = 300 - 10 = 290 22*15 = 330 - 10 = 320 25*15 = 375. We can't create a perfect linear model, but this means we have a "regression" model, or an equation that gets us close: M = 15G. Hope this helps.
 Graphs/252707: how to graph y=(-2/18)x+(9/18)1 solutions Answer 184760 by drk(1908)   on 2009-12-30 13:43:25 (Show Source): You can put this solution on YOUR website!graph FIrst i would reduce where possible. We get y = (-1/9)x + (1/2) Your slope = -1/9 and b value, y intercept is 1/2. STEP #1 - place a dot at 1/2 on the Y-axis. STEP #2 - from this dot, you will move down 1 unit and right 9 units. PLace a second dot. connect the dots. and you are done.
 Quadratic_Equations/252705: determine the vertex of quadratic function stating axis of symmetry,minimum or maximum value,and domain and range on y=10x^2+5x-1 and y=-24x^2+18x+11 I am not understanding even though i read over examples.1 solutions Answer 184759 by drk(1908)   on 2009-12-30 13:40:34 (Show Source): You can put this solution on YOUR website!let's start with the first equation and then move to the second: quadratics are expressed as Y = Ax^2 + Bx + C. -- vertex: We can find the vertex using -b/2a. -5/2*10 = -5/20 = -1/4. This is the x part of the vertex and now we put that into f(x) to get 10(1/4)^2 + 5(1/4)-1 = 10/16 + 5/4 - 1 = 14/16 = 7/8. vertex = (1/4,7/8) -- axis of symmetry: This is just the x value of the vertex x = 1/4. -- min: since the graph opens up, there will be a min at the vertex. min @ (1/4,7/8) -- domain:domain: For a parabola opening up or down, domain will be all reals. range: Since the parabola opens up, the minimum range is 7/8. So we have Y >= 7/8. -- EQUATION #2 {{y = -24x^2 + 18x + 11}} quadratics are expressed as Y = Ax^2 + Bx + C. -- vertex: We can find the vertex using -b/2a. -18/2*-24 = 18/48 = 3/8. This is the x part of the vertex and now we put that into f(x) to get -24(3/8)^2 + 18(3/8) + 11 = -27/8 + 27/4 + 11 = 115/4. vertex = (3/8, 115/4) -- axis of symmetry: This is just the x value of the vertex x = 3/8. -- min: No min in this case. max: SInce the graph opens down, there will be a max at the vertex. min @ (3/8, 115/4) -- domain: For a parabola opening up or down, domain will be all reals. range: Since the parabola opens down, the highest range is 115/4. So we have Y <= 115/4.
 Linear-equations/252704: Solving Linear Systems by Graphs and Tables Guided Practice: 2. y=3-x y=x+1 3. y = 1/2 x -3/2 y = 2x-6/4 4. y = x+3/2 y = 2x-3/41 solutions Answer 184757 by drk(1908)   on 2009-12-30 13:23:10 (Show Source): You can put this solution on YOUR website!Let's take them one at a time: --- 2. (i) y = 3 - x (ii)y = x + 1 Creating a table of values, we get: X . . . -2 . . -1 . . . 0 . . . 1 . . . 2 Y(i). . .5 . . . 4 . . . .3 . . . 2 . . . 1 Y(ii) . .-1 . . 0 . . . 1. . . .2 . . . 3 Notice the Y's are equal at 2, when X = 1. You should be able to graph this now. --- 3. (i) y = 1/2 x -3/2 (ii) y = 2x-6/4 Creating a table of values, we get: X . . . . .. . . -4 . . . . . . .-2 . . . . . . . . . 0 . . . . . . . . 2 . . . .. . . . 4 Y(i). . . . . -7/2 . . . .. . -5/2 . . . . . . . -3/2 . . .. . .-1/2 . . . . . 1/2 Y(ii) . . . .-19/2 . . . . . . -11/2 . . . . . -3/2 . . .. . . .5/2 . . . . . . 13/2 Notice the Y's are equal at -3/2, when X = 0. You should be able to graph this now. --- 4. (i)y = x+3/2 (ii)y = 2x-3/4 Creating a table of values, we get: X . . . . .. . . 0 . . . . . . .3/4 . . . . . . . . . 6/4 . . . . . . . . 9/4 . . . .. . . . 12/4 Y(i). . . . . 3/2 . . . .. . 9/4 . . . . . . . . . 3 . . . . . . . 15/4 . . . . . . . .9/2 Y(ii) . . . .-3/4 . . . . . . 3/4 . . . . . . 9/4 . . . . . . . . .15/4 . . . . . . . 21/4 Notice the Y's are equal at 15/4, when X = 9/4. You should be able to graph this now.
 Linear_Algebra/252703: Solve the following equations: 4ax+by=11ab 8ax-5by=ab1 solutions Answer 184756 by drk(1908)   on 2009-12-30 13:09:39 (Show Source): You can put this solution on YOUR website!OUr original equations are: (i) (ii) -- STEP #1 - multiply (i) equations by 5 (iii) (ii) -- STEP #2 - add down to eliminate by. (v) 28ax = 56ab. We must assume that a, b, x, and y are not all zero. x = 2b. -- STEP #3 - find y. Y = 3a.
 Quadratic_Equations/252702: convert y=x^2+6x-10 to vertex form completing the square. convert y=x^2-9x+3 to vertex form completing the square.1 solutions Answer 184755 by drk(1908)   on 2009-12-30 13:05:06 (Show Source): You can put this solution on YOUR website!Let's start with the first equation and then repeat process for second: (i) STEP #1: re write the equation as (ii) -- STEP #2: take 1/2 middle term number and square it. put that answer in the blanks. We get (iii) -- STEP #3: write the left side as a quantity squared and equalling the right. (iv) This is vertex form. -- -- (v) y = x^2 - 9x + 3 STEP #1: re write the equation as (ii) -- STEP #2: take 1/2 middle term number and square it. put that answer in the blanks. Sometimes it's easier to say [middle number/2]. Don't forget your signs. We get (iii) -- STEP #3: write the left side as a quantity squared and equalling the right. (iv) This is vertex form.
 Percentage-and-ratio-word-problems/250717: Two machines fill cereal boxes at the same rate. After the two machines work together for 4 hours, one machine breaks down. The second machine requires 26 more hours to finish filling the boxes. How long would it have taken one of the machines, working alone, to fill the boxes? (rate x time = work completed) (the work needs to be show using FRACTIONS)1 solutions Answer 184754 by drk(1908)   on 2009-12-30 12:48:10 (Show Source): You can put this solution on YOUR website!This is what I call job / time. Here is the formula: J1/T1 * (together time) + J2/T2 * (together time) = total number of jobs. J1 is firs persons number of jobs T1 is first persons time to do the jobs. Two machines fill cereal box. So, J1 = J2 = 1; B total cereal boxes. T1 = T2; same rate. At this pint we have the following equation: (1/t)(4) + (1/t)(4) + (1/t)(26) = B. We have to add the alone time of the second machine after the first breaks down. We don't know how many total boxes were to be filled. Continuing 8/t + 26/t = B 34 = Bt t = 34/B This gives you the time to fill B boxes. Hope this helps.
 Linear-equations/250715: company 1 one size fits all charges 4.00 dollars per shirt company 2 you draw it we print it charges 75 dollars plus 3 dollars per shirt question: For what number of t-shirts is the cost the same for both companies ? Explain how you got your answer. 1 solutions Answer 184753 by drk(1908)   on 2009-12-30 12:37:51 (Show Source): You can put this solution on YOUR website!The equation for company 1 is C = 4S, where C = total cost and S = cost per shirt. The equation for company 2 is C = 3S + 75. The cost is the same when both equations are equal to each other. So, 4S = 3S + 75 S = 75; the answer --- The check: If S = 75, the cost for company 1 is C = 4*75 = \$300 If S = 75, the cost for company 2 is C = 3*75 + 75 = 225 + 75 = \$300.
 Rational-functions/250706: Find an equation of a straight line that passes through the point (2,3) and is parallel to the line with equation 3x + 4y -8 = 01 solutions Answer 184752 by drk(1908)   on 2009-12-30 12:34:01 (Show Source): You can put this solution on YOUR website!Step #1 - solve 3x + 4y -8 = 0 for y. Y = -(3/4)X +2. STEP #2 - find the slope based on the equation from STEP #1. M = (-3/4). STEP #3 - parallel lines have the same slope. The slope you have from STEP #2 is the slope you want. m = (-3/4). STEP #4 - using the slope from STEP #3, pick a point (2,3) and put those into Y = mX + b. Solve for b. 3 = (-3/4)(2) + b. b = 9/2. STEP #5 - write the equation. Y = (-3/4)X + 9/2.
 Exponential-and-logarithmic-functions/250697: if f(x) = 3^(2 - 3x) then the value of [f(1 + x)][f(1 - x)] is....? Thanks, please show steps and explain! 1 solutions Answer 184751 by drk(1908)   on 2009-12-30 12:29:28 (Show Source): You can put this solution on YOUR website!Here is the original equation: (i) f(x) = 3^(2 - 3x) We want first, [f(1 + x)] wherever you see x replace it with 1 + X. We get f(1 + X) = 3^(2 - 3*(1 + X)) (ii) f(1 + X) = 3^(-3X - 1) Second, [f(1 - x)] wherever you see x replace it with 1 - X. We get f(1 - X) = 3^(2 - 3*(1 - X)) (iii) f(1 - X) = 3^(3X - 1) Now, we multiply (ii) and (iii) to get (iv) [f(1 + X)][f(1 - X)] = 3^(-3X - 1) * 3^(3X - 1) Since the bases are the same, we just add the exponents. We get (v) [f(1 + X)][f(1 - X)] = 3^(-2) = 1/9.
 percentage/252701: 2/3%of ?=33.31 solutions Answer 184750 by drk(1908)   on 2009-12-30 12:23:24 (Show Source): You can put this solution on YOUR website!Here is the question (i) 2/3%of ?=33.3 rewrite the percent as / 100. 2/300 * X = 33.3 --- Now we solve. multiply both sides by 300. 2X = 9990 divide by 2. X = 4995.
 Average/250698: What are the zeros of p(x)=x^4+7x^3+9x^2-17x-20 solved algebraically?1 solutions Answer 184749 by drk(1908)   on 2009-12-30 12:20:16 (Show Source): You can put this solution on YOUR website!We are given this polynomial: p(x) = x^4 + 7x^3 + 9x^2 - 17x - 20. Using PNI, we get P . . . N . . . I 1 . . . 3 . . . 0 1 . . . 1 . . . 2. So, I know there MUST be 1 positive root. Now I look at P/Q; all the factors of 20 over all the factors of 1. +-20 +-10 +-5 +-4 +-2 +-1. I use synthetic division until I find a hit: (X + 4) and (X + 1) are factors of P(x). So, (X + 4)(X + 1)[X^2 + 2X - 5] = P(x). The zero's become X = -4, -1, -1 + sqrt(6), -1 - sqrt(6).
 Triangles/250699: what kind of triangle (acute, obtuse, or right) is radical 73, radical 66, radical 81 solutions Answer 184748 by drk(1908)   on 2009-12-30 12:12:18 (Show Source): You can put this solution on YOUR website!We need the Pythagorean theorem: (i) a^2 + b^2 = C^2. There are really three choices: If a^2 + b^2 < C^2 then obtuse If a^2 + b^2 = C^2 then right If a^2 + b^2 > C^2 then acute --- The numbers given must be expressed from least to greatest: sqrt(8), sqrt(66), and sqrt(73). Put them into (i) and find out which of the three we get. (sqrt(8))^2 + (sqrt(66))^2 ? (sqrt(73))^2 8 + 66 ? 73 74 > 73. So we say acute.
 Linear-systems/250700: A 50 foot pipe is is cut into two pieces. The length of 1 piece is 9 times the length of the other. What is the length of the longer piece?1 solutions Answer 184746 by drk(1908)   on 2009-12-30 12:07:02 (Show Source): You can put this solution on YOUR website!The pipe is broken into two pieces. Let the first piece be X and the second piece is 9X. X + 9X = 50. 10X = 50 X = 5. One piece is 5 feet and the other piece is 45 feet.
 Linear-equations/250701: I have this problem that says simplify 5[42-(10-90)] i came up with 610 and I'm not so sure its right can someone help me thanks1 solutions Answer 184744 by drk(1908)   on 2009-12-30 12:05:06 (Show Source): You can put this solution on YOUR website!Here is the original equation: 5[42-(10-90)] --- Using order of operations, 10-90 first. 5[42-(-80)] --- a double negative is positive. So, 5[42+80] --- Now, we simplify the (_) 5[122] --- Finally multiply to get 610.
 Linear-systems/250702: The sum of two numbers is -64. Twice the first number is 1 more than the second. Find the two numbers 1 solutions Answer 184743 by drk(1908)   on 2009-12-30 12:02:24 (Show Source): You can put this solution on YOUR website!Let X = first number and Y = second number. The sum of two numbers is -64 can be translated as (i) X + Y = -64 Twice the first number is 1 more than the second can be translated as (ii) 2X = Y + 1. We can use substitution to solve. Solve the (ii) for Y. We get (iii) Y = 2X - 1 Substitute (iii) into (i) to get (iv) X + 2X - 1 = -64 Solve for X. 3X - 1 = -64 3X = -63 X = -21 Find Y. Y = -43.
 Linear-equations/250786: I need to solve a compound inequality 7>-4x+6 or 10≤-5x+4 I have the solution as (-∞,∞)is this correct? someone please, thank you1 solutions Answer 184742 by drk(1908)   on 2009-12-30 11:59:05 (Show Source): You can put this solution on YOUR website!You are given the following 7>-4x+6 or 10≤-5x+4. We first solve the left side: 7 > -4x + 6 1 > -4X -1/4 < X; notice the switch of inequality when dividing by (-). Now, we solve the right side: 10 ≤ -5x + 4 6 ≤ -5x X ≤ -(6/5); notice the switch of inequality when dividing by (-). So, the answer I have is: (-∞,-6/5] u (-1/4,∞).