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# Recent problems solved by 'ewatrrr'

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 Quadratic-relations-and-conic-sections/410585: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function f(x)=2x^2-12x+201 solutions Answer 288689 by ewatrrr(10682)   on 2011-02-17 10:42:46 (Show Source): You can put this solution on YOUR website! ``` Hi Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function f(x)=2x^2-12x+20 Using the vertex form of a parabola, where(h,k) is the vertex f(x)=2(x^2-6x)+20 |completing square to put into vertex form f(x)=2[(x-3)^2 - 9] +20 f(x) = 2(x-3)^2 -18 + 20 f(x) = 2(x-3)^2 + 2 |Vertex is Pt(3,2) Line of symmetry is x= 3 ```
 Numbers_Word_Problems/410577: What is : 7 more than a number1 solutions Answer 288687 by ewatrrr(10682)   on 2011-02-17 10:30:46 (Show Source): You can put this solution on YOUR website! ``` Hi What is : 7 more than a number Letting x represent the number, it would be: x + 7 ```
 Rate-of-work-word-problems/410433: a printer can print 50 pages in 2 minutes, how many pages can it print in 30 minutes 1 solutions Answer 288684 by ewatrrr(10682)   on 2011-02-17 10:28:46 (Show Source): You can put this solution on YOUR website! ``` Hi Let x represent pages that can be printed in 30 minutes Question states*** a printer can print 50 pages in 2 minutes Sets Up the Proportion 2x = 1500 x = 750, pages that can be printed in 30 minutes ```
 Rate-of-work-word-problems/410460: It takes 6 people to build a house in 8 days, how many people does it take to build a house in one day?1 solutions Answer 288680 by ewatrrr(10682)   on 2011-02-17 10:22:41 (Show Source): You can put this solution on YOUR website! ``` Hi Question states*** 6 people build a house in 8 days: that is 1/8 built per day and (1/8) /6 = 1/48 built per person per day how many people does it take to build a house in one day? 48 people. ```
 Rate-of-work-word-problems/410517: If 3 people working together at the same rate can do a job in 5 1/3 days, what fraction of that job can 2 of these people do in 1 day?1 solutions Answer 288677 by ewatrrr(10682)   on 2011-02-17 10:16:21 (Show Source): You can put this solution on YOUR website! ``` Hi 3 people working together at the same rate can do a job in 5 1/3 OR 16/3 days: that is: 3/16 of the job per day with each person doing (3/16)/3 = 3/48 = 1/16 per day what fraction of that job can 2 of these people do in 1 day? 2*1/16 = 2/16 = 1/8 of the job ```
 Rate-of-work-word-problems/410571: Jane, Paul and Peter can finish painting the fence in 2 hours. If Jane does the job alone she can finish it in 5 hours. If Paul does the job alone he can finish it in 6 hours. How long will it take for Peter to finish the job alone?1 solutions Answer 288675 by ewatrrr(10682)   on 2011-02-17 10:06:53 (Show Source): You can put this solution on YOUR website! ``` Hi Let x represent the time it would take Peter solo Question states*** Per hour the Equalizer 1/5 + 1/6 + 1/x = 1/2 Solving for x 6x + 5x + 30 = 15x |Multiplying thru by 30x so as all denominators = 1 30 = 4x x = 30/4 or 7.5 hrs, time it would take Peter solo CHECKING our Answer*** 6/30 + 5/30 + 4/30 = 15/30 = 1/2 ```
 Problems-with-consecutive-odd-even-integers/410564: Using correct mathematical notation and symbols, express the following in set-builder notation: Z = {17, 18, 19, 20, 21, 22, 23, 24, 25}1 solutions Answer 288673 by ewatrrr(10682)   on 2011-02-17 10:01:33 (Show Source): You can put this solution on YOUR website! ``` Hi Z = {17, 18, 19, 20, 21, 22, 23, 24, 25} in set-builder notation: {x Z |x ≥ 17 and x ≤ 25} Verbally this says: "the set of all x's that are a member of() the set of Integers(Z), such that(|) x is greater than or equal to 17 and less than or equal to 25" ```
 Travel_Word_Problems/410561: two trains are 330 miles apart. one train is traveling 20 mph faster than the other. find the speed of each train if they are traveling toward each other and will meet in 3 hours.1 solutions Answer 288671 by ewatrrr(10682)   on 2011-02-17 09:48:47 (Show Source): You can put this solution on YOUR website!``` Hi Let x and (x+20mph)represent their respective speeds. t = D/r Question states*** 330/x + 330/(x+20) = 3hr Solving for x 330(x+20) + 330x = 3x(x+20) 660x + 6600 = 3x^2 + 60x 3x^2 -600x - 6600 = 0 3(x^2 - 200x - 2200) = 0 x = 210.4536 |negative solution tossed out for speed CHECKING our Answer*** 330/210 + 330/230 = 3hr |to the nearest whole number ```
 Quadratic_Equations/410547: i would like to know the vertex and the axis of symmetry and how to get both of these with work shown thanks.: 1/4(x+2)^2+6 and another equation: 2(x+2)(x+4)1 solutions Answer 288665 by ewatrrr(10682)   on 2011-02-17 09:12:12 (Show Source): You can put this solution on YOUR website! ``` Hi Using the vertex form of a parabola, where(h,k) is the vertex y = 1/4(x+2)^2+6 |Vertex is Pt(-2,6), Axis of symmetry is x = -2 y = 2(x+2)(x+4) y = 2(x^2 + 6x + 8) y = 2[(x+3)^2 - 9 + 8] y = 2(x+3)^2 - 2 |Vertex is Pt(-3,-2), Axis of symmetry is x = -3 ```
 Exponential-and-logarithmic-functions/410548: Hi could you show me the steps to solving 8=2^(x-4)? Thank You :)1 solutions Answer 288662 by ewatrrr(10682)   on 2011-02-17 08:58:55 (Show Source): You can put this solution on YOUR website! ``` Hi 8 = 2^(x-4) 2^3 = 2^(x-4) 3 = (x-4) 7 = x CHECKING our Answer*** 8 = 2^(7-4) = 2^3 ```
 Exponential-and-logarithmic-functions/410544: Could you show me the steps you did to solve 64^x=16^(x-1)1 solutions Answer 288661 by ewatrrr(10682)   on 2011-02-17 08:55:43 (Show Source): You can put this solution on YOUR website! ``` Hi 64^x=16^(x-1) (2^6)^x = (2^4)^(x-1) 2^6x = 2^4(x-1) 6x = 4(x-1) 2x = -4 x = -2 CHECKING our Answer*** 64^-2 = 16 ^-3 1/4096 = 1/4096 ```
 Linear-equations/410355: Please help me solve this graph (y=1/5x-2).1 solutions Answer 288659 by ewatrrr(10682)   on 2011-02-17 08:47:40 (Show Source): You can put this solution on YOUR website!``` Hi graph (y=1/5x-2). y = (1/5)x - 2 |y-intercept is Pt(0,-2) Note: as y increases/decreases by 1, x increases/decreases by 5 Pt(5, -1) and Pt(-5, -3) on the Line. Plotting Pts and connecting with line ```
 Linear-equations/410537: Graph the line that passes through (3,1) parallel to a line whose slope is -0.51 solutions Answer 288657 by ewatrrr(10682)   on 2011-02-17 08:40:37 (Show Source): You can put this solution on YOUR website! ``` Hi Graph the line that passes through (3,1) parallel to a line whose slope is -0.5 y = -.5x + b |using order pair Pt(3,1) to solve for b 1 = -1.5 + b 2.5 = b y = (-1/2)x + 5/2 |y-intercept is Pt(0,5/2) Note: as y increases/decreases by 1, x increases/decreases by 2 in opposite direction Pt(2, 3/2) and Pt(-2, 7/2) on the Line. Plotting Pts and connecting with line ```
 Age_Word_Problems/410525: Paul is 12. His father is 33. How many years ago was the father 4 times as old as the son? 1 solutions Answer 288655 by ewatrrr(10682)   on 2011-02-17 08:33:50 (Show Source): You can put this solution on YOUR website! ``` Hi Paul is 12. His father is 33 Let x represent How many years ago was the father 4 times as old as the son? Question states*** 'x' years ago... 33-x = 4*(12-x) Solving for x 33-x = 48 - 4x 3x = 15 x = 5, the years ago the father was 4 times as old as the son CHECKING our Answer*** 33-5 = 28 = 4*(12-5) ```
 Age_Word_Problems/410520: Maria is now 3 years younger that her sister Ann. Four years ago, Maria's age was one-half Ann's age. How old is each girl now?1 solutions Answer 288654 by ewatrrr(10682)   on 2011-02-17 08:29:40 (Show Source): You can put this solution on YOUR website! ``` Hi Maria is now 3 years younger that her sister Ann. Let x and (x-3) represent Ann's and Maria's ages NOW respectively Question states***four years ago... (x-3) - 4 = x/2 Solving for x x - 7 = x/2 x/2 = 7 x = 14, Ann's age now. Maria is 11 (14-3) CHECKING our Answer*** 11-4 = 14 = 7 ```
 Problems-with-consecutive-odd-even-integers/399115: find 3 consecutive integers such that the sum of twice the second and three times the third is 5 less that six times the first1 solutions Answer 288650 by ewatrrr(10682)   on 2011-02-17 08:19:04 (Show Source): You can put this solution on YOUR website! ``` Hi Find three consecutive integers Let x, (x+1), (x+2) represent the three consecutive integers respectively Question states*** 2(x+1) + 3(x+2) = 6x - 5 Solving for x 5x + 8 = 6x - 5 13 = x The three consecutive integers are 13,14,15 CHECKING our Answer*** 2*14 + 3*15 = 73 = 78 - 5 ```
 Problems-with-consecutive-odd-even-integers/406344: Eight times the sum of three consecutive even integers is 108 more than 21 times the smallest of three integers1 solutions Answer 288648 by ewatrrr(10682)   on 2011-02-17 08:10:47 (Show Source): You can put this solution on YOUR website! ``` Hi Find three consecutive integers Let x, (x+1), (x+2) represent the three consecutive integers respectively Question states*** 8[x+ (x+1)+ (x+2)] = 21x + 108 Solving for x 8(3x + 3) = 21x + 108 24x + 24 = 21x + 108 3x = 84 x = 28 The three consecutive integers are 28,29,30 CHECKING our Answer*** 8*87 = 696 = 588 + 108 ```
 Problems-with-consecutive-odd-even-integers/408369: Find three consecutive integers such that the sum of the first and second is 9 more than half of the third.1 solutions Answer 288647 by ewatrrr(10682)   on 2011-02-17 08:05:45 (Show Source): You can put this solution on YOUR website! ``` Hi Find three consecutive integers Let x, (x+1), (x+2) represent the three consecutive integers respectively Question states*** x + (x+1) = (x+2)/2 + 9 Solving for x 2x + 1 - x/2 = 1 + 9 (3/2)x = 9 x = 6 The three consecutive integers are 6,7,8 CHECKING our Answer*** 6+7 = 4 + 9 ```
 Problems-with-consecutive-odd-even-integers/410527: one is twice another number.When the larger number is diminished by 10, the result is two greater than the smaller. Find the numbers.1 solutions Answer 288645 by ewatrrr(10682)   on 2011-02-17 08:00:50 (Show Source): You can put this solution on YOUR website! ``` Hi one is twice another number Let x and 2x represent the smaller number and larger number respectively Question states*** 2x - 10 = x+2 Solving for x x = 12, the smaller number. The larger number is 24. CHECKING our Answer*** 24-10 = 12 + 2 = 14 ```
 Probability-and-statistics/410115: 4. The number of baby deliveries in a small hospital was sampled over 6 hour periods. Below is the sample: 11 12 7 16 4 8 9 7 3 4 9 4 6 12 9 8 4 6 12 From this data set, compute the sample mean, median, mode and midrange. Compute the 1st quartile and 3rd and interpret their meanings.1 solutions Answer 288489 by ewatrrr(10682)   on 2011-02-16 14:41:26 (Show Source): You can put this solution on YOUR website! ``` Hi mean = 7.9473 (151/19) median = 8 |(19+1)/2 or tenth term mode = 4 (most frequent) midrange (16-3)/2 = 7.5 1st quartile = 4 |(19+1)/4 or the 5th term | 25% are less than this 3rd quartile = 9 |25% are greater than this 3 4 4 4 4 6 6 7 7 8 8 9 9 9 11 12 12 12 16 ```
 Graphs/410012: 1.what is the equation of line passes through points (4,-6) and has a slope of -3 2..what equation represent a line parallel to the graph of 2x-4y=161 solutions Answer 288485 by ewatrrr(10682)   on 2011-02-16 14:16:00 (Show Source): You can put this solution on YOUR website! ``` Hi 1.what is the equation of line passes through points (4,-6) and has a slope of -3 y = -3x + b |using ordered pair pt( 4,-6) to solve for b -6 = -12 6 = b | y = -3x+6 OR 3x+y = 6 2.what equation represent a line parallel to the graph of 2x-4y=16 2x-4y=16 OR y = (1/2)x - 4 |these 'parallel' lines would have m = (1/2) New Line y = (1/2)x + b | b can be any real value for this line ```
 Graphs/410104: What is the equation of a line with a slope of -5 and containing point (2,4)?1 solutions Answer 288484 by ewatrrr(10682)   on 2011-02-16 14:09:43 (Show Source): You can put this solution on YOUR website! ``` Hi What is the equation of a line with a slope of -5 and containing point (2,4)? y = -5x + b |using ordered pair pt(2,4) to solve for b 4 = -10 14 = b | y = -5x+14 OR 5x+y = 14 ```
 Graphs/410121: Find the slope and y-intercept of the line. Graph the line. 1/4y=x-21 solutions Answer 288483 by ewatrrr(10682)   on 2011-02-16 14:07:06 (Show Source): You can put this solution on YOUR website! ``` Hi Find the slope and y-intercept of the line. Graph the line: 1/4y=x-2 1/4y=x-2 OR y = 4x - 8 |slope m = 4 and the y-intercept is Pt(0,-8) ```
 Graphs/410116: Find the equation of the line that has the given properties. Express the equation in slope-intercept form. slope=-7; y-intercept=41 solutions Answer 288482 by ewatrrr(10682)   on 2011-02-16 14:04:45 (Show Source): You can put this solution on YOUR website! ``` Hi Find the equation of the line that has the given properties. Express the equation in slope-intercept form: slope=-7; y-intercept=4 slope=-7; y-intercept=4 | y = -7x + 4 ```
 Numbers_Word_Problems/410120: One number is 10 times as large as another, and their difference is 81. Find the numbers. If x represents the smaller number, then the larger number is 1 solutions Answer 288480 by ewatrrr(10682)   on 2011-02-16 14:02:25 (Show Source): You can put this solution on YOUR website! ``` Hi One number is 10 times as large as another Let x and 10x represent the numbers Question states*** 10x - x = 81 Solving for x 9x = 81 x = 9 The numbers are 9 and 90. CHECKING our Answer*** 90 - 9 = 81 ```
 Graphs/410119: Find the equation of the line that contains the point (6,-9) and has a slope that is undefined.1 solutions Answer 288479 by ewatrrr(10682)   on 2011-02-16 13:59:54 (Show Source): You can put this solution on YOUR website! ``` Hi Verical lines have undefined slopes: the x-value NEVER changes m = change(y)/change(x) (cannot divide by zero!) ```
 Miscellaneous_Word_Problems/410054: Is there a strategy which explains the step-by-step procedure for solving algebraic word problems? 1 solutions Answer 288475 by ewatrrr(10682)   on 2011-02-16 13:48:38 (Show Source): You can put this solution on YOUR website! ``` Hi My recommendation would be to follow the following steps: I.Defining the variable(s), might recommend using x for consistency majority of problems can be written in terms of one variable, Some require two variables and two equations, rare to see them here. II.Stating the Question Algebraically III.Solving for x IV.CHECKING the Answer*** Example: a movie was was attended by 212 people. Children's tickets were \$4 and adult tickets were \$8. If the amount from tickets sales was \$1448, how many children and how many adults attended? I.Let x and (212-x) represent the number of adult and children's tickets respectively II.Question states*** 8x + 4(212-x) = 1448 III.Solving for x 4x = 600 x = 150, number of adult tickets. 62 children's tickets. (212-150) Iv.CHECKING our Answer*** \$8*150 + \$4*62 = \$1200 + \$248 = \$1448 ```
 Linear-equations/409915: 1) What is the equation of the line whose y-intercept is 3 and slope is 1? y = x - 3 y = x + 3 y = 3x + 1 2) What is the slope of a line parallel to the line whose equation is y - x = 5? -1 1 5 3)What is the equation of a line that passes through points (-1, 2) and (5, 2)? y - 2 = 0 x - 2 = 0 y - x - 2 = 0 4)What is the equation of a line with a slope of -2 and a y-intercept of 8? x + 2y - 8 = 0 2x + y - 8 = 0 2x - y + 8 = 0 5)What is the equation of the line that passes through the point (1, 1) and has a y-intercept of 2. x - y + 2 = 0 x + y - 2 = 0 x - y - 2 = 0 1 solutions Answer 288452 by ewatrrr(10682)   on 2011-02-16 11:39:33 (Show Source): You can put this solution on YOUR website! ``` Hi Using the point-slope formula, 1) What is the equation of the line whose y-intercept is 3 and slope is 1 y = x + 3 2) What is the slope of a line parallel to the line whose equation is y - x = 5 y-x=5 Or y = x+5 |slope of these parallel lines is m = 1 3)What is the equation of a line that passes through points (-1, 2) and (5, 2)? (-1, 2) and (5, 2) m = 0 y = 2 OR y-2 = 0 4)What is the equation of a line with a slope of -2 and a y-intercept of 8? y = -2x + 8 OR 2x+ y -8 = 0 5)What is the equation of the line that passes through the point (1, 1) and has a y-intercept of 2, thus Pt(0,2) (1,1) (0,2) m = -1 y = -x + b |using ordered pair Pt(0,2) to solve for b 2 = b y = -x + 2 ```
 Linear-equations/409730: Write the slope-intercept equation for the line that passes through (5,4) and (7,8). Please show all of work.1 solutions Answer 288451 by ewatrrr(10682)   on 2011-02-16 11:25:11 (Show Source): You can put this solution on YOUR website! ``` Hi Write the slope-intercept equation for the line that passes through (5,4) and (7,8) Using the point-slope formula, (5,4) and (7,8) m = -4/-2 = 2 y = 2x + b |using ordered pair Pt(5,4) to solve for b 4 = 10 + b -6 = b y = 2x -6 ```
 Linear-equations/409777: find the linear equation passing through the given point: (4,2) (-3,5)1 solutions Answer 288450 by ewatrrr(10682)   on 2011-02-16 11:20:40 (Show Source): You can put this solution on YOUR website! ``` Hi find the linear equation passing through (4,2) (-3,5) Using the point-slope formula, ( 4,2) (-3,5) m = -3/7 y = (-3/7)x + b |using ordered pair Pt(4,2) to solve for b 2 = -12/7 + b 26/7 = b y = (-3/7)x + 26/7 ```
 Linear-equations/410040: Find the slope and y-intercept of the line in the given equation Y=4/9x-20 1 solutions Answer 288449 by ewatrrr(10682)   on 2011-02-16 11:12:41 (Show Source): You can put this solution on YOUR website! ``` Hi Find the slope and y-intercept of the line in the given equation y=4/9x-20 y = (4/9)x-20 |slope= 4/9 and y-intercept is Pt(0,-20) ```