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# Recent problems solved by 'oberobic'

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 Linear-equations/283026: graph the line containing the given pair of points and find the slope. (5,4),(-4,-3) graph it on a y is -10,10 graph and x is -10 an 10 graph. then find the slope- m=1 solutions Answer 205542 by oberobic(2304)   on 2010-03-20 12:21:20 (Show Source): You can put this solution on YOUR website!The slope-intercept form is: y = mx+b, where m is the slope and b is the y-intercept (the point were x=0). . The slope is defined as the rise over the run, which is the change in 'y' divided by the change in 'x'. . m = (y2-y1)/x2-x1) . (x1,y1) = (5,4) (x2,y2) = (-4,-3) . m = (-3 -4)/(-4-5) m = -7/-9 = 7/9 . y = 7/9x + b . Substitute what we know already to find 'b'. . For example, we know the point (5,4) is on the line. . 4 = 7/9(5) + b . Multiply through by 9 to remove the fraction . 36 = 7(5) + 9b 36 = 35 + 9b 1 = 9b 9b = 1 b = 1/9 . Now we can find the x-intercept, which is the point where y=0. 0 = 7/9x + 1/9 . multiply through by 9 . 9(0) = 7x + 1 0 = 7x + 1 x = -1/7 (-1/7,0) . So, to summarize: Equation is: y = 7/9x + 1/9 y-intercept is: (0, 1/9) x-intercept is: (-1/7, 0) . Graphing it helps confirm your work. . Done
 Mixture_Word_Problems/283127: A farmer wants to mix a liquid fertilizer that contains 2% nitrogen with one that contains 10% nitrogen to obtain 40 gallons of a fertilizer that contains 8% nitrogen. How many gallons of each fertilizer should be used?1 solutions Answer 205539 by oberobic(2304)   on 2010-03-20 12:08:15 (Show Source): You can put this solution on YOUR website!When solving solution problems, you need to keep track of how much 'pure' stuff you need. In this case the problem states you need 40 gal. of 8% nitrogen fertilizer: 40*.08 = 3.2 gal. 'pure' nitrogen. . The materials on hand include 2% and 10% nitrogen in liquid form, so we assume we have as much of these two as we may need. . Since the final amount needed is 40 gal., we can define the two mixtures in terms of the variable 'x'. x = amount of 2% nitrogen fertilizer 40 - x = amount of 10% fertilizer. . The objective equation we need to solve thus becomes: . .02x + .10(40-x) = .08*40 = 3.20 gal. . multiplying through by 100 will remove the decimals . 2x + 10(40-x) = 320 . expanding . 2x + 400 - 10x = 320 . collecting . -8x = 320 - 400 = -80 . divide both sides by -8 . x = -80/-8 = 80/8 = 10 . Since we need 10 gal. of 2% solution, we need 40-10 = 30 gal of 10%. . 40-x = 30 . Therefore, we think that we need 10 gal. of 2% and 30 gal. of 10%. . But we always need to check our answer... . How much 'pure' stuff do we have in the 40 gallons we propose? . 10 gal. @ 2% = .02*10 = 0.2 gal. 30 gal. @ 10% = .10*30 = 3 gal. 0.2+3 = 3.2 gal. Correct . Answer: Mix 10 gallons of 2% and 30 gallons of 10% nitrogen fertilizer to produce 40 gallons of 8% solution. . Done.
 Problems-with-consecutive-odd-even-integers/282962: th ediffrence between 2 numbers is 34. the larger number is 4 more than 3 times the smaller number. whats the numbers?1 solutions Answer 205428 by oberobic(2304)   on 2010-03-19 18:57:18 (Show Source): You can put this solution on YOUR website!We have two numbers: x & y. . The difference is 34. . x - y = 34 . The larger number is 4 more than 3 times the smaller. . Well, since I decided that x-y is a positive number, then x > y. . x = 3y + 4 . Since x - y = 34, then . x = y + 34 . Substitute x = y+34 to find the value of 'y' . y+34 = 3y + 4 . subtract y from both sides . y -y +34 = 3y-y + 4 . 34 = 2y + 4 . subtract 4 from both sides . 34-4 = 2y +4-4 . 30 = 2y . so . 2y = 30 . divide both sides by 2 . y = 15 . substitute y=15 into the first equation to find 'x' . x - 15 = 34 . x = 49 . check this answer by substituting these values for x and y into the second equation . x = 3y + 4 . 49 = 3(15) + 5 Correct . Answer: x = 49 y = 15 . Done.
 Square-cubic-other-roots/282954: how do i factor sqrt 48a^2b1 solutions Answer 205415 by oberobic(2304)   on 2010-03-19 17:54:34 (Show Source): You can put this solution on YOUR website!Assuming, the expression is: . . . . . Done
 Linear-equations/282931: Find the volume of a cylinder with a diameter of 12 feet and a height of 15 feet. Round the answer to the nearest whole number.1 solutions Answer 205414 by oberobic(2304)   on 2010-03-19 17:47:26 (Show Source): You can put this solution on YOUR website!Volume of a cylinder= pi*r^2*h where pi = the constant pi r = radius r^2 = r*r h = height . diameter = 12, so radius =6 . height = 15 . V = pi * 6 ft * 6 ft * 15 ft . V = pi * 36 ft^2 * 15 ft . V = pi * 540 ft^3 . V = 1696.46 ft^3 . Done.
 Linear-equations/282943: 8 Solve for x: ( 4x – 6)/2 = -3x + 2 1 solutions Answer 205412 by oberobic(2304)   on 2010-03-19 17:35:33 (Show Source): You can put this solution on YOUR website! . . Add 3x to both sides... . Add 3 to both sides . Divide both sides by 5 . Check... . Correct . Answer: x=1 . Done
 Expressions-with-variables/282723: I tried to figure this one out but I am having problems with it, can you help me with this one? I put x+1hr. =500 500 divided by x. Problem: If a trucker drives 500 miles in x+1 hours, then what is his average speed?1 solutions Answer 205266 by oberobic(2304)   on 2010-03-18 23:08:29 (Show Source): You can put this solution on YOUR website!In this case, speed is measured in miles per hr, which is shown as 'mph' but really is miles/hours. . The average speed = distance / time. . miles/hr . Done
 Expressions-with-variables/282722: Can you please help me with this problem. I was trying to figure it out, so I wrote 100pnds divided by x. If a wholesaler buys 100 pounds of shrimp for x dollars, then what is the price per pound?1 solutions Answer 205264 by oberobic(2304)   on 2010-03-18 23:03:00 (Show Source): You can put this solution on YOUR website!The key to this problem is to keep track of your units of measurement. Oftentimes the units of measurement will help you figure out what to divide by what or what to multiply by what. . The shrimp is priced at \$ per lb, which is shown as \$/lb. That tells you you need to divide the \$ by the lb. . He paid \$x for 100 lb. . So it would be \$x/100 lb = x/100 \$/lb . Done.
 Distributive-associative-commutative-properties/282693: factor completely factor 2t^3z^4 - 2t^31 solutions Answer 205262 by oberobic(2304)   on 2010-03-18 22:58:01 (Show Source): You can put this solution on YOUR website!Here's a start...
 Linear_Equations_And_Systems_Word_Problems/282709: The population of the US was 151 nillion in 1950 and 249 million in 1990. find the slope of the line through the 2 points defined by the population data. Write a linear equation to model the population fo the US t years after 19501 solutions Answer 205259 by oberobic(2304)   on 2010-03-18 22:50:20 (Show Source): You can put this solution on YOUR website!Start with 1950, which which we are told should be year t=0. y = 151 million in 1950. y = mx + b is the slope-intercept form. . We're using the year to predict the population, so t=x-axis. The population is plotted on y-axis as the dependent variable. . So we would define it as: y = mt + 151, which define defines the point (0,151) . 1990 would be t=40 1990 population is 249 million So it would be plotted at (40,249) . The slope = rise/run rise = change in y = 249-151 = 98 run = change in x = change in t = 40-0 = 40 m = slope m = 98/40 . That means our equation is: . y = 98/40*t + 151 . Graph it to check . .
 Rectangles/282715: a rectangles lengeth is five inches less than four times its width. if the perimeter is fourty inches what are the dimensions of the rectangle 1 solutions Answer 205253 by oberobic(2304)   on 2010-03-18 22:36:37 (Show Source): You can put this solution on YOUR website!L = length W = width P = 2L + 2W = perimeter . P = 40 :: given . L = 4W -5 :: length is 5 less than 4*Width . Substitute and solve for W. . 2L + 2W = P 2(4W-5) + 2W= 40 8W -10 + 2W = 40 10W -10 = 40 10W = 50 W = 5 . L = 4W-5 L = 4(5) -5 L = 20 - 5 L = 15 . Checking the perimeter will tell if this is the right answer 2L + 2W = 40?? . 2(15) = 30 2(5) = 10 30+10 = 40 Correct. . Answer: The dimensions of the rectangle are length = 15 and width = 5. . Done.
 Linear-systems/282711: Four gallons of a 45% acid solution is obtained by mixing a 90% solution with a 30% solution. How many gallons of each solution must be used to obtain the desired mixture?1 solutions Answer 205250 by oberobic(2304)   on 2010-03-18 22:31:47 (Show Source): You can put this solution on YOUR website!When solving solution problems, you need to focus on how much 'pure' stuff you need. In this case, you need to produce 4 gal. of a desired 45% solution. That means you will need .45*4 = 1.8 gal. of the 'pure' stuff. The simplest way would be to take 1.8 of 'pure' stuff and add 2.2 gal. of water, but you do not have that option. Instead you have to use 90% and 30% solutions. . Defining the amounts of is critical. x = amount of 90% solution y = amount of 30% solution 4 = total amount of 45% solution . So y = 4-x, which will make the job of solving easier. . .9x + .3(4-x) = .45*4 .9x + 1.2 -.3x = 1.8 .6x + 1.2 = 1.8 .6x = .6 x = 1 . That means you would propose to use 1 gal. of 90% solution + 3 gal. of 30% solution. . Check by determining if that is enough 'pure' stuff. 1*.9 = .9 3*.3 = .9 .9 + .9 = 1.8, which is what you needed. . Answer: Mix 1 gal. of 90% solution with 3 gal. of 30% solution to obtain 4 gal. of 45% solution. . Done.
 Distributive-associative-commutative-properties/282710: Factor 7x^2+xy+2y+14x1 solutions Answer 205241 by oberobic(2304)   on 2010-03-18 22:18:42 (Show Source): You can put this solution on YOUR website!7x^2 + xy + 2y + 14x . 7x^2 + 14x + xy + 2y . 7x(x+2) + y(x+2) . (7x+y)(x+2) . Done
 Linear-equations/282706: If i needed 2 points to be in Y intercept form, what would the answer be for (-5,2) and (4,1)? y=mx+b should bt the form. Thanks.1 solutions Answer 205239 by oberobic(2304)   on 2010-03-18 22:16:11 (Show Source): You can put this solution on YOUR website!y = mx+b is slope-intercept form, where m = slope b = y-intercept (defined by x=0) . Two points can be used to draw a line. (-5,2) and (4,1) . You also can determine the slope by computing the rise over the run. rise = change in y = y2 - y1 run = change in x = x2 - x1 . We can define either point what we want, but we have to keep consistent. (x1, y1) = (-5, 2) (x2, y2) = (4, 1) . rise = 1-2 = -1 run = 4 -(-5) = 4+5 = 9 . So, m = -1/9 . That means y= -1/9x + b . Now we have to compute 'b' to ensure it goes through the points given. . We know that when x=4, y=1 Substituting, we find 'b' . 1 = -1/9*4 + b 1 + 4/9 = b 9/9 + 4/9 = b 13/9 = b . So, we now have the equation: y = -1/9x + 13/9 Slope = -1/9 y-intercept = (0, 13/9) . The x-intercept occurs where y=0, so we can solve by substitution again. 0 = -1/9x + 13/9 The obvious answer is x=13, so the point is (13,0). . Graphing is a good way to check your work. .
 expressions/282705: factor 3y - 3w + yt - tw1 solutions Answer 205236 by oberobic(2304)   on 2010-03-18 22:05:33 (Show Source): You can put this solution on YOUR website!3y - 3w + yt - tw = 3(y-w) + t(y-w) = (3+t)(y-w) . Done.
 Rectangles/282703: A certain rectangle's length is 5 feet longer than its width. If the area of the rectangle is 50 square feet, find its larger dimension1 solutions Answer 205234 by oberobic(2304)   on 2010-03-18 22:01:56 (Show Source): You can put this solution on YOUR website!L = length W = width Area= L*W, for a rectangle A = 50 ft^2 :: given . L = W + 5 :: Length is 5 ft longer than the width, so you have to add 5 to W to make them equal . Substitute L=W+5 . (W+5) * W = 50 . Collect and simplify . W^2 + 5W = 50 W^2 + 5W - 50 = 0 (W + 10)(W - 5) = 0 . So our candidate solutions are W= -10 and W=5. But a negative width is nonsensical, so our only practical option is W=5. . Substituting W=5, we can find L. . L = W+5 L = 5+5 = 10 . Checking the answer, we see 5*10 = 50, which matches the setup 10 = 5+5, which also matches the setup . Answer: The larger dimension is the length, which is 10. The width is 5. . Done.
 Systems-of-equations/282501: what is the answer in (x,y) form? 4x+2y=6 4x-5y=-1 1 solutions Answer 205204 by oberobic(2304)   on 2010-03-18 19:31:00 (Show Source): You can put this solution on YOUR website!Solve using a system of linear equations. . 4x +2y = 6 4x -5y = -1 . subtract them . 7y = 7 y = 1 . substitute y=1 into the first equation . 4x +2(1) = 6 4x = 4 x = 1 . So it appears the solution is (1,1). . Graph the two equations it to check, but first you need to get them into y = mx+b form. . 4x+2y = 6 2y = -4x+6 y = -2x + 3 . 4x -5y = -1 -5y = -4x -1 y = 4/5x + 1/5 .
 Numbers_Word_Problems/282584: The product of the numbers on two consecutive pages in a book is 600. Find the page numbers. x(x+1)=600 2x=600 x=300?1 solutions Answer 205199 by oberobic(2304)   on 2010-03-18 19:16:24 (Show Source): You can put this solution on YOUR website!Two consecutive page numbers would be, for example, 1 & 2 or 323 and 324 or x and x+1. . x(x+1) = 600 x^2 + x - 600 = 0 (x-24)(x+25) = 0 . So there are two solutions: x=24 and x=-25. . But a negative page number does not make any sense. So the answer is: . x = 24 x+1= 25 . Done
 Distributive-associative-commutative-properties/282600: factor x^2+4x-121 solutions Answer 205196 by oberobic(2304)   on 2010-03-18 19:08:26 (Show Source): You can put this solution on YOUR website!x^2 +4x -12 = (x +6)(x -2) . check using FOIL (first, outer, inner, last) . x*x + x*(-2) + 6*x + 6*(-2) = x^2 +4x -12 . Done
 Polynomials-and-rational-expressions/282606: x^-x-30=0 I need help on how to figure this problem1 solutions Answer 205195 by oberobic(2304)   on 2010-03-18 19:05:33 (Show Source): You can put this solution on YOUR website!Assuming you problem is to solve: . x^2 -x -30 = 0 . Factoring this is the best approach. We notice that we need a + and a - term to result in -30. And the two factors need to 1 apart. There are a number of ways we can multiply two numbers to result in 30. 3*10 = 30, but they are 7 apart. 5*6 = 30, and they are 1 apart. So that's it. . (x -6)(x +5) = 0 . checking this using FOIL (first, outer, inner, last): . x*x + x*5 + (-6)x + (-6)*5 = x^2 -x -30. . So, the solutions that make the equation true are: x=6 and x= -5. . We also can graph it.
 Linear_Algebra/282517: Linear equations w/ substitution . . . . y=3x and x+y=81 solutions Answer 205115 by oberobic(2304)   on 2010-03-18 16:05:24 (Show Source): You can put this solution on YOUR website!y=3x x+y = 8 . substitute y=3x into the second equation x+y = 8 x + 3x= 8 4x = 8 x = 2 . substitute x=2 into the first equation . y = 3(2) = 6 . check by substituting x=2 and y=6 into the second equation . x+y = 8?? 2 + 6 = 8 correct . Answer: x = 2 y = 6 . Done.
 Linear-systems/282515: How do you solve 2y=6x+4?1 solutions Answer 205112 by oberobic(2304)   on 2010-03-18 16:00:26 (Show Source): You can put this solution on YOUR website!First, get it into slope-intercept form: y = mx + b where y = value of y that depends on the value of x m = slope of the line b = y-intercept (the point where x=0) . 2y = 6x+4 . Divide both sides of the equation by 2. . y = 3x + 2 . When x=0 . y = 3*0 + 2 = 2 which defines the point (0,2). . The x-intercept occurs where y=0. . 0 = 3x + 2 or 3x +2 = 0 . Subtract 2 from both sides. . 3x = -2 . Divide both sides by 3. . x = -2/3, which defines the point (-2/3,0). . Given you have two points, you can graph a straight line. . . That's about all you need to know about this equation. . y = 3x + 2 The slope = 3, which means it goes up to the right. The y-intercept = (0,2). The x-intercept = (-2/3,0). The graph is shown above. You could test another value of x to make sure it is on the line, but I leave that to you. . Done.
 Distributive-associative-commutative-properties/282497: what are the steps to doing a pre algebra problem like 6(2b+7)3= I am learning about distributive property and Im in speacial education for my poor math skills1 solutions Answer 205106 by oberobic(2304)   on 2010-03-18 15:50:16 (Show Source): You can put this solution on YOUR website!Show the multiplication to help keep yourself straight... 6(2b+7)3 = 6 * (2b + 7) * 3 . Since it doesn't matter what you multiply first, you can multiply what is outside the parentheses... . 6 * (2b + 7) * 3 = 6*3 * (2b+7) = 18 * (2b + 7) . Now multiply that times what is inside the parentheses... . 18 * (2b+7) = 18*2b + 18*7 . Simplify.. . 18*2b + 18*7 = 36b + 126 . Done
 Percentage-and-ratio-word-problems/282512: The ratio of chocolate to vanilla cupcakes is 5 to 4. If there are 45 cupcakes, how many of them are vanilla?1 solutions Answer 205100 by oberobic(2304)   on 2010-03-18 15:42:55 (Show Source): You can put this solution on YOUR website!The ratio of 5:4 means that 4/9 are vanilla. Given there are 45 in total... . 4/9 = x/45 180 = 9x 20 = x x=20 . There are 20 vanilla.
 Miscellaneous_Word_Problems/282503: A number, when increased by six, is a perfect square. When the same number doubled is decreased by four, the result is the same. What is the number?1 solutions Answer 205098 by oberobic(2304)   on 2010-03-18 15:38:49 (Show Source): You can put this solution on YOUR website!The setup ignores the perfect square statement and instead focuses on the relationship. x+6=2x-4 . Solving for 'x' . -x=-10 x = 10 . Now we can check for the perfect square... . x+6 = 16 :: a perfect square . Continue checking for the other condition... 2x-4= 20-4 = 16, which =x+6 Correct! . Answer: The number is 10. . Done.
 Unit_Conversion_Word_Problems/282126: If I have 8ft of and wanna make banners that require 9in of fabric how much left over frabic will I have1 solutions Answer 204953 by oberobic(2304)   on 2010-03-17 21:25:48 (Show Source): You can put this solution on YOUR website!1 ft = 12 inches 8 ft = 8 ft * 12 inches/ft = 96 inches . Divide 96 by 9 = 10 2/3. . So, you can make 10 banners at 9 inches each. That leaves you with 6 inches of material (96 -90 = 6). . Note that the remainder of '2/3' when you divided by 9 is '2/3 of 9' = 2/3*9 = 2*3 = 6. . Done
 Quadratic_Equations/282233: 3x^3+4x^2-32x=01 solutions Answer 204950 by oberobic(2304)   on 2010-03-17 21:20:17 (Show Source): You can put this solution on YOUR website!3x^3+4x^2-32x=0 . separate the common 'x' . x*(3x^2+4x-32)=0 . factor . (3x^2+4x-32)=(3x - 8 )(x + 4) . so... . x(3x-8)(x+4)=0 . That means there are three roots: x = 0 x = 8/3 x = -4 .
Quadratic_Equations/282231: use the quadratic formula to determine the x-intercept problem = f(x)=1/4x^2
1 solutions

Answer 204946 by oberobic(2304)   on 2010-03-17 21:08:24 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=0 is zero! That means that there is only one solution: . Expression can be factored: Again, the answer is: 0, 0. Here's your graph:

 Geometry_Word_Problems/282202: The perimeter of an equilateral triangle is 45 inches.A rectangle whose width is 1-3 its length has a perimeter of 48 inches.Which figure has the longest side and why?1 solutions Answer 204944 by oberobic(2304)   on 2010-03-17 21:05:38 (Show Source): You can put this solution on YOUR website!The perimeter of an equilateral triangle = 3s, where s=length of the each side. 3s = 45 s = 15 . A rectangle has perimeter = 2(l+w) We're told w = l-3 and perimeter = 48 48 = 2(l + l-3) 2(2l -3) = 48 2l -3 = 24 2l = 27 l = 13.5 . w = l-3 = 13.5-3 = 10.5 . checking perimeter 2(13.5 + 10.5) = 48?? 2(24) = 48 correct! so l = 13.5 w = 10.5 . The question asks which figure has the longest side. Answer: Equilateral triangle has the longest sides at 15 inches. . Done
 expressions/282209: is 5a- 3b+ 9c an expression or equation1 solutions Answer 204939 by oberobic(2304)   on 2010-03-17 20:57:46 (Show Source): You can put this solution on YOUR website!Equations have a equal sign. Expressions do not.
 Graphs/282218: through (7,2) parallel to 3x-y=8 written in slope intercept form and standard form?1 solutions Answer 204935 by oberobic(2304)   on 2010-03-17 20:55:22 (Show Source): You can put this solution on YOUR website!First, get the main equation into slope-intercept form: y = mx + b . 3x -y = 8 -y = -3x +8 y = 3x - 8 . Second, you recall that any line with slope = 3 will be parallel to this line. Your problem is define such a line that goes through the point (7,2). Well, plug x=7 into the equation and then adjust 'b' to make y=2. . y = 3x -b 2 = 3(7) -b 2 = 21 -b -19 = -b b = 19 . so, y = 3x -19 will be parallel and will go through the point. . Check by graphing the two equations. y=3x-8 is red; y=3x-19 is green. . Rechecking the question, this equation needs to be shown in slope-intercept and in standard form. y = 3x-19 :: slope-intercept form . Standard form is: Ax + By = C . subtract 3x from both sides -3x + y = -19 . multiply both sides by -1 . 3x -y = 19 :: standard form . Done