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# Recent problems solved by 'oberobic'

oberobic answered: 2303 problems
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 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
 Graphs/282204: Is (2, -3) a solution of x^2 + 2y = -2? Tell why or why not. 1 solutions Answer 204916 by oberobic(2304)   on 2010-03-17 20:29:34 (Show Source): You can put this solution on YOUR website!Rearrange the equation into: y = whatever format . . subtract x^2 from both sides . . divide both sides by 2 . . So you want to know if (2,-3) is on the graph? Plug the value of 'x' into the equation and see. . . Yes, the point (2,-3) is on the graph. . Done
 Linear-equations/282189: How do I solve for this using substitution. 5x+8y=18 x=6-2y1 solutions Answer 204909 by oberobic(2304)   on 2010-03-17 20:13:31 (Show Source): You can put this solution on YOUR website!Substitution is done by...well...substitution. You use one equation to find a value for 'x'. Then you substitute that into the other equation. . 5x + 8y = 18 x = 6 -2y . So the second equation is a easy substitution candidate into the first equation. . 5(6-2y) +8y = 18 30 -10y +8y = 18 30 -2y = 18 -2y = -12 y = 6 . Now substitute back to find 'x'. . x = 6 -2(y) x = 6 -2(6) x = 6 -12 x = -6 . Check by plugging these values into the other equation to ensure they're right. . 5x + 8y = 18 5(-6) + 8(6) = 18?? -30 +48 = 18 Correct! . Answer: x = -6 y = 6 . Done.
 Parallelograms/282201: What is the formula P=2(B)+2(H) used to find?1 solutions Answer 204906 by oberobic(2304)   on 2010-03-17 20:06:22 (Show Source): You can put this solution on YOUR website!Looks like a perimeter, where B = base of the figure and H = height.
 Rational-functions/282196: y=-6/x identify any excluded values1 solutions Answer 204905 by oberobic(2304)   on 2010-03-17 20:05:33 (Show Source): You can put this solution on YOUR website!'x' cannot = 0 because you cannot divide by 0.
 Numbers_Word_Problems/282198: Find 3 consecutive even numbers where the product of the smaller two numbers is 40 less than the square of the largest number.1 solutions Answer 204903 by oberobic(2304)   on 2010-03-17 20:04:09 (Show Source): You can put this solution on YOUR website!Three consecutive numbers could be called: a, b, c. But it is far better to define them as: . :: the product of the two smaller is 40 less than the square of the largest . . Checking... So Correct. . Answer: The three consecutive numbers are: 12, 13, and 14. . Done.
 Rectangles/282194: A rectangular field is 12cm longer than it is wide. Its perimeter is 52 cms find the width???? how i do this1 solutions Answer 204899 by oberobic(2304)   on 2010-03-17 19:56:45 (Show Source): You can put this solution on YOUR website!Perimeter = P = 2L + 2W P = 52 L = W+12 :: Length is 12 more than width, so you'd have to add 12 to L to make it equal. . 2L + 2W = 2(L+W) 2(L+W) = 52 L+W = 26 (W+12)+W = 26 2W+12=26 2W = 14 W = 7 . L=W+12 L=7+12 L=19 . Check perimeter to be sure it is 52. 2(7+19) = 2(26) = 52 . State answer: W = 7 L = 19 . Done
 Linear-equations/282192: 3x - 2y = 10 5x + 3y = 4 How would you describe how to solve this system?1 solutions Answer 204898 by oberobic(2304)   on 2010-03-17 19:53:14 (Show Source): You can put this solution on YOUR website!3x - 2y = 10 5x + 3y = 4 . It is presents itself as a system of linear equations. . Multiply the first equation by 3. Multiply the second equation by 2. Add the equations to eliminate the 'y' term. Solve for 'x'. Substitute to find 'y'. Check. Done.
 Numeric_Fractions/281389: three tired and hungry men went to sleep with a bag of apples. one man woke up, ate 1/3 of the applaes, then went back to sleep. later a second man woke up and ate 1/3 of the remaining alpples. when he was fiished there were 8 apples left. how many apples were in the bag originally * create a solution that uses algebre and show all steps uses 1 solutions Answer 204395 by oberobic(2304)   on 2010-03-15 23:35:42 (Show Source): You can put this solution on YOUR website!x = number of apples in the bag originally . We are told the first man ate 1/3 of the apples. . That means that 2/3 of the apples were left in the bag. . We are told the second man ate 1/3 of the apples that he found in the bag. . BUT notice that he did NOT eat 1/3 of x apples. . He ate 1/3 of the 2/3 of the apples that were left in the bag. . 1/3*2/3 = 2/9 . So the second man ate 2/9 of the x total apples. . That means the two men ate a total of 1/3x plus 2/9x, leaving 8 apples in the bag. . 1/3x + 2/9x = 3/9x + 2/9x = 5/9x . However, notice that the above tells us how many apples they ate, not how many apples are left. . x - 5/9x is how many apples are left, which is 9/9x - 5/9x = 4/9x. . 4/9x is how many apples are left. . 4/9x = 8 . 4x = 72 x = 18 . Checking our work... How many apples are 1/3 of 18? 1/3*18 = 6 So the first man ate 6 apples, leaving 12 in the bag. How many apples are 1/3 of 12? 1/3*12 = 4 So the second man ate 4 apples, leaving 8 apples in the bag. Correct. . Answer: There were 18 apples in the bag originally. . Done.
 Miscellaneous_Word_Problems/281386: the sum of two numbers is 45. the first is 9 less than the second find the numbers1 solutions Answer 204390 by oberobic(2304)   on 2010-03-15 23:20:27 (Show Source): You can put this solution on YOUR website!x = one number y = another number x + y = 45 :: given x = y + 9 :: y is 9 less than x . substitute x = y+9 in the first equation . y+9 + y = 45 2y = 36 y = 18 . now substitute y=18 in the second equation x + y = 45 x + 18 = 45 x = 27 . checking... Is the smaller number 9 less than the larger number? Yes. . Answer: The two numbers are 18 and 27. . Done
 Linear-equations/281376: Find the x intercept and y intercept of the line given by the equation. 5x-8y=-151 solutions Answer 204389 by oberobic(2304)   on 2010-03-15 23:15:36 (Show Source): You can put this solution on YOUR website!Start by getting the equation into slope-intercept form: y = mx + b. . 5x -8y = -15 . subtract 5x from both sides... . -8y = -5x -15 . divide both sides by -8 . y = -5/(-8)x - 5/(-8) y = 5/8x + 5/8 . The y-intercept is the point where x=0. y = 5/8(0) + 5/8 y = 5/8 (0, 5/8) . The x-intercept is the point where y=0. 0 = 5/8x + 5/8 x = -1 (-1,0) . Graphing is a good way to check.
 Linear-equations/281373: Graph the line thru (1,1) wiht a slope of 31 solutions Answer 204386 by oberobic(2304)   on 2010-03-15 23:06:29 (Show Source): You can put this solution on YOUR website!The slope of 3 means that for a change of 1 'x' there will be a change of 3 'y'. . m = rise/run = 3/1 . We have the point (1,1), so the next point would be (2,4). With two points, you can graph a straight line. . Or we can address the problem in terms of y = mx + b, which is the slope-intercept form of an equation. . y = 3x + b . But then the question is, "What is the value 'b' to be sure it goes through the point (1,1)?" . Well, (1,1) means that when x=1, y =1, so we can show this as: 1 = 3(1) + b b = -2 . This suggests the equation of the line with slope = 3 that goes through the point (1,1) is: y = 3x -2 . Graphing it we can see... . That looks correct. . We also can do additional checking. Some other points of interest are the y-intercept and the x-intercept. The y-intercept is where x=0. y = 3(0)-2 = -2 (0, -2) . The x-intercept is where y=0. 0 = 3x -2 x = 2/3 (2/3, 0) . By inspecting the graph, you can see these points are on the line, too. . Done
 Finance/281242: What is the slope of the line connecting the points (-3,5) and (6,-1)1 solutions Answer 204383 by oberobic(2304)   on 2010-03-15 22:52:41 (Show Source): You can put this solution on YOUR website!The slope, 'm', is defined as the rise divided by the run. The rise is the change in 'y'. The run is the change in 'x'. The change in 'y' is defined as y2 - y1. The change in 'x' is defined as x2 - x1. . We have two points: (-3, 5) = (x1, y1) (6, -1) = (x2, y2) . y2 - y1 = -1 -5 = -6 x2 - x1 = 6 - (-3) = 9 . m = -6/9 = -2/3 . Done
Quadratic_Equations/281364: Write a quadratic equation having the given numbers as solutions. -3.5, 2.2

1 solutions

Answer 204377 by oberobic(2304)   on 2010-03-15 22:41:26 (Show Source):
You can put this solution on YOUR website!
The general form of a quadratic equation that has been solved is to have two factors that are multiplied. In this case, you're told the solutions are x= -3.5 and x=2.2. So the factored form of the equation would be:
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(x + 3.5)(x - 2.2) = 0
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Using FOIL...
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x^2 -2.2x +3.5x -7.7 = 0
x^2 + 1.3x - 7.7 = 0
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multiply by 10 to get rid of the decimals...
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10x^2 + 13x - 77 = 0
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Checking this equation using the quadratic formula, you can determine if the solutions are x= -3.5 and x= 2.2...
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.
 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=3249 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 2.2, -3.5. Here's your graph:

.
Done

 Probability-and-statistics/281350: the price of the orchestra level tickets were \$125. Balcony tickets were \$70. A total of 195 tickets were sold for \$26650. Determine the number of orchestra level tickets and the number of balcony level tickets sold.1 solutions Answer 204373 by oberobic(2304)   on 2010-03-15 22:26:32 (Show Source): You can put this solution on YOUR website!b = number of balcony tickets sold o = number of orchestra tickets sold . b + o = 195 :: given or, b = 195 - o and o = 195-b . 125o = value of the orchestra tickets sold 70b = value of the balcony tickets sold . 125o + 70b = 26650 :: given . substitute b = 195 - o: . 125o + 70(195 - o) = 26650 125o + 13650 - 70o = 26650 , collect and simplify . 125o - 70o = 26650 - 13650 55o = 13000 o = 236.36 . That is an odd result because it calls for selling a fraction of a ticket, and it calls for selling more than 195 tickets. . If ONLY orchestra tickets were sold @ \$125 each, then that would be 213.2 tickets, which is more than 195. . So there appears to be something wrong with your problem statement. . Done
 Systems-of-equations/281267: 4.Solve by Elimination-Multiplication. ( ) 3x-2y=3 -x+y=11 solutions Answer 204365 by oberobic(2304)   on 2010-03-15 22:02:29 (Show Source): You can put this solution on YOUR website!The given equations are... 3x -2y = 3 -x + y = 1 . Multiply the second equation by 2 to set up for elimination... . -2x + 2y = 2 . Then add the two equations... . 3x -2y = 3 -2x +2y = 2 x = 5 . Substitute x=5 into first equation to find y... . 3x - 2y = 3 3(5) -2y = 3 15 -2y = 3 -2y = 3 -15 y = -12/-2 = 6 . Check answer by substituting into the 2nd equation... . -x + y = 1 -5 + 6 = 1 Correct! . Answer: x = 5 y = 6 . Done
 Triangles/281292: What is the area of a triangle in which b = (x + 1)ft and h = 8x ft?1 solutions Answer 204359 by oberobic(2304)   on 2010-03-15 21:55:20 (Show Source): You can put this solution on YOUR website!The area of a triangle is 1/2*base*height. . b = base = (x+1) ft . h = height = 8x ft . Area = 1/2*(x+1)*8x ft^2 . A = 1/2(8x^2+8x) ft^2 . A = 4x^2 + 4x ft^2 . A = 4x(x+4) ft^2 . Done
 Length-and-distance/280830: the perimeter of a rectangle is 132 inches. The length exceeds the width by 46 inches. Find the length and width.1 solutions Answer 204092 by oberobic(2304)   on 2010-03-14 21:42:37 (Show Source): You can put this solution on YOUR website!Perimeter of a rectangle = 2*length + 2*width. l = length w = width . P = 132 :: given . l = w+46 :: given . Substituting into the perimeter equation... . 2l + 2w = 132 2(w+46) + 2w = 132 2w + 92 + 2w = 132 4w + 92 = 132 4w = 40 w = 10 . l = w+46 = 56 . Checking this answer... . P = 2*56 + 2*10 P = 112 + 20 P = 132 Correct. . Answer: Length = 56 Width = 10 . Done
 Expressions-with-variables/280832: The sum of the digits of a two digit number is 14. If 36 is subtracted from the number, the resulting number is the original number with its digits interchangeable. Find the Number.1 solutions Answer 204089 by oberobic(2304)   on 2010-03-14 21:34:14 (Show Source): You can put this solution on YOUR website!When doing sum of digits problems, you have to remember that numbers like 'xy' are not being multiplied. Consider the number 23. It really is not "one" number, but instead it means 2*10 + 3*1. . So the number is 'xy' but that is NOT x*y, it's just 'x' next to 'y'. The value of the number 'xy' = 10x + y. . x + y = 14 :: given . 36 is a value, so to subtract it, you have to calculate the value of xy: . 10x+y -36 = 10y + x . Setting up a system of equations: . 10x + y - 36 - 10y - x = 0 9x - 9y = 36 x - y = 4 . x + y = 14 x - y = 4 . adding . 2x = 18 x = 9 . x + y = 14 given x = 9 y = 5 . so the original number, 'xy', appears to be 95. . checking... 'yx' would be 59. . so, is 95 - 36 = 59? Yes, it is. . Answer: The number is 95. . Done.
 Linear-equations/280831: How would you graph linear equation 3x+5y=151 solutions Answer 204087 by oberobic(2304)   on 2010-03-14 21:18:15 (Show Source): You can put this solution on YOUR website!First, get the equation into slope-intercept form: y = mx+b . 3x + 5y = 15 5y = -3x + 15 y = -3/5x+ 3 . The y-intercept is where x=0, which equals 3. The point is (0, 3). . The x-intercept is where y = 0. 0 = -3/5x + 3 x = 5 The point is: (5,0) . With two points, you can draw a line. . . Done
 Linear-systems/280839: translate to algebracia expression: the product of 37% and some number? 1 solutions Answer 204084 by oberobic(2304)   on 2010-03-14 21:12:30 (Show Source): You can put this solution on YOUR website!37% = .37 . x = some number . So, we can state algebraically: .37x
 Numbers_Word_Problems/280834: The sum of two numbers is seven. The sum of the squares of the two numbers is twenty-nine. Find the two numbers.1 solutions Answer 204083 by oberobic(2304)   on 2010-03-14 21:11:23 (Show Source): You can put this solution on YOUR website!x + y = 7 x = 7-y . x^2 + y^2 = 29 . (7-y)^2 + y^2 = 29 (7-y)(7-y) +y^2 = 29 49 -7y - 7y + y^2 + y^2 = 29 2y^2 -14y + 49 = 29 2y^2 - 14y + 49 - 29 = 0 2y^2 - 14y + 20 = 0 y^2 - 7y + 10 = 0 (y-2)(y-5) = 0 . y=2 OR y=5 . But it is possible that one of these is NOT an answer. . Checking... . x+y = 7 . Substituting y = 2, then x = 5 2^2 = 4 5^2 = 25 4+25 = 29 So, y=2 and x=5 is a solution. . Substituting y=5, then x = 2. That works too. . Answer: The two numbers are 2 and 5. . Done
 Expressions-with-variables/280828: if f(x)=SQRT of x what is f(-100) and f(48)1 solutions Answer 204079 by oberobic(2304)   on 2010-03-14 20:58:35 (Show Source): You can put this solution on YOUR website! . . i is an imaginary number that represents . . . Done
 Linear_Equations_And_Systems_Word_Problems/280817: A dj must play 14 commericals during an hour of play time. After 1 hour and 11 minutes the dj played how many 30 second commericals and how many 60 second commericals?1 solutions Answer 204077 by oberobic(2304)   on 2010-03-14 20:50:38 (Show Source): You can put this solution on YOUR website!We need more information to solve this. Is there a total number of minutes of commercials per hour? Is there some ratio of 30-sec and 60-sec commercials? As stated, the DJ could have played 14 30-sec commericals or 14 60-sec commericals, or any combination.
 Travel_Word_Problems/280810: A motorboat traveling with the current can go 36 miles in 2 hours. against the current it takes 3 hours to go to the same distance. Find the rate of the motorboat in calm water.1 solutions Answer 204075 by oberobic(2304)   on 2010-03-14 20:45:35 (Show Source): You can put this solution on YOUR website!d = r*t is the basic distance equation. s = speed of the motor boat in calm water c = speed of current s + c = speed of the boat traveling with the current s - c = speed of the boat traveling against the current . traveling with the current the boat went 36 miles in 2 hrs d = 36 r = s+c t = 2 36 = (s+c)*2 . traveling against the current the boat can return 36 miles in 3 hrs d = 36 r = s-c t = 3 36 = (s-c)*3 . We've got two unknowns and we've got two unknowns, so this can be approached as a system of linear equations. . 2s + 2c = 36 3s - 3c = 36 . Multiply the first equation by 3 and the second by 2 to enable elimination. . 3(2s + 2c) = 3(36) = 6s + 6c = 108 2(2s - 2c) = 2(36) = 6s - 6c = 72 . 6s + 6c = 108 6s - 6c = 72 . adding them to eliminate the 6c and -6c. . 12s = 180 . divide by 12 . s = 15 = speed of the boat in calm water . substituting back into our first equation . 36 = (s+c)*2 2s + 2c = 36 2(15) + 2c = 36 2c = 6 c = 3 = speed of the current . checking... . traveling with the current, the boat's speed = 15+3 = 18 to travel 36 miles, it would take 2 hr, which is what the problem stated. . traveling against the current, the boat's speed = 15 -3 = 12 again we can see that to travel the 36 miles it would take 3 hrs, which is also what was stated. . Answer: s = 15 = speed of the boat in calm water c = 3 = speed of the current . Done
 Numbers_Word_Problems/280816: A 3-ft by 6-ft picnic table is placed on an outdoor patio measuring x ft by x ft. Find a polynomial for the remaining open space on the patio ( in square feet).1 solutions Answer 204067 by oberobic(2304)   on 2010-03-14 20:25:02 (Show Source): You can put this solution on YOUR website!The area of the patio is x*x = x^2. The area of the table is 3*6 = 18. The area of the patio remaining is x^2 - 18.
 Linear-equations/280815: How do I solve a elimination problem like this 175,00000x + 200,00000 y = 720.000001 solutions Answer 204064 by oberobic(2304)   on 2010-03-14 20:22:47 (Show Source): You can put this solution on YOUR website!You cannot solve one equation with two unknowns. With two equations with two unknowns, you can set up a system of equations and add or subtract them. That is the elimination step.
 Numbers_Word_Problems/280799: What are 4 consecutive positive integers whose sum equals 5 times the smallest integer?1 solutions Answer 204060 by oberobic(2304)   on 2010-03-14 20:07:38 (Show Source): You can put this solution on YOUR website!Four consecutive positive integers can be described as a, b, c, and d. But it is better to define them in terms of one another. a = x b = x+1 c = x+2 d = x+3 . We are told the sum is 5 times the smallest number. . x + (x+1) + (x+2) + (x+3) = 5x . collecting terms... 4x + 6 = 5x 6 = x x = 6 . So the possible consecutive positive integers are 6, 7, 8 and 9. . Checking the solution, is the sum = 5*6 = 30? 6+7+8+9 =30 Correct! . Answer: The consecutive positive digits are 6, 7, 8 and 9. . Done
 Rectangles/280802: The width of a rectangle is 6 inches less than one-half the length. Find the length and the width of the rectangle if the perimeter of the rectangle is 72 inches.1 solutions Answer 204055 by oberobic(2304)   on 2010-03-14 19:55:46 (Show Source): You can put this solution on YOUR website!w = width l = length w = 1/2*l - 6 P = 2(l+w) = 72 2l + 2w = 72 . substitute w = 1/2*l -6 . 2l + 2w= 72 2l + 2(1/2*l - 6) = 72 2l + l - 12 = 72 3l = 84 l= 28 . w = 1/2*l -6 = 1/2*28 - 6 = 14-6 = 8 . checking 2l + 2w = 72? 2l = 2*28 = 56 2w = 2*8 = 16 56+16= 72 Correct. . Answer: length = 28 width = 8 . Done
 Mixture_Word_Problems/280774: What quantity of 70 per cent acid solution must be mixed with a 30 solution to produce 1080 mL of a 50 per cent solution?1 solutions Answer 204052 by oberobic(2304)   on 2010-03-14 19:47:30 (Show Source): You can put this solution on YOUR website!A key part of solving these types of problems is keeping track of how much 'pure' stuff you need. You need 1080 mL of 50% solution = .5*1080 = 540 mL of pure acid. . x = volume of 70% acid you will use y = volume of 30% acid you will use . BUT since you know x+y = 1080, it is better to define the volumes in terms of 'x' only . y = 1080-x . Set up an equation that will describe the two parts and the final result . .7x + .3(1080-x) = .5*1080 . multiply by 10 to get rid of decimals 7x + 3(1080-x) = 5*1080 = 5400 . expand, collect, simplify... . 7x + 3240 - 3x = 5400 4x = 2160 x = 540 . y = 1080 - 540 = 540 . So our proposed solution is 540 mL of 70% acid and 540 mL of 30% solution. By inspection that makes sense because (.7+.3)/2 = .5 But we need to check our work...always... . How much 'pure' acid will be in the final solution compared to how much you need. You need 540 mL. . .7*540 = 378 .3*540 = 162 378 + 162 = 540 Correct! . Answer: You need to mix 540 mL of 70% acid with 540 mL of 30% acid to produce 1080 mL of 50% acid. . Done
 Numbers_Word_Problems/280794: how do i start off solvin this problem..... one number is 5 greater than another and has a product of 36.find the numbers1 solutions Answer 204050 by oberobic(2304)   on 2010-03-14 19:29:34 (Show Source): You can put this solution on YOUR website!x = one number y = another number x = y+5 :: x is 5 greater than y x*y = 36 . substitute x = y+5 . (y+5) * y = 36 . expand, collect, simplify, factor, solve... . good luck!