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 test/750924: The cost c(in dollars) of operating a certain concrete-cutting machine is related to the number of minutes n the machine is run by C(n)=2.6n^2-26n+640. What is the minimum cost?1 solutions Answer 456886 by jim_thompson5910(28715)   on 2013-05-20 18:45:01 (Show Source): You can put this solution on YOUR website!Min occurs at n = -b/(2a) = -(-26)/(2*2.6) = 5 So min occurs at n = 5, plug it in to get the min cost C(n) = 2.6n^2-26n+640 C(5) = 2.6(5)^2-26(5)+640 C(5) = 575 The min cost is $575  Linear-equations/750921: (-3,?) Is a solution of y=4-3x1 solutions Answer 456884 by jim_thompson5910(28715) on 2013-05-20 18:40:03 (Show Source): You can put this solution on YOUR website!y=4-3x y=4-3(-3) ... plug in x = -3 y=4 + 9 y=13 So (-3, 13) is a solution of y = 4 - 3x  Polynomials-and-rational-expressions/750923: 1 solutions Answer 456883 by jim_thompson5910(28715) on 2013-05-20 18:39:13 (Show Source): You can put this solution on YOUR website!problem missing, please post the full problem, thanks  Geometry_Word_Problems/750920: The area of a patio is 90 square feet. The length of the patio is 1 foot longer than the width. What is the length of the patio?1 solutions Answer 456882 by jim_thompson5910(28715) on 2013-05-20 18:38:41 (Show Source): You can put this solution on YOUR website!x(x+1) = 90 x^2+x = 90 x^2+x-90 = 0 (x+10)(x-9) = 0 x+10=0 or x-9=0 x=-10 or x = 9 Ignore the negative solution. The only solution that makes sense is x = 9, so x+1 = 10 The length is 10 ft.  Linear-systems/750913: y=2x,y-2x=0 1 solutions Answer 456880 by jim_thompson5910(28715) on 2013-05-20 18:35:12 (Show Source): You can put this solution on YOUR website!If you want to graph y=2x, then... Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is note: really looks like Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 2 and the run is 1. This means that to go from point to point, we can go up 2 and over 1 So starting at , go up 2 units and to the right 1 unit to get to the next point Now draw a line through these points to graph So this is the graph of through the points and  Polynomials-and-rational-expressions/750917: How do you simplify this expression? w2 - 9/w2 - 4w - 211 solutions Answer 456879 by jim_thompson5910(28715) on 2013-05-20 18:33:59 (Show Source): You can put this solution on YOUR website! Final Answer:  expressions/750911: Wendy bought 7 bags. Each bag costs the same amount. She paid the cashier$90 and received g dollars as change. What was the cost of each bag in terms of g?1 solutions Answer 456876 by jim_thompson5910(28715)   on 2013-05-20 18:31:13 (Show Source): You can put this solution on YOUR website!let b = cost of each bag Since she bought 7 bags, this means the total cost of them is 7b dollars. Since she received g dollars in change after paying \$90, this implies that 7b < 90 and g = 90 - 7b since that's how you compute change (change = amount paid - cost) Now solve for b So the cost of each bag, in terms of g, is
 Mixture_Word_Problems/750912: please help me find the answer! suppose you have 80 ml of a solution that is 60% acid and 40% water. how much acid do you need to add to make a solution that is 75% acid. 1 solutions Answer 456874 by jim_thompson5910(28715)   on 2013-05-20 18:27:31 (Show Source): You can put this solution on YOUR website!you have 80 ml of a solution that is 60% acid so you have 80*0.6 = 48 mL of pure acid Let x = amount of pure acid If you add x mL of pure acid to 48 mL of pure acid, then you'll have 48+x mL of pure acid total. This is out of 80 + x mL of new total solution. This ratio (48+x)/(80+x) must be equal to 0.75 since we want this new percentage to be 75%, so (48+x)/(80+x) = 0.75 now solve for x (48+x)/(80+x) = 0.75 48+x = 0.75(80+x) 48+x = 60+0.75x x = 60+0.75x - 48 x-0.75x = 60 - 48 0.25x = 12 x = 12/0.25 x = 48 So you need to add 48 mL of pure acid.
 Radicals/750910: x^(2/3) + 15 =241 solutions Answer 456872 by jim_thompson5910(28715)   on 2013-05-20 18:21:19 (Show Source): You can put this solution on YOUR website!x^(2/3) + 15 =24 x^(2/3) = 24-15 x^(2/3) = 9 [ x^(2/3) ]^(3/2) = 9^(3/2) x = 9^(3/2) x = ( sqrt(9) )^3 x = ( 3 )^3 x = 27
 Geometry_Word_Problems/750907: Find two consecutive integers that have a product of 182.1 solutions Answer 456870 by jim_thompson5910(28715)   on 2013-05-20 18:20:02 (Show Source): You can put this solution on YOUR website!x(x+1) = 182 x^2 + x = 182 x^2 + x - 182 = 0 Use the quadratic formula to solve for x Plug in , , or or or or So the two numbers are either 13 and 14 or -14 and -13
 Equations/750885: write the equation of the line passing through the points (5,-2) and (9,-2)1 solutions Answer 456866 by jim_thompson5910(28715)   on 2013-05-20 18:03:16 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Rewrite as Distribute Multiply Subtract 2 from both sides. Combine like terms. Simplify So the equation that goes through the points and is Notice how the graph of goes through the points and . So this visually verifies our answer. Graph of through the points and
 Equations/750887: write the equation of the line passing through the points (8,-39) and (1,3)1 solutions Answer 456864 by jim_thompson5910(28715)   on 2013-05-20 18:02:39 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Rewrite as Distribute Multiply Subtract 39 from both sides. Combine like terms. So the equation that goes through the points and is
 Equations/750888: find a third degree equation that has a solution set of (4,5,-8) 1 solutions Answer 456863 by jim_thompson5910(28715)   on 2013-05-20 18:01:50 (Show Source): You can put this solution on YOUR website!x = 4 or x = 5 or x = -8 x - 4 = 0 or x - 5 = 0 or x + 8 = 0 (x - 4)(x - 5)(x + 8) = 0 (x - 4)(x^2 + 3x - 40) = 0 x(x^2 + 3x - 40) - 4(x^2 + 3x - 40) = 0 x^3 + 3x^2 - 40x - 4x^2 - 12x + 160 = 0 x^3 - x^2 - 52x + 160 = 0 Final Answer: y = x^3 - x^2 - 52x + 160
 Geometry_Word_Problems/750883: The length of a rectangle is 8 inches greater than it' width. Find the width of a rectangle if it's area is 105 square feet.1 solutions Answer 456861 by jim_thompson5910(28715)   on 2013-05-20 17:58:37 (Show Source): You can put this solution on YOUR website!A = LW 105 = (x+8)(x) 105 = x^2 + 8x x^2 + 8x = 105 x^2 + 8x - 105 = 0 (x + 15)(x - 7) = 0 x + 15 = 0 or x - 7 = 0 x = -15 or x = 7 Toss out x = -15 So the only solution that makes sense is x = 7 Width: 7 Length: 15
 Geometry_Word_Problems/750884: The sum of the squares of two consecutive positive numbers is 41. What is the smaller number?1 solutions Answer 456860 by jim_thompson5910(28715)   on 2013-05-20 17:56:09 (Show Source): You can put this solution on YOUR website!x^2 + (x+1)^2 = 41 x^2 + x^2 + 2x+1 = 41 2x^2 + 2x+1 = 41 2x^2 + 2x+1 - 41 = 0 2x^2 + 2x - 40 = 0 2(x^2 + x - 20) = 0 2(x + 5)(x - 4) = 0 x + 5 = 0 or x - 4 = 0 x = -5 or x = 4 Ignore -5 (since the two numbers are both positive). So one number is 4 and the other number is 5. Answer: The smaller number is 4.
 Equations/750882: Choose the equation of the line passing through the point (4,5) and perpendicular to y=1/4x+91 solutions Answer 456858 by jim_thompson5910(28715)   on 2013-05-20 17:48:59 (Show Source): You can put this solution on YOUR website!Perpendicular Slope: -4 (flip the fraction and sign of 1/4) So the equation of the perpendicular line is
 Equations/750868: This was the first problem I had. I do not understand equations whatsoever. Not two-part equations, not one-part equations, not any equation! Please help me! First, I tried: (1/3)(9x-12)=4x-9 1/3(9x)-1/3(12)=4x-9 (3x-4)=4x-9 3x-4x=-1x 4x-4x=0 -1x-4=-9 -9+4=-5 -1x=-5 x=-5 I got this question wrong, but I don't know how! Thank-you for your time, Sarah 1 solutions Answer 456856 by jim_thompson5910(28715)   on 2013-05-20 17:47:18 (Show Source): You can put this solution on YOUR website!you were doing great until you reached the last step You have -1x = -5 and you need to divide both sides by -1 to isolate x -1x = -5 (-1x)/(-1) = -5/(-1) (1x)/1 = 5/1 1x = 5 x = 5 So final answer is x = 5
 Equations/750881: find the equation of the line passing through (3, - 3) and parallel to 7x + y = 4.1 solutions Answer 456854 by jim_thompson5910(28715)   on 2013-05-20 17:44:46 (Show Source): You can put this solution on YOUR website!Anything of the form 7x + y = C is parallel to 7x + y = 4 7x + y = C 7(3) + (-3) = C ... plug in the given point and solve for C 21 - 3 = C 18 = C C = 18 The equation of the parallel line in standard form is 7x + y = 18
 Polygons/750879: 13/x+2 - 6/x squared + 2x1 solutions Answer 456853 by jim_thompson5910(28715)   on 2013-05-20 17:43:32 (Show Source): You can put this solution on YOUR website! So simplifies to
 test/750878: 1 solutions Answer 456852 by jim_thompson5910(28715)   on 2013-05-20 17:42:17 (Show Source): You can put this solution on YOUR website!problem missing
 Equations/750877: Find the equation of a line passing through the point (- 10, 1) and perpendicular to the line y = 2.1 solutions Answer 456850 by jim_thompson5910(28715)   on 2013-05-20 17:40:33 (Show Source): You can put this solution on YOUR website!Anything perpendicular to y = 2 will be of the form x = h, which is a vertical line. The value of h must be -10 since all points on x = -10 have an x coordinate of -10. So the final answer is x = -10
 test/750853: Factor..show steps thank u asquared-ab-56b square 1 solutions Answer 456849 by jim_thompson5910(28715)   on 2013-05-20 17:32:49 (Show Source): You can put this solution on YOUR website!a^2-ab-56b^2 a^2+7ab-8ab-56b^2 ... Note: 7 and -8 both add to -1 and multiply to -56 (a^2+7ab)+(-8ab-56b^2) a(a+7b)+(-8ab-56b^2) a(a+7b)-8b(a+7b) (a-8b)(a+7b) --------------------------------------------------------------------------- a^2-ab-56b^2 completely factors to (a-8b)(a+7b)
 Equations/750876: Write the equation of the line with slope = - 4 and containing the point (- 2, 5). 1 solutions Answer 456847 by jim_thompson5910(28715)   on 2013-05-20 17:31:19 (Show Source): You can put this solution on YOUR website! So the equation of the line is
 test/750874: Factor show steps -108+2xsquared-6x1 solutions Answer 456846 by jim_thompson5910(28715)   on 2013-05-20 17:30:41 (Show Source): You can put this solution on YOUR website!Note: x squared = x^2 -108+2x^2-6x 2x^2-6x-108 2(x^2-3x-54) 2(x^2+6x-9x-54) 2((x^2+6x)+(-9x-54)) 2(x(x+6)+(-9x-54)) 2(x(x+6)-9(x+6)) 2(x-9)(x+6) Final Answer: 2(x-9)(x+6)
 Geometry_Word_Problems/750872: ha ha what is 5+4*8-91 solutions Answer 456844 by jim_thompson5910(28715)   on 2013-05-20 17:28:59 (Show Source): You can put this solution on YOUR website!Use PEMDAS 5+4*8-9 ... Start with the given expression. 5+32-9 ... PEMDAS (M for Multiplication) 37-9 ... PEMDAS (A for Addition) 28 ... PEMDAS (S for Subtraction) ======================================================= So 5+4*8-9 = 28
 Numeric_Fractions/750818: how can you make sure that a rational expression does not get undefined? 1 solutions Answer 456807 by jim_thompson5910(28715)   on 2013-05-20 15:20:30 (Show Source): You can put this solution on YOUR website!To make sure it never gets undefined, you have to exclude all values of the variable that make the denominator zero.
 absolute-value/750792: Solve: 5|1-4x|-15=01 solutions Answer 456794 by jim_thompson5910(28715)   on 2013-05-20 14:34:22 (Show Source): You can put this solution on YOUR website!5|1-4x|-15=0 5|1-4x| = 15 |1-4x| = 15/5 |1-4x| = 3 1-4x = 3 or 1-4x = -3 -4x = 3-1 or -4x = -3-1 -4x = 2 or -4x = -4 x = 2/(-4) or x = -4/(-4) x = -1/2 or x = 1
 Average/750734: how do I solve this equation? (y-6)-(y+5)= 2y1 solutions Answer 456793 by jim_thompson5910(28715)   on 2013-05-20 14:32:31 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Add to both sides. Subtract from both sides. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is which in decimal form is
 Square-cubic-other-roots/750728: cube root of 3681 solutions Answer 456792 by jim_thompson5910(28715)   on 2013-05-20 14:29:54 (Show Source):
 test/750726: graph the equation y=6-2x1 solutions Answer 456790 by jim_thompson5910(28715)   on 2013-05-20 14:28:24 (Show Source): You can put this solution on YOUR website!6-2x is the same as -2x + 6 Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is -2 and the run is 1. This means that to go from point to point, we can go down 2 and over 1 So starting at , go down 2 units and to the right 1 unit to get to the next point Now draw a line through these points to graph So this is the graph of through the points and
 test/750801: how many combinations can be formed from the letters in LEAST, taking them 2 at a time?1 solutions Answer 456789 by jim_thompson5910(28715)   on 2013-05-20 14:27:42 (Show Source): You can put this solution on YOUR website!There are 5 C 2 = (5!)/(2!*(5-2)!) = 10 different combinations.