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 Linear-equations/647481: what is the y-intercept of -10x-1/2y=5?1 solutions Answer 406218 by jim_thompson5910(28504)   on 2012-09-07 17:54:17 (Show Source): You can put this solution on YOUR website!Plug in x = 0 and solve for y -10x-1/2y=5 -10(0)-1/2y=5 0-1/2y=5 -1/2y=5 -y=5*2 -y=10 y = -10 So the y-intercept is (0, -10) -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Rational-functions/647400: graph the function -3x^3+9x^2-2x+31 solutions Answer 406173 by jim_thompson5910(28504)   on 2012-09-07 14:05:29 (Show Source): You can put this solution on YOUR website!Use a graphing calculator to get -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
1 solutions

Answer 406171 by jim_thompson5910(28504)   on 2012-09-07 14:02:15 (Show Source):
You can put this solution on YOUR website!

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,3,6,9,18
-1,-2,-3,-6,-9,-18

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*18 = 18
2*9 = 18
3*6 = 18
(-1)*(-18) = 18
(-2)*(-9) = 18
(-3)*(-6) = 18

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First NumberSecond NumberSum
1181+18=19
292+9=11
363+6=9
-1-18-1+(-18)=-19
-2-9-2+(-9)=-11
-3-6-3+(-6)=-9

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

===============================================================

So factors to .

In other words, .

Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).

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If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
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 Subset/647386: R = {10, 15, 20} S = {20, 25} R ∪ S =1 solutions Answer 406170 by jim_thompson5910(28504)   on 2012-09-07 13:58:55 (Show Source): You can put this solution on YOUR website!R ∪ S = {Combination of both sets} R ∪ S = {10,15,20,20,25} R ∪ S = {10,15,20,25} -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Inequalities/645993: -9+4r=4r-3-61 solutions Answer 405681 by jim_thompson5910(28504)   on 2012-09-04 23:31:46 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the right side. Add to both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Simplify. Since this equation is always true for any r value, this means r can equal any number. So there are an infinite number of solutions. -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Polynomials-and-rational-expressions/645982: factor completely 30r^3-40r^2+270r-3601 solutions Answer 405680 by jim_thompson5910(28504)   on 2012-09-04 23:22:01 (Show Source): You can put this solution on YOUR website! Start with the given expression Group the terms in two pairs Factor out the GCF out of the first group. Factor out the GCF out of the second group Since we have the common term , we can combine like terms Now factor out 10 from So factors to In other words, for all values of r. -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Equations/645973: (2x+3y-18)+(8x+12)1 solutions Answer 405677 by jim_thompson5910(28504)   on 2012-09-04 22:43:56 (Show Source): You can put this solution on YOUR website!(2x+3y-18)+(8x+12) 2x+3y-18+8x+12 (2x+8x)+3y+(-18+12) 10x+3y-6 So (2x+3y-18)+(8x+12) simplifies 10x+3y-6 -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Linear-equations/645934: sketch a graph of y=f(x) f(x)=-4x+2 1 solutions Answer 405667 by jim_thompson5910(28504)   on 2012-09-04 21:54:51 (Show Source): You can put this solution on YOUR website!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 -4 and the run is 1. This means that to go from point to point, we can go down 4 and over 1 So starting at , go down 4 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
 Equations/645930: How do you solve equations fot the variable indicated Example: N-6m=8 for n1 solutions Answer 405665 by jim_thompson5910(28504)   on 2012-09-04 21:53:05 (Show Source): You can put this solution on YOUR website!N-6m=8 N-6m+6m=8 + 6m N = 8 + 6m
 Inequalities/645858: 9-x<41 solutions Answer 405638 by jim_thompson5910(28504)   on 2012-09-04 20:26:38 (Show Source): You can put this solution on YOUR website!9-x < 4 -x < 4-9 -x < -5 x > -5/(-1) x > 5 -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Equations/645852: -6(-2m+7)=5m-6(m-6)1 solutions Answer 405635 by jim_thompson5910(28504)   on 2012-09-04 20:20:00 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the right side. Add to both sides. Add to both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Equations/645836: solve equation for x. then state any restrictions ax-bx=2a1 solutions Answer 405629 by jim_thompson5910(28504)   on 2012-09-04 20:06:27 (Show Source): You can put this solution on YOUR website! So the final answer is where -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Graphs/645831: -5(w-4)-(7+7w)=-13w1 solutions Answer 405628 by jim_thompson5910(28504)   on 2012-09-04 20:05:17 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Subtract from both sides. Add to both sides. Combine like terms on the left side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Graphs/645776: Write the equation of the line Through twompoints (-6,10) and (3,1)1 solutions Answer 405616 by jim_thompson5910(28504)   on 2012-09-04 19:19:53 (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 Add 10 to both sides. Combine like terms. Simplify So the equation that goes through the points and is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Coordinate-system/645762: Write an equation of the line A line passing through (-2,-7) with slope -3/21 solutions Answer 405612 by jim_thompson5910(28504)   on 2012-09-04 19:12:46 (Show Source): You can put this solution on YOUR website! So the equation of the line is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Expressions-with-variables/645740: Four times the difference of 8 and a number x.1 solutions Answer 405610 by jim_thompson5910(28504)   on 2012-09-04 19:03:29 (Show Source): You can put this solution on YOUR website!Four times the difference of 8 and a number x translates to 4(x - 8)
 Graphs/645681: -12(y+1)+6(3y-6)=5(y-3)+121 solutions Answer 405586 by jim_thompson5910(28504)   on 2012-09-04 18:34:34 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Combine like terms on the right side. Add to both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the solution is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Polynomials-and-rational-expressions/645585: what does this h(3), mean. I have no clue1 solutions Answer 405540 by jim_thompson5910(28504)   on 2012-09-04 15:54:41 (Show Source): You can put this solution on YOUR website!If you have something like h(x) = x+5, then you replace every 'x' with 3 and evaluate. Does that make sense?
 Number-Line/645555: Where would you plot -9/2 on a number line?1 solutions Answer 405529 by jim_thompson5910(28504)   on 2012-09-04 15:19:50 (Show Source): You can put this solution on YOUR website!-9/2 = -4.5 So you plot this number exactly halfway between -5 and -4 on the number line. -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Number-Line/645556: 1/3 - 4/91 solutions Answer 405521 by jim_thompson5910(28504)   on 2012-09-04 15:13:25 (Show Source): You can put this solution on YOUR website!1/3 - 4/9 3/9 - 4/9 -1/9 So 1/3 - 4/9 = -1/9 -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Permutations/645497: 5. Ten individuals are candidates for positions of president, vice president of an organization. How many possibilities of selections exist? __________________________ 1 solutions Answer 405497 by jim_thompson5910(28504)   on 2012-09-04 12:53:00 (Show Source): You can put this solution on YOUR website!There are 10 people to choose from for the first slot, 9 for the second, and 8 for the third. So there are 10*9*8 = 720 different possibilities. -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 decimal-numbers/645485: HI tutors! I have this problem in my college math book: The decimal expansion of the irrational number pi symbol begins 3.141592653589793 . . . . Use your calculator to determine which of the following rational numbers is the best approximation for the irrational number pi symbol: 22/7 , 355/113 , 103,993/33,102 , 2,508,429,787/798,458,000. Your calculator may tell you that some of these numbers are equal to pi symbol, but that just indicates that the number agrees with pi symbol for as many decimal places as your calculator can handle (usually 10-14). No rational number is exactly equal to pi symbol. Here is what I get from left to right for these fractions: 3.142857143 , 3.14159292 , 3.141592653 , and 3.141592654. The book's answer is the last fraction. Why is the last fraction the right answer?1 solutions Answer 405496 by jim_thompson5910(28504)   on 2012-09-04 12:50:02 (Show Source): You can put this solution on YOUR website!The fractions below 22/7, 355/113, 103993/33102, 2508429787/798458000 convert to the following numbers in decimal form 3.14285714285714, 3.14159292035398, 3.1415926530119, 3.141592653589794 ---------------------------------------------------------------------- Now compare this with the given value of pi, which is 3.141592653589793... First Rational Approximation (22/7) 3.141592653589793 3.14285714285714 Note: first number is the given value of pi and second number is the rational approximation Notice how 22/7 only matches up to 3.14 and then it's off for the rest of the expansion. ------------------------------------------------------------------ Second Rational Approximation (103993/33102) 3.141592653589793 3.14159292035398 Note: first number is the given value of pi and second number is the rational approximation We got a better approximation this time since it matches 3.141592 So far, the second approximation is better ------------------------------------------------------------------ Third Rational Approximation (355/113) 3.141592653589793 3.1415926530119 Note: first number is the given value of pi and second number is the rational approximation We got a better approximation this time since it matches 3.141592653 So far, the third approximation is best ------------------------------------------------------------------ Fourth Rational Approximation (2508429787/798458000) 3.141592653589793 3.141592653589794 Note: first number is the given value of pi and second number is the rational approximation We get the most accurate match this time since it matches 3.14159265358979 The only difference between this rational approximation and the given decimal expansion is that the '3' at the end doesn't match with the 4. ========================================================================== Answer: So the fraction 2508429787/798458000 gives the best approximation of pi -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Equations/645490: 3/4x - 2/3 = 1/51 solutions Answer 405493 by jim_thompson5910(28504)   on 2012-09-04 12:37:07 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Equations/645407: 5x + 3x = 101 solutions Answer 405485 by jim_thompson5910(28504)   on 2012-09-04 12:15:23 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Linear-equations/645472: what is the slope-intercept form of Slope = 1, y-intercept = 11 solutions Answer 405483 by jim_thompson5910(28504)   on 2012-09-04 12:13:52 (Show Source): You can put this solution on YOUR website!y = mx+b y = 1x+1 y = x+1 -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 real-numbers/645294: I would like your assistance in solving a problem. I know for sure that the value of x is a fraction. The problem is: 3(-x+2)=5(x-3) So far I have tried this: 3(-x+2)=5(x-3) (-3x+6)=(5x-15) +3x +3x 6=8x-15 +15 +15 21= 8x 1 solutions Answer 405418 by jim_thompson5910(28504)   on 2012-09-03 22:50:58 (Show Source): You can put this solution on YOUR website!You're doing great. To finish up, divide both sides by 8 to completely isolate x. So the solution is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Linear-systems/645151: I keep getting fractions and decimals when my teacher said the answers were whole/real numbers. but the problem is: 2w-x+5y+z=-3 3w+2x+2y-6z=-32 w+3x+3y-z=-47 5w-2x-3y+3z=49 find w,x,y,and z.1 solutions Answer 405387 by jim_thompson5910(28504)   on 2012-09-03 19:51:05 (Show Source): You can put this solution on YOUR website!2w-x+5y+z=-3 3w+2x+2y-6z=-32 w+3x+3y-z=-47 5w-2x-3y+3z=49 translates to the matrix $\LARGE \begin{bmatrix} 2 & -1 & 5 & 1 & -3\\ 3 & 2 & 2 & -6 & -32\\ 1 & 3 & 3 & -1 & -47\\ 5 & -2 & -3 & 3 & 49 \end{bmatrix}$ Now use row reduction to get (Solution provided by the Linear Algebra Toolkit) (Solution provided by the Linear Algebra Toolkit) So the solutions are , , ,
 Numbers_Word_Problems/645142: between what consecutive intergers is 125% do not understand how to get that1 solutions Answer 405384 by jim_thompson5910(28504)   on 2012-09-03 19:20:16 (Show Source): You can put this solution on YOUR website!125% converts to 1.25 in decimal form (move the decimal over to the left 2 spots). The number 1.25 is between 1 and 2.
 Rectangles/645115: At what measurements is the area the greatest? Length Width Area 1 15 15 2 14 28 3 13 39 4 12 48 5 11 55 6 10 60 7 9 63 8 8 64 9 7 63 10 6 60 11 5 55 12 4 48 13 3 39 14 2 28 15 1 15 1 solutions Answer 405382 by jim_thompson5910(28504)   on 2012-09-03 19:17:35 (Show Source): You can put this solution on YOUR website!The max area is highlighted in the red row. The max area is 64 square units and it occurs when both the length and width are 8 units.  Length Width Area 1 15 15 2 14 28 3 13 39 4 12 48 5 11 55 6 10 60 7 9 63 8 8 64 9 7 63 10 6 60 11 5 55 12 4 48 13 3 39 14 2 28 15 1 15 
 Sequences-and-series/645136: 175% of 40 is what number?1 solutions Answer 405379 by jim_thompson5910(28504)   on 2012-09-03 19:14:59 (Show Source): You can put this solution on YOUR website!175% of 40 = (175/100)*40 175% of 40 = 1.75*40 175% of 40 = 70
 Square-cubic-other-roots/645122: help me solve the cubed root of 16x^3y^51 solutions Answer 405375 by jim_thompson5910(28504)   on 2012-09-03 19:05:53 (Show Source): You can put this solution on YOUR website! So simplifies to -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------