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 Equations/521796: what is the ansewr step by step for 3-f=6f+81 solutions Answer 346585 by jim_thompson5910(28595)   on 2011-10-26 18:54:35 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Subtract from 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
 Travel_Word_Problems/521792: if 40 laps is 2. kilometers then how much is 1 lap 1 solutions Answer 346584 by jim_thompson5910(28595)   on 2011-10-26 18:52:30 (Show Source): You can put this solution on YOUR website!40/2 = 1/x 40x = 2*1 40x = 2 x = 2/40 x = 1/20 So 1 lap is 1/20th of a kilometer (which is 0.05 km) 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
 Circles/521788: calculate the area of a circle whose radius is 2cm1 solutions Answer 346580 by jim_thompson5910(28595)   on 2011-10-26 18:44:42 (Show Source): You can put this solution on YOUR website! A = pi*r^2 A = (3.14159)*(2)^2 A = (3.14159)*(4) A = 12.56636 So the area is approximately 12.56636 square cm 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
 Distributive-associative-commutative-properties/521725: 2x+3=-2x+51 solutions Answer 346578 by jim_thompson5910(28595)   on 2011-10-26 18:37:07 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from 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/521765: 3x+7=-31 solutions Answer 346577 by jim_thompson5910(28595)   on 2011-10-26 18:36:39 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from 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
 Square-cubic-other-roots/521783: sqrt( 3x + 1)- 2=01 solutions Answer 346576 by jim_thompson5910(28595)   on 2011-10-26 18:35:45 (Show Source): You can put this solution on YOUR website!sqrt(3x+1)-2=0 sqrt(3x+1)=2 (sqrt(3x+1))^2=2^2 3x+1=4 3x=4-1 3x=3 x=3/3 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
Equations/521778: factor trinomial using trial and error
6x^2+39x+60
or is it not factorable?

1 solutions

Answer 346575 by jim_thompson5910(28595)   on 2011-10-26 18:33:58 (Show Source):
You can put this solution on YOUR website!

Start with the given expression.

Factor out the GCF .

Now let's try to factor the inner expression

---------------------------------------------------------------

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 :
1,2,4,5,8,10,20,40
-1,-2,-4,-5,-8,-10,-20,-40

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

These factors pair up and multiply to .
1*40 = 40
2*20 = 40
4*10 = 40
5*8 = 40
(-1)*(-40) = 40
(-2)*(-20) = 40
(-4)*(-10) = 40
(-5)*(-8) = 40

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

First NumberSecond NumberSum
1401+40=41
2202+20=22
4104+10=14
585+8=13
-1-40-1+(-40)=-41
-2-20-2+(-20)=-22
-4-10-4+(-10)=-14
-5-8-5+(-8)=-13

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 then factors further to

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

Answer:

So completely 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).

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

 Geometry_Word_Problems/521356: 1 solutions Answer 346438 by jim_thompson5910(28595)   on 2011-10-25 23:57:05 (Show Source): You can put this solution on YOUR website!J+16=35 J=35-16 J=19
 Number-Line/521333: Can you represent (-5)(-3) on a number line?1 solutions Answer 346433 by jim_thompson5910(28595)   on 2011-10-25 23:44:13 (Show Source): You can put this solution on YOUR website!(-5)(-3) = 15 So you can represent (-5)(-3) on a number line Simply draw a straight line and mark it like a ruler with numbers 0, 1, 2, 3, ..., 10, 11, 12, 13, 14, 15, 16, 17, ... etc Then label (-5)(-3) at 15
 Polynomials-and-rational-expressions/521189: simplify the following expression |5-3|- |3-5|1 solutions Answer 346375 by jim_thompson5910(28595)   on 2011-10-25 19:58:25 (Show Source): You can put this solution on YOUR website!|5-3|- |3-5| |2|- |-2| 2 - 2 0 So |5-3|- |3-5| = 0 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
 Sequences-and-series/521188: hi i was wondering what the numerical pattern is for 7,19,31,431 solutions Answer 346374 by jim_thompson5910(28595)   on 2011-10-25 19:56:54 (Show Source): You can put this solution on YOUR website!You're adding 12 each time. How do I know that? Well after a while you get used to seeing patterns like this, but notice how 19-7 = 12, 31-19 = 12, and 43-31 = 12 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/521178: 17=8c-71 solutions Answer 346370 by jim_thompson5910(28595)   on 2011-10-25 19:47:46 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Subtract from both sides. 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/521169: is the ordered pair (7,8) a solution to the equation x-y=5?1 solutions Answer 346369 by jim_thompson5910(28595)   on 2011-10-25 19:47:15 (Show Source): You can put this solution on YOUR website!x-y=5 7-8=5 ... note: replace x with 7 and y with 8 (since (7,8) means x=7 and y=8) -1 = 5 Since the last equation is false, the ordered pair is not a solution. 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/521177: factor 9x^4-81y^21 solutions Answer 346365 by jim_thompson5910(28595)   on 2011-10-25 19:45:01 (Show Source): You can put this solution on YOUR website! Use the difference of squares factoring formula here. So factors to In other words, 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/521162: (-x2)(-x)1 solutions Answer 346359 by jim_thompson5910(28595)   on 2011-10-25 19:33:33 (Show Source): You can put this solution on YOUR website!(-x^2)(-x) = (-1*-1)*(x^2*x) = x^3 So (-x^2)(-x) = x^3 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/521161: (x+1)(x3+7x2+5x+4)1 solutions Answer 346357 by jim_thompson5910(28595)   on 2011-10-25 19:32:24 (Show Source): You can put this solution on YOUR website! Start with the given expression. Expand. Distribute. Multiply. Now combine like terms. So expands to . In other words, . 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/521136: Please help me in this question i got it for h.w and i need it for tomorrow please help! Thanks so much i really appreciate it! Question: Why is it impossible for any point to lie on both y=3x+5 and on y=3x-2? Please help and show how you got to it. Thanks! :) 1 solutions Answer 346351 by jim_thompson5910(28595)   on 2011-10-25 19:16:59 (Show Source): You can put this solution on YOUR website!If y=3x+5 and y=3x-2, then 3x+5 = 3x-2 ( I started with y=3x-2, then replaced 'y' with '3x+5' on the left side) Solve this equation to get 3x+5=3x-2 3x=3x-2-5 3x-3x=-2-5 0x=-2-5 0x=-7 0=-7 Since this equation is NEVER true for any x value, this means that there are no solutions. So because there are no solutions for x, there are no solutions for y as well. Therefore, there are no points that lie on both lines at the same time. So the two lines never intersect. 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/521123: 8x+17< or = to 6x-251 solutions Answer 346342 by jim_thompson5910(28595)   on 2011-10-25 19:05:07 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Subtract from both sides. Subtract from 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
 real-numbers/521101: My question is " the set of whole numbers is closed under subtraction. if false, give a counterexample." First what are whole number? And what does it mean by closed under subtraction1 solutions Answer 346340 by jim_thompson5910(28595)   on 2011-10-25 18:57:59 (Show Source): You can put this solution on YOUR website!The set of whole numbers is the set {0, 1, 2, 3, 4, 5, 6, ...} This is the set of positive integers (ie numbers that have no decimal/fractional part) with zero included. --------------------------- For a set to be closed under subtraction, EVERY possible subtraction of ANY two elements must lie in the set. So if you subtract ANY two elements in a certain set, and that result is also in the same set, then that set is closed under subtraction For example, the set of integers is closed under subtraction since subtracting ANY two integers gives you an integer. --------------------------- Using this info, we'll find that the statement "the set of whole numbers is closed under subtraction" is false since 0 - 2 = -2 (this is the counterexample) Notice we're subtracting 2 from 0 (both of which are whole numbers) to get -2 (which is NOT a whole number) 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/520818: Solve for a using the addition and multiplication principles: 14-6a= -2a+3 1 solutions Answer 346332 by jim_thompson5910(28595)   on 2011-10-25 18:40:44 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from 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/520989: in this problem 15x-8-3x=16 how do you figure out what x reprsents1 solutions Answer 346331 by jim_thompson5910(28595)   on 2011-10-25 18:38:14 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Add to both sides. 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
 expressions/520999: simplify the expression 6+9(-8x+6)1 solutions Answer 346329 by jim_thompson5910(28595)   on 2011-10-25 18:37:26 (Show Source): You can put this solution on YOUR website!6+9(-8x+6) 6+9(-8x)+9(6) 6-72x+54 -72x+60 So 6+9(-8x+6)=-72x+60 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/521097: 3-4q=10q+10 1 solutions Answer 346328 by jim_thompson5910(28595)   on 2011-10-25 18:34:03 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Subtract from 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/521043: -x-(13+4x)=-3(5-9x)+21 solutions Answer 346326 by jim_thompson5910(28595)   on 2011-10-25 18:32:59 (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. 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
 Graphs/520829: 2(x-1)=41 solutions Answer 346244 by jim_thompson5910(28595)   on 2011-10-25 13:21:12 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Add to both sides. 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
 Average/520879: Solve for K A=(B+K)/G How do you do this?1 solutions Answer 346243 by jim_thompson5910(28595)   on 2011-10-25 13:19:45 (Show Source): You can put this solution on YOUR website!A=(B+K)/G AG=B+K AG-B=K K = AG - B 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/520876: find product (2x-4y)(2x+4y)1 solutions Answer 346242 by jim_thompson5910(28595)   on 2011-10-25 13:18:45 (Show Source): You can put this solution on YOUR website!(2x-4y)(2x+4y) 2x(2x+4y)-4y(2x+4y) 4x^2+8xy-8xy-16y^2 4x^2-16y^2 So (2x-4y)(2x+4y) = 4x^2-16y^2 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
 Exponents/520601: I am suppose to rewrite using positive exponents 8x^-2y Would the answer be 8y/x^2 ?1 solutions Answer 346130 by jim_thompson5910(28595)   on 2011-10-24 22:13:19 (Show Source): You can put this solution on YOUR website!Yes, where x is not zero
 logarithm/520571: Change the logarithmic expression to an equivalent expression involving an exponent. log3(1/9)= -21 solutions Answer 346114 by jim_thompson5910(28595)   on 2011-10-24 21:31:57 (Show Source): You can put this solution on YOUR website!log3(1/9)= -2 converts to 3^(-2) = 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
 Exponents/520576: help show work for simplifying: sqrt(72)1 solutions Answer 346113 by jim_thompson5910(28595)   on 2011-10-24 21:31:07 (Show Source): You can put this solution on YOUR website!sqrt(72) sqrt(36*2) sqrt(36)*sqrt(2) 6*sqrt(2) So sqrt(72) = 6*sqrt(2) 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
 Surface-area/519989: Find the volume of the figure where a = 5 ft, b = 9 ft, and c = 10 ft i have no clue how to do this, can you show me the steps so i have a beter idea and can solve the rest of the problems? thanks1 solutions Answer 345889 by jim_thompson5910(28595)   on 2011-10-23 23:45:49 (Show Source): You can put this solution on YOUR website!If this figure is a rectangular solid (like a building block), then the volume is simply Volume = Length x Width x Height V = L x H x W V = 5 x 9 x 10 V = 45 x 10 V = 450 So the volume is 450 cubic ft 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