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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 
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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 Number | Second Number | Sum | | 1 | 40 | 1+40=41 | | 2 | 20 | 2+20=22 | | 4 | 10 | 4+10=14 | | 5 | 8 | 5+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 
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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
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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
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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
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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 subtraction
1 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.
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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
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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? thanks
1 solutions
Answer 345889 by jim_thompson5910(28595) on 2011-10-23 23:45:49 (Show Source):
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