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 Expressions-with-variables/640495: A company uses two different sized trucks to deliver sand. The first truck can transport x cubic yards. The second truck can transport y cubic yards. The first truck makes S trips to a job site. The second truck makes T trips. What do the following expressions represent in practical terms? S+T x+y xS+yT1 solutions Answer 403234 by jim_thompson5910(28595)   on 2012-08-23 16:39:18 (Show Source): You can put this solution on YOUR website!S+T represents the total number of trips the first and second truck make. x+y represents the total amount both trucks can carry (in one load per truck). xS+yT represents the total amount both trucks can carry (for all the trips combined).
 test/640497: 7-y-y=-11 solutions Answer 403232 by jim_thompson5910(28595)   on 2012-08-23 16:37:42 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 real-numbers/640491: is -22 a integer? whole number? rational number? irrational number? and natural number? I need to know all that apply1 solutions Answer 403229 by jim_thompson5910(28595)   on 2012-08-23 16:30:15 (Show Source): You can put this solution on YOUR website!-22 is an integer and a rational number.
 Quadratic_Equations/640490: Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. x^2 + 8x + ? 1 solutions Answer 403228 by jim_thompson5910(28595)   on 2012-08-23 16:29:04 (Show Source): You can put this solution on YOUR website!Take half of the middle coefficient 8 to get 8/2 = 4 Now square 4 to get 4^2 = 16 So x^2 + 8x + 16 is a perfect square.
 Average/640413: The mean marks of students are 15, 20, 25, 35, 45 x. If the marks of each students are doubled what is the new mean ?  1 solutions Answer 403227 by jim_thompson5910(28595)   on 2012-08-23 16:28:11 (Show Source): You can put this solution on YOUR website!If you have a set of scores, and you double each score, then the mean will double as well.
 Equations/640400: how can i simplify x-(1/y)/(x/y) ?1 solutions Answer 403225 by jim_thompson5910(28595)   on 2012-08-23 16:22:59 (Show Source): You can put this solution on YOUR website! So simplifies to
Polynomials-and-rational-expressions/640411: Could you help me with this problem about factoring polynomials completely
12x^3+8x^2-20x
Thank you for your time and help!
1 solutions

Answer 403223 by jim_thompson5910(28595)   on 2012-08-23 16:21:11 (Show Source):
You can put this solution on YOUR website!

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 :
1,3,5,15
-1,-3,-5,-15

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

These factors pair up and multiply to .
1*(-15) = -15
3*(-5) = -15
(-1)*(15) = -15
(-3)*(5) = -15

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

First NumberSecond NumberSum
1-151+(-15)=-14
3-53+(-5)=-2
-115-1+15=14
-35-3+5=2

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

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

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).

Polynomials-and-rational-expressions/640408: Could you help me with this problem about factoring polynomials completely
4x^2-20x+25
Thank you for your time and help!
1 solutions

Answer 403222 by jim_thompson5910(28595)   on 2012-08-23 16:20:49 (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 :
1,2,4,5,10,20,25,50,100
-1,-2,-4,-5,-10,-20,-25,-50,-100

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

These factors pair up and multiply to .
1*100 = 100
2*50 = 100
4*25 = 100
5*20 = 100
10*10 = 100
(-1)*(-100) = 100
(-2)*(-50) = 100
(-4)*(-25) = 100
(-5)*(-20) = 100
(-10)*(-10) = 100

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

First NumberSecond NumberSum
11001+100=101
2502+50=52
4254+25=29
5205+20=25
101010+10=20
-1-100-1+(-100)=-101
-2-50-2+(-50)=-52
-4-25-4+(-25)=-29
-5-20-5+(-20)=-25
-10-10-10+(-10)=-20

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

Condense the terms.

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

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).

 Quadratic_Equations/640486: Complete the trinomial so it is a perfect square. 16x^2 + ___+ 251 solutions Answer 403221 by jim_thompson5910(28595)   on 2012-08-23 16:20:19 (Show Source): You can put this solution on YOUR website!Take the square root of 16 to get 4. Take the square root of 25 to get 5. Now multiply 4 and 5 to get 20. Double this to get 40. So 40x is the missing term, which means that 16x^2 + _40x_+ 25 is a perfect square trinomial.
 Polynomials-and-rational-expressions/640406: Could you help me with this problem about factoring polynomials completely 12x^2-20x Thank you for your time and help!1 solutions Answer 403219 by jim_thompson5910(28595)   on 2012-08-23 16:18:27 (Show Source): You can put this solution on YOUR website!Factor out the GCF 4x to get
 test/640404: 23f1 solutions Answer 403217 by jim_thompson5910(28595)   on 2012-08-23 16:17:45 (Show Source): You can put this solution on YOUR website!What do you want to do here? Something seems missing...
 Polynomials-and-rational-expressions/640405: Could you help me with this problem about factoring polynomials completely 6x^5-18x^2 Thank you for your time and help! 1 solutions Answer 403216 by jim_thompson5910(28595)   on 2012-08-23 16:16:55 (Show Source): You can put this solution on YOUR website!Factor out the GCF 6x^2 to get
Polynomials-and-rational-expressions/640407: Could you help me with this problem about factoring polynomials completely
2x^2+5x-12
Thank you for your time and help!
1 solutions

Answer 403214 by jim_thompson5910(28595)   on 2012-08-23 16:16:08 (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 :
1,2,3,4,6,8,12,24
-1,-2,-3,-4,-6,-8,-12,-24

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

These factors pair up and multiply to .
1*(-24) = -24
2*(-12) = -24
3*(-8) = -24
4*(-6) = -24
(-1)*(24) = -24
(-2)*(12) = -24
(-3)*(8) = -24
(-4)*(6) = -24

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

First NumberSecond NumberSum
1-241+(-24)=-23
2-122+(-12)=-10
3-83+(-8)=-5
4-64+(-6)=-2
-124-1+24=23
-212-2+12=10
-38-3+8=5
-46-4+6=2

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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 Trigonometry-basics/640471: |-2-x|>-3 1 solutions Answer 403211 by jim_thompson5910(28595)   on 2012-08-23 16:14:45 (Show Source): You can put this solution on YOUR website!Since the absolute value of any number is either 0 or positive, this means that |-2-x| is NEVER negative. So it is ALWAYS greater than any negative number. So |-2-x| > -3 has an infinite number of solutions since any real number will work for x and satisfy that inequality.
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