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 Rational-functions/187079: This question is from textbook algebra2 Find all of the rational zeros of each function 26. p(x)= x^3+3x^2-25x+21 p= (+or-)1, (+or-)3, (+or-)7, (+or-)21 q= (+or-)1 1/1 1/3, 1/7, 1/211 solutions Answer 140229 by jim_thompson5910(28476)   on 2009-03-17 16:26:17 (Show Source): You can put this solution on YOUR website!Any rational zero can be found through this equation where p and q are the factors of the last and first coefficients So let's list the factors of 21 (the last coefficient): Now let's list the factors of 1 (the first coefficient): Now let's divide each factor of the last coefficient by each factor of the first coefficient Now simplify These are all the distinct rational zeros of the function that could occur Note: these are all of the possible roots. To find the actual rational roots (if there are any), you need to plug each possible root into the given polynomial. If you get a result of 0, then the corresponding input is a zero.
 Rational-functions/187076: This question is from textbook algebra2 Find all of the rational zeros of each function 22. f(x)=2x^5-x^4-2x+11 solutions Answer 140226 by jim_thompson5910(28476)   on 2009-03-17 16:12:28 (Show Source): You can put this solution on YOUR website!Any rational zero can be found through this equation where p and q are the factors of the last and first coefficients So let's list the factors of 1 (the last coefficient): Now let's list the factors of 2 (the first coefficient): Now let's divide each factor of the last coefficient by each factor of the first coefficient Now simplify These are all the distinct rational zeros of the function that could occur
 Polynomials-and-rational-expressions/187075: Perform and simplify 2/x+5 + 6/x-51 solutions Answer 140225 by jim_thompson5910(28476)   on 2009-03-17 16:11:39 (Show Source): You can put this solution on YOUR website! Start with the given expression. Take note that the LCD is Multiply the first fraction by Distribute Multiply the second fraction by Distribute Combine the fractions. Combine like terms. So where or
 Rational-functions/187071: a^+2a+1/2a^+3a+11 solutions Answer 140223 by jim_thompson5910(28476)   on 2009-03-17 16:07:55 (Show Source): You can put this solution on YOUR website!I'm going to assume that you meant to write Start with the given expression. Factor to get . Factor to get . Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words, where or
 Numeric_Fractions/187073: If the area of a rectangle with length (4/p) is known to be (pq/18), what is the width?1 solutions Answer 140222 by jim_thompson5910(28476)   on 2009-03-17 16:04:02 (Show Source): You can put this solution on YOUR website! Start with the given equation. Plug in and Multiply both sides by "p". Multiply Multiply both sides by . Multiply the fractions. So the width is
 Rational-functions/187074: This question is from textbook algebra2 List all the possible rational zeros of each function 16. p(x)=3x^3-5x^2-11x+3 p= (+or-)1, (+or-)3 q= (+or-)1, (+or-)3 1/1, 1/3, 1/-3, -3/-3 rational zeros 1,3,-3 Making sure if i did the division & simplifying part correct?1 solutions Answer 140221 by jim_thompson5910(28476)   on 2009-03-17 16:00:27 (Show Source): You can put this solution on YOUR website!Any rational zero can be found through this equation where p and q are the factors of the last and first coefficients So let's list the factors of 3 (the last coefficient): Now let's list the factors of 3 (the first coefficient): Now let's divide each factor of the last coefficient by each factor of the first coefficient Now simplify These are all the distinct rational zeros of the function that could occur
 Rational-functions/187067: This question is from textbook algebra2 List all the possible rational zeros of each function 15. n(x)=x^5+6x^3-12x+18 p= (+or-)2; (+or-)9; (+or-)3; (+or-)6 (+or-)18 q= (+or-) 1 1/2, 1/9, 1/3, 1/6, 1/18 Rational Zeros 1,9,3,6,18 I'm wondering if i solved this problem correctly?1 solutions Answer 140219 by jim_thompson5910(28476)   on 2009-03-17 15:39:43 (Show Source): You can put this solution on YOUR website!Any rational zero can be found through this equation where p and q are the factors of the last and first coefficients So let's list the factors of 18 (the last coefficient): Now let's list the factors of 1 (the first coefficient): Now let's divide each factor of the last coefficient by each factor of the first coefficient Now simplify These are all the distinct rational zeros of the function that could occur
 Rational-functions/187061: This question is from textbook algebra2 List all the possible rational zeros of each function 14) f(x)= 3x^4+15 p=(+or-)1: (+or-)15: (+or-)3: (+or-)5: q= (+or-) 3 " if q isn't right then, how would you know what is q? 1 solutions Answer 140217 by jim_thompson5910(28476)   on 2009-03-17 15:13:39 (Show Source): You can put this solution on YOUR website!Any rational zero can be found through this equation where p and q are the factors of the last and first coefficients So let's list the factors of 15 (the last coefficient): Now let's list the factors of 3 (the first coefficient): Now let's divide each factor of the last coefficient by each factor of the first coefficient Now simplify These are all the distinct rational zeros of the function that could occur
 Rational-functions/187057: This question is from textbook algebra2 List all the possible rational zeros of this function. 13. h(x)=x^3+8x+6 1 solutions Answer 140215 by jim_thompson5910(28476)   on 2009-03-17 14:47:49 (Show Source): You can put this solution on YOUR website!Any rational zero can be found through this equation where p and q are the factors of the last and first coefficients So let's list the factors of 6 (the last coefficient): Now let's list the factors of 1 (the first coefficient): Now let's divide each factor of the last coefficient by each factor of the first coefficient Now simplify These are all the distinct rational zeros of the function that could occur
 Exponents-negative-and-fractional/187040: how do you solve (64)-2/3 that is the number 64 with a negative 2/3 as an exponent1 solutions Answer 140214 by jim_thompson5910(28476)   on 2009-03-17 14:46:53 (Show Source): You can put this solution on YOUR website! ... Start with the given expression. ... Flip the fraction to make the exponent positive Convert to radical notation Take the cube root of 64 to get 4. Note: which tells us that Square 4 to get 16 So
 Exponents/187053: How do I simplify 1 solutions Answer 140199 by jim_thompson5910(28476)   on 2009-03-17 13:34:20 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite as . Rewrite as . Rewrite as Multiply the outer exponent by EVERY exponent in the parenthesis Multiply Square -2 to get 4. Cube 2 to get 8 Reduce to get (these are the coefficients). Subtract the exponents to divide the monomials. Subtract Flip the variable that has the negative exponent to make the exponent positive. So where or

12z^2+z=6
1 solutions

Answer 140170 by jim_thompson5910(28476)   on 2009-03-17 00:22:45 (Show Source):
You can put this solution on YOUR website!

Subtract 6 from both sides.

Let's factor the left side:

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 :
1,2,3,4,6,8,9,12,18,24,36,72
-1,-2,-3,-4,-6,-8,-9,-12,-18,-24,-36,-72

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

These factors pair up and multiply to .
1*(-72)
2*(-36)
3*(-24)
4*(-18)
6*(-12)
8*(-9)
(-1)*(72)
(-2)*(36)
(-3)*(24)
(-4)*(18)
(-6)*(12)
(-8)*(9)

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

First NumberSecond NumberSum
1-721+(-72)=-71
2-362+(-36)=-34
3-243+(-24)=-21
4-184+(-18)=-14
6-126+(-12)=-6
8-98+(-9)=-1
-172-1+72=71
-236-2+36=34
-324-3+24=21
-418-4+18=14
-612-6+12=6
-89-8+9=1

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 .

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

So becomes

Now set each factor equal to zero:
or

or Now solve for z in each case

or

 Quadratic_Equations/187007: please help me solve and factor. m^2+9m=0 thank you1 solutions Answer 140168 by jim_thompson5910(28476)   on 2009-03-17 00:07:25 (Show Source): You can put this solution on YOUR website! Start with the given equation Factor out the GCF "m" Now set each factor equal to zero: or or Now solve for "m" in each case So our answers are or

12a^2=5a+28

thank you
1 solutions

Answer 140166 by jim_thompson5910(28476)   on 2009-03-16 23:55:09 (Show Source):
You can put this solution on YOUR website!

Get every term to the left side.

Now let's factor

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 :
1,2,3,4,6,7,8,12,14,16,21,24,28,42,48,56,84,112,168,336
-1,-2,-3,-4,-6,-7,-8,-12,-14,-16,-21,-24,-28,-42,-48,-56,-84,-112,-168,-336

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

These factors pair up and multiply to .
1*(-336)
2*(-168)
3*(-112)
4*(-84)
6*(-56)
7*(-48)
8*(-42)
12*(-28)
14*(-24)
16*(-21)
(-1)*(336)
(-2)*(168)
(-3)*(112)
(-4)*(84)
(-6)*(56)
(-7)*(48)
(-8)*(42)
(-12)*(28)
(-14)*(24)
(-16)*(21)

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

First NumberSecond NumberSum
1-3361+(-336)=-335
2-1682+(-168)=-166
3-1123+(-112)=-109
4-844+(-84)=-80
6-566+(-56)=-50
7-487+(-48)=-41
8-428+(-42)=-34
12-2812+(-28)=-16
14-2414+(-24)=-10
16-2116+(-21)=-5
-1336-1+336=335
-2168-2+168=166
-3112-3+112=109
-484-4+84=80
-656-6+56=50
-748-7+48=41
-842-8+42=34
-1228-12+28=16
-1424-14+24=10
-1621-16+21=5

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 .

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

So then becomes (after factoring the left side)

Now set each factor equal to zero (use the zero product property):

or

Now let's solve each individual equation:

Combine like terms on the right side.

Divide both sides by to isolate . This is one of the solutions.

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

Move onto the second equation.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate . This is the other solution.

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

So the solutions are or

 Quadratic_Equations/186991: find the function value f(x) =x^2-5x-2 find f(-2)1 solutions Answer 140151 by jim_thompson5910(28476)   on 2009-03-16 23:03:47 (Show Source): You can put this solution on YOUR website! Start with the given equation. Plug in . Square to get . Multiply and to get . Multiply and to get . Combine like terms.
 Expressions-with-variables/186952: Evaluate the expressin for n. 1. 48 divided n n= 2, 6, 121 solutions Answer 140122 by jim_thompson5910(28476)   on 2009-03-16 20:16:07 (Show Source): You can put this solution on YOUR website!Simply plug in the given values and simplify n = 2: n = 6: n = 12:
 Miscellaneous_Word_Problems/186950: x varies directly as the square of y and inversely as z. When y6 and z=3, x=112. What is x when y=3 and z=3?1 solutions Answer 140120 by jim_thompson5910(28476)   on 2009-03-16 20:13:26 (Show Source): You can put this solution on YOUR website!"x varies directly as the square of y and inversely as z" translates to (let me know if you need help with the translation) Start with the given equation. Plug in y=6, z=3 and x=112 Multiply both sides by 3. Multiply Square 6 to get 36 Divide both sides by 36 to isolate 'k'. Reduce So the constant is ------------------------------- So the equation is: Plug in , y=3 and z=3 Square 3 to get 9 Multiply and reduce

3x^2+8x+4=0

thanks
1 solutions

Answer 140118 by jim_thompson5910(28476)   on 2009-03-16 20:05:14 (Show Source):
You can put this solution on YOUR website!
Let's factor

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 :
1,2,3,4,6,12
-1,-2,-3,-4,-6,-12

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

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

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

First NumberSecond NumberSum
1121+12=13
262+6=8
343+4=7
-1-12-1+(-12)=-13
-2-6-2+(-6)=-8
-3-4-3+(-4)=-7

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 .

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

So then transforms to

Now set each factor equal to zero:

or

or Solve for x in each case

or

4x^2-11x+6=0 and show work so i can do this on my own tomorrow. thanks

1 solutions

Answer 140114 by jim_thompson5910(28476)   on 2009-03-16 19:35:15 (Show Source):
You can put this solution on YOUR website!
First, factor

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
2*12
3*8
4*6
(-1)*(-24)
(-2)*(-12)
(-3)*(-8)
(-4)*(-6)

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

First NumberSecond NumberSum
1241+24=25
2122+12=14
383+8=11
464+6=10
-1-24-1+(-24)=-25
-2-12-2+(-12)=-14
-3-8-3+(-8)=-11
-4-6-4+(-6)=-10

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 .

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

So becomes

Now set each factor equal to zero (by the use of the zero product property):

or

or Now solve for x in each case

So the solutions are

or

 Rational-functions/186941: This question is from textbook Algebra 2 List all of the possible rational zeros of this function. 12. f(x)=x^3+6x+21 solutions Answer 140112 by jim_thompson5910(28476)   on 2009-03-16 19:32:32 (Show Source): You can put this solution on YOUR website!Any rational zero can be found through this equation where p and q are the factors of the last and first coefficients So let's list the factors of 2 (the last coefficient): Now let's list the factors of 1 (the first coefficient): Now let's divide each factor of the last coefficient by each factor of the first coefficient Now simplify These are all the distinct rational zeros of the function that could occur
 Exponential-and-logarithmic-functions/186942: log base 3 (x+1) - log base 3 x = log base 3 81 solutions Answer 140111 by jim_thompson5910(28476)   on 2009-03-16 19:31:32 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine the logs on the left side using the identity Raise both sides as exponents with the base of 3 (this will cancel out the log base 3) Simplify Multiply both sides by 8. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is which approximates to .
 Linear-equations/186940: Write an equation for the line containing points D and E D(-3, 6), E(-1,0)1 solutions Answer 140110 by jim_thompson5910(28476)   on 2009-03-16 19:21:51 (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 and is the second point . 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 6 to 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/186904: This question is from textbook (((9(x+2)-3(x+3)=2(x-1)+7 what is x equal to?))) 1. (((4x+6/9-2x-6/9=12x+8/12 -x what is x equal to?))) 2.1 solutions Answer 140096 by jim_thompson5910(28476)   on 2009-03-16 14:36:00 (Show Source): You can put this solution on YOUR website!# 1 Start with the given equation. Distribute. Combine like terms on the left side. Combine like terms on the right side. 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 answer is # 2 Start with the given equation. Multiply EVERY term by the LCD 36 to clear the fractions. Distribute. Combine like terms on the left side. Combine like terms on the right side. 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 answer is
Exponents/186892: 2xsquared-12xy-32ysquared
1 solutions

Answer 140091 by jim_thompson5910(28476)   on 2009-03-16 13:18:41 (Show Source):
You can put this solution on YOUR website!
I'm assuming that you want to factor.

Factor out the GCF

Now let's focus on the inner expression

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

Looking at we can see that the first term is and the last term is where the coefficients are 1 and -16 respectively.

Now multiply the first coefficient 1 and the last coefficient -16 to get -16. Now what two numbers multiply to -16 and add to the middle coefficient -6? Let's list all of the factors of -16:

Factors of -16:
1,2,4,8

-1,-2,-4,-8 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -16
(1)*(-16)
(2)*(-8)
(-1)*(16)
(-2)*(8)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to -6? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -6

First NumberSecond NumberSum
1-161+(-16)=-15
2-82+(-8)=-6
-116-1+16=15
-28-2+8=6

From this list we can see that 2 and -8 add up to -6 and multiply to -16

Now looking at the expression , replace with (notice combines to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

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

So our expression goes from and factors further to

------------------
 Numeric_Fractions/186822: This equation is not from a textbook, it's directly from my professor. I'm having difficulties trying to remember how to solve for 'x' in the following situation: ($80 + ($1,000 - X) / 12) / ((\$1,000 + X) / 2) = 0.07 If I divide by the denominator, I end up with Xs on both sides of the equation. Please help! Thank You!1 solutions Answer 140038 by jim_thompson5910(28476)   on 2009-03-15 20:04:38 (Show Source): You can put this solution on YOUR website! Start with the given equation. Take note that the LCD of the inner fractions is 12. Multiply EVERY term (that's either part of a fraction or by itself) by the LCD 12 to clear the inner fractions. Note: because we're multiplying every term on the left side by the same number, it's like we're multiplying the left side by which is simply 1. So the equation has NOT changed. Simplify Multiply Combine like terms. Distribute Multiply both sides by . Distribute Multiply Multiply both sides by 100 to clear out the decimals. Distribute and multiply. 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 answer is which approximates to . Note: since this problem looks like it deals with money, I would go with the approximated solution and round it to two places to get