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Polynomials-and-rational-expressions/181934: These need to be factored completely
30z^8 + 44z^5 +16z^2 Could it be 2z^2(3z^ + 2)(5z^3 +4)
24x² + 14xy +2y²
(m+n)(x+3) + (m+n)(5+5) Could it be (m+n+3)(x+y+5)
Solve using the principal of zero products
(x+ 1/7)(x-4/5) = 0
Find the x-intercepts for the graph of the equation
Y = x² + 4x -45 Could it be (-9,0,(5,0)
Factor by grouping
-36x² -30x + 36 Could it be -6(3x-2)(2x+3)

1 solutions

Answer 136554 by jim_thompson5910(28595)   on 2009-02-14 14:25:55 (Show Source):
You can put this solution on YOUR website!
I'll do the first two, which will hopefully help you with the rest of the problems. If not, then repost.

# 1

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 15 and 8 respectively.

Now multiply the first coefficient 15 and the last coefficient 8 to get 120. Now what two numbers multiply to 120 and add to the middle coefficient 22? Let's list all of the factors of 120:

Factors of 120:
1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

-1,-2,-3,-4,-5,-6,-8,-10,-12,-15,-20,-24,-30,-40,-60,-120 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 120
1*120
2*60
3*40
4*30
5*24
6*20
8*15
10*12
(-1)*(-120)
(-2)*(-60)
(-3)*(-40)
(-4)*(-30)
(-5)*(-24)
(-6)*(-20)
(-8)*(-15)
(-10)*(-12)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 22? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 22

First NumberSecond NumberSum
11201+120=121
2602+60=62
3403+40=43
4304+30=34
5245+24=29
6206+20=26
8158+15=23
101210+12=22
-1-120-1+(-120)=-121
-2-60-2+(-60)=-62
-3-40-3+(-40)=-43
-4-30-4+(-30)=-34
-5-24-5+(-24)=-29
-6-20-6+(-20)=-26
-8-15-8+(-15)=-23
-10-12-10+(-12)=-22

From this list we can see that 10 and 12 add up to 22 and multiply to 120

Now looking at the expression , replace with (notice adds up 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

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

So completely factors to

# 2

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 12 and 1 respectively.

Now multiply the first coefficient 12 and the last coefficient 1 to get 12. Now what two numbers multiply to 12 and add to the middle coefficient 7? Let's list all of the factors of 12:

Factors of 12:
1,2,3,4,6,12

-1,-2,-3,-4,-6,-12 ...List the negative factors as well. This will allow us to find all possible combinations

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

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 7? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 7

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 this list we can see that 3 and 4 add up to 7 and multiply to 12

Now looking at the expression , replace with (notice adds up 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

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

So completely factors to

 Graphs/181883: The line through (2,-3) that is perpendicular to the line y= -4x + 8 written in standard form containing only integer coefficients. I am having a horrible time with these graphs, any help is greatly appreciated!1 solutions Answer 136508 by jim_thompson5910(28595)   on 2009-02-13 23:38:02 (Show Source): You can put this solution on YOUR website! We can see that the equation has a slope and a y-intercept . Now to find the slope of the perpendicular line, simply flip the slope to get . Now change the sign to get . So the perpendicular slope is . Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope and the coordinates of the given point . Start with the point slope formula Plug in , , and Rewrite as Multiply both sides by 4. Distribute Subtract 12 from both sides. Subtract "x" from both sides. Combine like terms. Rearrange the terms. Multiply EVERY term by -1 to make the "x" coefficient positive. ============================================= Answer: So the equation of the line that is perpendicular to and goes through the point (2,-3) in standard form is Here's the graph of the two lines to verify the answer: Graph of the original equation (red) and the perpendicular line (green) through the point .
 Graphs/181882: The line through (-2,-1) that is parallel to the line 5x + 3y =9. I am having a horrible time trying to write solve this and then write it into standard form containing only integer coefficients.1 solutions Answer 136507 by jim_thompson5910(28595)   on 2009-02-13 23:12:05 (Show Source): You can put this solution on YOUR website! Start with the given equation. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. We can see that the equation has a slope and a y-intercept . Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is . Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope and the coordinates of the given point . Start with the point slope formula Plug in , , and Rewrite as Rewrite as Multiply both sides by 3. Distribute Add 5x to both sides. Subtract 3 from both sides. Combine and rearrange the terms. ======================================= Answer: So the equation of the line that is parallel to and that goes through (-2,-1) is: Also, the equation is in standard form where , , and
 Polynomials-and-rational-expressions/181878: This question is from textbook 5 - x-1 ____ ____ = 4 over x-x Is this correct? Thanks x x1 solutions Answer 136503 by jim_thompson5910(28595)   on 2009-02-13 22:24:20 (Show Source): You can put this solution on YOUR website! Start with the given expression. Combine the fractions. This is only possible if the denominators are equal (and they are) Distribute Combine like terms. So where
 Distributive-associative-commutative-properties/181868: Factor completely and show steps: x^2-3wx+2xy-6wy1 solutions Answer 136493 by jim_thompson5910(28595)   on 2009-02-13 20:21:39 (Show Source): You can put this solution on YOUR website! Start with the given expression Group like terms 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 So factors to
 Expressions-with-variables/181877: I have tried this but I am having trouble, can you please help. Use substitution to solve each system. If it does not have one solution then put no solution or indinitely many solutions. 4X-5Y=-7 Y=5X1 solutions Answer 136491 by jim_thompson5910(28595)   on 2009-02-13 20:17:28 (Show Source): You can put this solution on YOUR website! Start with the given system Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute Combine like terms on the left side Divide both sides by -21 to isolate x Reduce Now that we know that , we can plug this into to find Substitute for each Multiply So our answer is and which also looks like
 Polynomials-and-rational-expressions/181870: Factor completely and show steps: 4x^2-36y^21 solutions Answer 136490 by jim_thompson5910(28595)   on 2009-02-13 20:12:19 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite as . Rewrite as . Notice how we have a difference of squares where in this case and . So let's use the difference of squares formula to factor the expression: Start with the difference of squares formula. Plug in and . So this shows us that factors to . In other words .
Polynomials-and-rational-expressions/181869: Factor completely and show steps:
x^2-5x-14
1 solutions

Answer 136489 by jim_thompson5910(28595)   on 2009-02-13 20:11:25 (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 :
1,2,7,14
-1,-2,-7,-14

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

These factors pair up and multiply to .
1*(-14)
2*(-7)
(-1)*(14)
(-2)*(7)

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

First NumberSecond NumberSum
1-141+(-14)=-13
2-72+(-7)=-5
-114-1+14=13
-27-2+7=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 .

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

Polynomials-and-rational-expressions/181871: Factor completely and show steps:
6x^2-13x-5

1 solutions

Answer 136488 by jim_thompson5910(28595)   on 2009-02-13 20:10:38 (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 :
1,2,3,5,6,10,15,30
-1,-2,-3,-5,-6,-10,-15,-30

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

These factors pair up and multiply to .
1*(-30)
2*(-15)
3*(-10)
5*(-6)
(-1)*(30)
(-2)*(15)
(-3)*(10)
(-5)*(6)

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

First NumberSecond NumberSum
1-301+(-30)=-29
2-152+(-15)=-13
3-103+(-10)=-7
5-65+(-6)=-1
-130-1+30=29
-215-2+15=13
-310-3+10=7
-56-5+6=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 .

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

 Polynomials-and-rational-expressions/181848: This question is from textbook 3x^2+18x-48 ___________ 2x+16 Lowest terms Thank you1 solutions Answer 136443 by jim_thompson5910(28595)   on 2009-02-13 15:26:11 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor the numerator Factor the denominator Highlight the common terms. Cancel out the common terms. Simplify Distribute ======================================= Answer: So simplifies to In other words, where
 Functions/181843: Write an equation of the line given the y-intercept and slope:m=1/2,b=31 solutions Answer 136441 by jim_thompson5910(28595)   on 2009-02-13 15:14:49 (Show Source): You can put this solution on YOUR website! Start with the general slope-intercept equation Plug in and So the equation of the line is
 Polynomials-and-rational-expressions/181838: This question is from textbook 4x^4-10x^3+8x^2 _______________ 2x Thank you, I am really confused.1 solutions Answer 136439 by jim_thompson5910(28595)   on 2009-02-13 15:05:49 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor out the GCF Break down into Highlight the common terms. Cancel out the common terms. Simplify (by removing the canceled terms) Distribute ================================== Answer: So simplifies to In other words, where
 Graphs/181828: Find the slope and y-intercept of the line y = 3x + 4 I tried so hard I just can't get it.1 solutions Answer 136420 by jim_thompson5910(28595)   on 2009-02-13 13:41:52 (Show Source): You can put this solution on YOUR website!Notice how the line is of the form where "m" is the slope and "b" is the y-intercept. So this simply means that and which tells us that the slope is 3 and the y-intercept is 4
 Quadratic-relations-and-conic-sections/181822: Find an equation of the circle with center (-2,4) and radius 3 THANK YOU SO MUCH1 solutions Answer 136418 by jim_thompson5910(28595)   on 2009-02-13 13:33:18 (Show Source): You can put this solution on YOUR website!General circle equation: Note: (h,k) is the center and "r" is the radius So in our case, , and , since the center is (-2,4), and (since the radius is 3) Start with the given equation Plug in , , and Square 3 to get 9 Rewrite as ================================== Answer: So the equation of the circle is
Graphs/181816: This question is from textbook Elementary and Intermediate
-x+5y=4
1 solutions

Answer 136414 by jim_thompson5910(28595)   on 2009-02-13 13:27:02 (Show Source):
You can put this solution on YOUR website!

 Equations/181818: (36b)^1/2(2b^1/4) equals nb^r where n the coefficient is: and r the exponent of b is:1 solutions Answer 136412 by jim_thompson5910(28595)   on 2009-02-13 13:25:39 (Show Source): You can put this solution on YOUR website!Note: So This means that So Now add the exponents and multiply: So where
Functions/181820: Write the equation of the line passing through (2,3) and (-3,-7) in slope-intercept form?
By the way, thank you for your continued help, much appreciated!
karen
1 solutions

Answer 136411 by jim_thompson5910(28595)   on 2009-02-13 13:19:42 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: Finding the Equation of a Line First lets find the slope through the points (,) and (,) Start with the slope formula (note: (,) is the first point (,) and (,) is the second point (,)) Plug in ,,, (these are the coordinates of given points) Subtract the terms in the numerator to get . Subtract the terms in the denominator to get Reduce So the slope is ------------------------------------------------ Now let's use the point-slope formula to find the equation of the line: ------Point-Slope Formula------ where is the slope, and (,) is one of the given points So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Distribute Multiply and to get Add to both sides to isolate y Combine like terms and to get ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line which goes through the points (,) and (,) is: The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver) Graph of through the points (,) and (,) Notice how the two points lie on the line. This graphically verifies our answer.

 Linear-systems/180906: Solving Linear Systems graphically d) 3x+2y=6 g) 2x-5y=10 y=4-x x+3y=-6 Thankssssssss and ppleaseeeeeeeeeeeeeee1 solutions Answer 135634 by jim_thompson5910(28595)   on 2009-02-08 14:51:23 (Show Source): You can put this solution on YOUR website! I'll do the first one to get you started d) Start with the given system of equations: In order to graph these equations, we must solve for y first. Let's graph the first equation: Start with the first equation. Subtract from both sides. Divide both sides by to isolate . Rearrange the terms and simplify. Now let's graph the equation: Graph of . Note: let me know if you need help graphing equations ------------------------------------------------------------------- Now let's graph the second equation : Graph of . ------------------------------------------------------------------- Now let's graph the two equations together: Graph of (red). Graph of (green) From the graph, we can see that the two lines intersect at the point . So the solution to the system of equations is . This tells us that the system of equations is consistent and independent.
Polynomials-and-rational-expressions/180901: Fill in the missing blank!
x^2x^5 ________
x^-8 x^-8
These are fractions!
a) x^7
b) x^-3
c) x^-10
d) x^10
How did you get the answer

1 solutions

Answer 135631 by jim_thompson5910(28595)   on 2009-02-08 14:43:36 (Show Source):
You can put this solution on YOUR website!
Let's simplify

Error, solver not defined for name 'monomial_arithmetic'.
 Error occurred executing solver 'monomial_arithmetic' .

So this means that

which means that the answer choice is A)

Polynomials-and-rational-expressions/180900: Simply the expression:
2n^2y^19n^11y^5 2
the 2 at the end has no variable or exponent!
How did you get the answer
1 solutions

Answer 135627 by jim_thompson5910(28595)   on 2009-02-08 14:34:56 (Show Source):
You can put this solution on YOUR website!
Is the expression ??? If so, then...

Error, solver not defined for name 'monomial_arithmetic'.
 Error occurred executing solver 'monomial_arithmetic' .

 Polynomials-and-rational-expressions/180894: 8-(5/y+2)=1/y+11 solutions Answer 135622 by jim_thompson5910(28595)   on 2009-02-08 13:56:56 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply EVERY term by the LCD to clear out the fractions. Multiply and simplify FOIL Distribute Subtract y from both sides. Subtract 2 from both sides. Combine like terms. Notice we have a quadratic equation in the form of where , , and Let's use the quadratic formula to solve for y Start with the quadratic formula Plug in , , and Square to get . Multiply to get Subtract from to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the answers are or
 Exponents-negative-and-fractional/180893: Please help me solve this algebraic equation! 7ab^-41 solutions Answer 135620 by jim_thompson5910(28595)   on 2009-02-08 13:52:51 (Show Source): You can put this solution on YOUR website!You CANNOT solve this (since there is no equals sign). So I'm assuming that you just want to simplify. Start with the given expression. Rewrite as Multiply So simplifies to
 Quadratic_Equations/180892: I need to find the vertex form/function in form, axis of symmetry and max or min of the following equation, and am really confused. y=x^2+6x+51 solutions Answer 135619 by jim_thompson5910(28595)   on 2009-02-08 13:35:44 (Show Source): You can put this solution on YOUR website! In order to find the vertex, we first need to find the x-coordinate of the vertex. To find the x-coordinate of the vertex, use this formula: . Start with the given formula. From , we can see that , , and . Plug in and . Multiply 2 and to get . Divide. So the x-coordinate of the vertex is . Note: this means that the axis of symmetry is also . Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex. Start with the given equation. Plug in . Square to get . Multiply and to get . Multiply and to get . Combine like terms. So the y-coordinate of the vertex is . So the vertex is . Now because (which is positive), this means that the parabola opens upward and that there is a minimum. So the min is the same as the y-coordinate of the vertex. This means that the min is Here's a graph to confirm our answers: Graph of