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 expressions/153295: evaluate: 3^01 solutions Answer 112831 by jim_thompson5910(28595)   on 2008-08-25 08:54:02 (Show Source): You can put this solution on YOUR website! note: where . In other words, any number to the zeroth power (except zero) is 1.
 Numeric_Fractions/153296: convert to a decimal: (2/3)^-11 solutions Answer 112830 by jim_thompson5910(28595)   on 2008-08-25 08:52:57 (Show Source):
Polynomials-and-rational-expressions/153300: factor completly:
36m^2-48m+16

1 solutions

Answer 112829 by jim_thompson5910(28595)   on 2008-08-25 08:51:42 (Show Source):
You can put this solution on YOUR website!

Factor out the GCF

Now let's focus on 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 :
1,2,3,4,6,9,12,18,36
-1,-2,-3,-4,-6,-9,-12,-18,-36

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

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

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

First NumberSecond NumberSum
1361+36=37
2182+18=20
3123+12=15
494+9=13
666+6=12
-1-36-1+(-36)=-37
-2-18-2+(-18)=-20
-3-12-3+(-12)=-15
-4-9-4+(-9)=-13
-6-6-6+(-6)=-12

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

So factors to

This means that the expression goes from and factors further to

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

So factors to

Expressions-with-variables/153303: Factor the expression 4n^3 + 8n^2 - 5n - 10
Factor k^2 + kf - 2f^2
Factor 6g^2 + 11g - 35

I am not sure how to factor these. I am especially "stuck" on the one that uses kf.
Can you help? Thanks!
1 solutions

Answer 112828 by jim_thompson5910(28595)   on 2008-08-25 08:49:14 (Show Source):
You can put this solution on YOUR website!
# 1

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

# 2

Looking at we can see that the first term is and the last term is where the coefficients are 1 and -2 respectively.

Now multiply the first coefficient 1 and the last coefficient -2 to get -2. Now what two numbers multiply to -2 and add to the middle coefficient 1? Let's list all of the factors of -2:

Factors of -2:
1,2

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

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

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

Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1

First NumberSecond NumberSum
1-21+(-2)=-1
-12-1+2=1

From this list we can see that -1 and 2 add up to 1 and multiply to -2

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 factors to

# 3

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 :
1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
-1,-2,-3,-5,-6,-7,-10,-14,-15,-21,-30,-35,-42,-70,-105,-210

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

These factors pair up and multiply to .
1*(-210)
2*(-105)
3*(-70)
5*(-42)
6*(-35)
7*(-30)
10*(-21)
14*(-15)
(-1)*(210)
(-2)*(105)
(-3)*(70)
(-5)*(42)
(-6)*(35)
(-7)*(30)
(-10)*(21)
(-14)*(15)

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

First NumberSecond NumberSum
1-2101+(-210)=-209
2-1052+(-105)=-103
3-703+(-70)=-67
5-425+(-42)=-37
6-356+(-35)=-29
7-307+(-30)=-23
10-2110+(-21)=-11
14-1514+(-15)=-1
-1210-1+210=209
-2105-2+105=103
-370-3+70=67
-542-5+42=37
-635-6+35=29
-730-7+30=23
-1021-10+21=11
-1415-14+15=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).

 expressions/153286: simplify: 1 solutions Answer 112809 by jim_thompson5910(28595)   on 2008-08-25 00:12:22 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute the negative Group the common terms Combine like terms So
 Exponents-negative-and-fractional/153260: 4x^2-811 solutions Answer 112794 by jim_thompson5910(28595)   on 2008-08-24 20:28:50 (Show Source): You can put this solution on YOUR website!Do you want to factor this? Start with the given expression. Rewrite as . Rewrite as . Notice how we have a difference of squares. So let's use the difference of squares formula to factor the expression: Factor the expression using the difference of squares. So factors to . In other words .
 Expressions-with-variables/153250: This question is from textbook Algebra Structure and Method Please help with this problem. 1-3/4(v+2)=-5 1 solutions Answer 112789 by jim_thompson5910(28595)   on 2008-08-24 19:50:56 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Distribute again. 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 answer is
 Equations/153241: This question is from textbook intermediate algebra on page 58 of the textbook. the problem is a=180-(a-2/n) solve for n. this is what i got so far up to point where i am stuck. a=180(1-2/n) distribute a=180-360/n +360/n 360/n=180-a -a ? am i doing this right so far? Also im not sure of the next step. After i got to this point i didnt know what to do1 solutions Answer 112772 by jim_thompson5910(28595)   on 2008-08-24 17:56:23 (Show Source): You can put this solution on YOUR website!So the equation is ? Start with the given equation. Divide both sides by 180. Subtract 1 from both sides. Combine the fractions. Multiply both sides by "n". Multiply both sides by 180. Multiply Divide both sides by .
 percentage/153239: what percent of one u.s. dollar is $.25?1 solutions Answer 112771 by jim_thompson5910(28595) on 2008-08-24 17:52:23 (Show Source): You can put this solution on YOUR website!Note:$0.25 = 25 cents and $1 = 100 cents Start with the given formula. Plug in 25 cents for the numerator and 100 cents for the denominator Cancel like terms Simplify So$0.25 is 25% of one U.S. dollar
 Linear-systems/153240: you have used all of a $50 gift certificate watching movies at the local theater. Afternoon movies are$4 and evening movies are $6. you have watched a total of 10 movies. HOw much have you spent on evening movies?1 solutions Answer 112770 by jim_thompson5910(28595) on 2008-08-24 17:48:17 (Show Source): You can put this solution on YOUR website!Let x=# of$6 movies and y=# of $4 movies Since "you have watched a total of 10 movies", this means that the first equation is Also, since you only have$50 to spend, this means that the second equation is So we have the system of equations: Let's use substitution to solve this system. Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y. So let's isolate y in the first equation Start with the first equation Subtract from both sides Rearrange the equation --------------------- Since , we can now replace each in the second equation with to solve for 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 to Multiply Combine like terms on the left side Subtract 40 from both sides Combine like terms on the right side Divide both sides by 2 to isolate x Divide -----------------First Answer------------------------------ So the first part of our answer is: Since we know that we can plug it into the equation (remember we previously solved for in the first equation). Start with the equation where was previously isolated. Plug in Multiply Combine like terms -----------------Second Answer------------------------------ So the second part of our answer is: -----------------Summary------------------------------ So our answers are: and This means that you bought 5 $6 movies and 5$4 movies
 Linear-equations/153233: c=2n+201 solutions Answer 112768 by jim_thompson5910(28595)   on 2008-08-24 17:42:36 (Show Source): You can put this solution on YOUR website!What do you want to do with this equation? Do you want to solve for n? Start with the given equation. Subtract 20 from both sides. Divide both sides by 2. Rearrange the equation
 Polynomials-and-rational-expressions/153238: (3u^2v – 2)(4u^2v + 6) this is what I got...but to be honest i'm confused a little. (3u^2v – 2)(4u^2v + 6) 12u^2v + 18u^2v 8u^2v - 12 12u^2v + 26u^2v – 12 38u^4v^2 – 12 1 solutions Answer 112767 by jim_thompson5910(28595)   on 2008-08-24 17:40:58 (Show Source): You can put this solution on YOUR website! Start with the given expression. Now let's FOIL the expression. Remember, when you FOIL an expression, you follow this procedure: Multiply the First terms:. Multiply the Outer terms:. Multiply the Inner terms:. Multiply the Last terms:. Now collect every term to make a single expression. Now combine like terms. So FOILs to . In other words, .
 Expressions-with-variables/153182: B 2b ----+---- b-1 b squared - 11 solutions Answer 112764 by jim_thompson5910(28595)   on 2008-08-24 17:32:30 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Notice how the LCD is Multiply the first term by . The goal is to get the first denominator equal to the LCD Combine the fractions. Distribute Add the fractions. Combine like terms. So where or
 Graphs/153223: on my book i have this question graph the inequality x>-2 and i dont get it can you help me ohh and it asks for the open or close dot cant you explain that to me 1 solutions Answer 112763 by jim_thompson5910(28595)   on 2008-08-24 17:27:22 (Show Source): You can put this solution on YOUR website! Start with the given inequality Plot the point on a number line Now plug in into the inequality Since is true, this means that we shade the entire region that is in. So shade to the right of . Note: there is a open circle at
 Exponential-and-logarithmic-functions/153228: This question is from textbook elementary and intermediate algebra Simplify and write with positive exponents: 7yx^-5 ______ 28y^-5 Simplify and write with positive exponents x^-4 y^5 ________ z^-1 Evaluate (1/3)^2 + 1/4 -(4/3)^2 * (1/2)^3 Evaluate 2*(5 - 3)^3 + 8 ÷ 2 + (9 - 4)^2 Evaluate {3(7 - 9) + 16}^3 ÷ (-5) - 2^4 Thanks everyone for your help. :)1 solutions Answer 112761 by jim_thompson5910(28595)   on 2008-08-24 17:23:51 (Show Source): You can put this solution on YOUR website!# 1 Start with the given expression. Divide the coefficients and to get When you divide monomials, simply subtract the exponents. Subtract. Rewrite as Combine the fractions. So where or # 2 Note: and So where and # 3 So # 4 So # 5 So
 Polynomials-and-rational-expressions/153225: For all r not equal to + or - 2, r^2-5r+6/r^2-41 solutions Answer 112759 by jim_thompson5910(28595)   on 2008-08-24 17:10:03 (Show Source): You can put this solution on YOUR website! 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
 Triangles/153234: what is the perimeter of a triangle which sides measure 6,8,and 10 inches?1 solutions Answer 112758 by jim_thompson5910(28595)   on 2008-08-24 17:07:55 (Show Source): You can put this solution on YOUR website!Perimeter of a triangle: P=side1+side2+side3 P=6+8+10=14+10=24 So the perimeter of the triangle is 24 inches
 Functions/153214: This question is from textbook find a function formula that takes the x values and produces the y values x y 0 -2 1 1 2 4 3 7 4 10 I will send a check for your help can you give me a mailing address1 solutions Answer 112747 by jim_thompson5910(28595)   on 2008-08-24 14:56:14 (Show Source): You can put this solution on YOUR website!Notice how as x goes up by 1, y goes up by 3. So this implies a linear relationship. This means that the equation is a line. So let's find equation of the line through the first two points (0,-2) and (1,1) (note: you can pick any pair of points) First let's find the slope of the line through the points and Start with the slope formula. Plug in , , , , , 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 Subtract 2 from both sides. Combine like terms. Simplify So the equation that goes through the points and is -------------------------------------- Answer: So the function takes the x values and produces the y values is Notice how the graph of goes through the points (0,-2), (1,1), (2,4), (3,7) and (4,10). So this visually verifies our answer. Graph of
 Linear-equations/153217: Find the slope of the line containing the points (2,5) and (4,9).1 solutions Answer 112745 by jim_thompson5910(28595)   on 2008-08-24 14:50:43 (Show Source): You can put this solution on YOUR website! Start with the slope formula. Plug in , , , , , Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is
 Graphs/153218: Find the equation of the line in point slope form that passes through (4,3)and is parallel to the line 3x-y=7.1 solutions Answer 112743 by jim_thompson5910(28595)   on 2008-08-24 14:49:42 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. 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 Distribute Multiply Add 3 to both sides. Combine like terms. So the equation of the line parallel to that goes through the point is . Here's a graph to visually verify our answer: Graph of the original equation (red) and the parallel line (green) through the point .
 Linear_Algebra/153216: two lines are parallel if and only if their slopes are _____________.1 solutions Answer 112741 by jim_thompson5910(28595)   on 2008-08-24 14:48:36 (Show Source): You can put this solution on YOUR website!Two lines are parallel if and only if their slopes are equal.
Angles/153211: Find the surface area and volume of a sphere with a radius of 14cm.
Thanks,
Pat
1 solutions

Answer 112739 by jim_thompson5910(28595)   on 2008-08-24 14:19:18 (Show Source):
You can put this solution on YOUR website!
Surface Area:

 Solved by pluggable solver: To calculate Surface area of a sphere Geometry Surface Area and Volume of 3 Dimensional Figures The Formula for Surface area Sphere is Hence, The Surface Area of Sphere of radius 14 is 2463.0086376. For more on this topic, See the lessons on Geometry: Area and Surface Area Some more is on Surface Area and Volume and Perimeter and Area.

Volume:

 Solved by pluggable solver: FIND volume of a sphere Volume of a sphere

Angles/153212: Find the surface area of a circular cylinder with radius of 4cm and a height of 10.2cm.
1 solutions

Answer 112738 by jim_thompson5910(28595)   on 2008-08-24 14:17:42 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: Surface area and Volume of a cylinder The surface area (SA) of a cylinder, excluding the base area and top area, is given by When the areas of base and top are included, the surface area becomes The volume of the cone can be found by the formula In our case the desired values are thus: SA (without base and top) = SA (with base and top) = V = For more on this topic, refer to Surface area and Volume.

 Polynomials-and-rational-expressions/153196: simplify: [-(-2x^2)^2]^3 1 solutions Answer 112736 by jim_thompson5910(28595)   on 2008-08-24 14:12:07 (Show Source): You can put this solution on YOUR website! [-(-2x^2)^2]^3 = [-(-2x^2)(-2x^2)]^3 = [-(4x^4)]^3 = [-4x^4]^3 = -64x^12 
 Polynomials-and-rational-expressions/153197: simpify: -4[5x-6(-5+x)] 1 solutions Answer 112734 by jim_thompson5910(28595)   on 2008-08-24 14:10:29 (Show Source): You can put this solution on YOUR website! -4[5x-6(-5+x)] = -4[5x+30-6x] = -4[-x+30] = 4x-120 
Polynomials-and-rational-expressions/153194: simplify:
(2x^3+2x^2-3x+2) / (x+2)

thanks
1 solutions

Answer 112733 by jim_thompson5910(28595)   on 2008-08-24 14:08:54 (Show Source):
You can put this solution on YOUR website!

Let's simplify this expression using synthetic division

First lets find our test zero:

Set the denominator equal to zero

Solve for x.

so our test zero is -2

Now set up the synthetic division table by placing the test zero in the upper left corner and placing the coefficients of the numerator to the right of the test zero.
 -2 | 2 2 -3 2 |

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 2)
 -2 | 2 2 -3 2 | 2

Multiply -2 by 2 and place the product (which is -4) right underneath the second coefficient (which is 2)
 -2 | 2 2 -3 2 | -4 2

Add -4 and 2 to get -2. Place the sum right underneath -4.
 -2 | 2 2 -3 2 | -4 2 -2

Multiply -2 by -2 and place the product (which is 4) right underneath the third coefficient (which is -3)
 -2 | 2 2 -3 2 | -4 4 2 -2

Add 4 and -3 to get 1. Place the sum right underneath 4.
 -2 | 2 2 -3 2 | -4 4 2 -2 1

Multiply -2 by 1 and place the product (which is -2) right underneath the fourth coefficient (which is 2)
 -2 | 2 2 -3 2 | -4 4 -2 2 -2 1

Add -2 and 2 to get 0. Place the sum right underneath -2.
 -2 | 2 2 -3 2 | -4 4 -2 2 -2 1 0

Since the last column adds to zero, we have a remainder of zero. This means is a factor of

Now lets look at the bottom row of coefficients:

The first 3 coefficients (2,-2,1) form the quotient

So

 Inequalities/153199: for what value of x will k(x)=4x-16 be greater than zero1 solutions Answer 112731 by jim_thompson5910(28595)   on 2008-08-24 14:07:30 (Show Source): You can put this solution on YOUR website! Start with the given equation. Set the right side greater than zero. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is which means that any value of x that is greater than 4 will make greater than zero.
 Inequalities/153202: For what value(s)of x will k(x)=4x-16 be grater than Zero1 solutions Answer 112730 by jim_thompson5910(28595)   on 2008-08-24 14:06:59 (Show Source): You can put this solution on YOUR website! Start with the given equation. Set the right side greater than zero. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is which means that any value of x that is greater than 4 will make greater than zero.
 Linear-systems/153208: how do you solve y= 1/3x - 3 and y= -2x + 4 algebraically? this is the question; Solve the above system of equations algebraically, use the elimination or substitution method. PLEASE HELP!!!!1 solutions Answer 112729 by jim_thompson5910(28595)   on 2008-08-24 14:05:15 (Show Source): You can put this solution on YOUR website! Start with the first equation. Plug in Multiply both sides by the LCD to clear any fractions. 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. This is the first part of our answer. Move onto the second equation Plug in x=3 Simplify. This is the second part of our answer. --------------------------------------------- Answer: So the solutions are and which form the ordered pair (3,-2)
 Functions/153209: Can someone help me out, please? Thank you! The owners of a parking garage have determined that their weekly revenue and cost in dollars are given by the following: R(x) = 56x - 2x^2 C(x) = 24x + 101 find the break even point.1 solutions Answer 112727 by jim_thompson5910(28595)   on 2008-08-24 14:00:55 (Show Source): You can put this solution on YOUR website!Remember, Profit = Revenue - Cost which is symbolically: Plug in and Distribute the negative. Combine like terms Now the break even point occurs when you neither gain money nor lose money. In other words, break even point happens when the profit is zero. So this means that the break even point occurs when Plug in Notice we have a quadratic equation in the form of where , , and Let's use the quadratic formula to solve for x Start with the quadratic formula Plug in , , and Square to get . Multiply to get Subtract from to get Multiply and to get . Simplify the square root (note: If you need help with simplifying square roots, check out this solver) or Break up the expression. So the answers are or which approximate to or So the break even points occur when the price is either $4.33 or$11.67