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 Graphs/277162: how do i solve a the problem 5/3(6)+8 what is the answer and is it a negative 1 solutions Answer 201825 by jim_thompson5910(28504)   on 2010-03-04 13:03:16 (Show Source): You can put this solution on YOUR website!If the expression is , then On the other hand, if the expression is , then Or if the expression is , then The answer will depend on the grouping of the terms.
 Equations/277025: How could I solve this equation dealing with fractions. x/x+4 - 2 = 12/x-121 solutions Answer 201760 by jim_thompson5910(28504)   on 2010-03-04 01:12:41 (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. Simplify Rearrange the terms. FOIL Distribute Get every term to the left side. Combine like terms. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "x": Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Rewrite as Add to 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 solutions are or I'll let you check these solutions.
 absolute-value/276997: |7-10|-|-5| =-2 (I don't understand and I can not work out how this equation works at all.1 solutions Answer 201752 by jim_thompson5910(28504)   on 2010-03-03 23:49:47 (Show Source): You can put this solution on YOUR website!First, 7-10 = -3, but remember that the absolute value of any number is positive. So |7 - 10| = |-3| = 3 This also applies to |-5| which means that |-5|=5 Put this all together to get: |7 - 10| - | -5 | = | -3 | - | -5 | = 3 - 5 = -2 In the end, |7 - 10| - | -5 | = -2
Quadratic_Equations/277006: What is 6x^2-8xy-8y^2 equal to?
My book states the answer to be (3x+2y)(2x-4y), how do I get to this answer?
1 solutions

Answer 201751 by jim_thompson5910(28504)   on 2010-03-03 23:46:07 (Show Source):
You can put this solution on YOUR website!

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 3 and -4 respectively.

Now multiply the first coefficient 3 and the last coefficient -4 to get -12. Now what two numbers multiply to -12 and add to the middle coefficient -4? 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, the product of a negative and a positive number is a negative number

Now which of these pairs add to -4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -4

First NumberSecond NumberSum
1-121+(-12)=-11
2-62+(-6)=-4
3-43+(-4)=-1
-112-1+12=11
-26-2+6=4
-34-3+4=1

From this list we can see that 2 and -6 add up to -4 and multiply to -12

Now looking at the expression , replace with (notice combines back 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 factors to

Note: if you distribute the 2 into the first group, you get .

 Quadratic_Equations/276999: Put the equation 5x^2-10x-2 in turning point form a(x-h)^2+k, by completing the square.1 solutions Answer 201749 by jim_thompson5910(28504)   on 2010-03-03 23:36:25 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor out the coefficient . This step is very important: the coefficient must be equal to 1. Take half of the coefficient to get . In other words, . Now square to get . In other words, Now add and subtract inside the parenthesis. Make sure to place this after the "x" term. Notice how . So the expression is not changed. Group the first three terms. Factor to get . Combine like terms. Distribute. Multiply. So after completing the square, transforms to . So .
 Square-cubic-other-roots/276973: √14÷√7 1 solutions Answer 201741 by jim_thompson5910(28504)   on 2010-03-03 22:42:03 (Show Source): You can put this solution on YOUR website! So
Polynomials-and-rational-expressions/276797: Factor.
2y^2+17y+30
1 solutions

Answer 201671 by jim_thompson5910(28504)   on 2010-03-03 18:05:18 (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 :
1,2,3,4,5,6,10,12,15,20,30,60
-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60

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

These factors pair up and multiply to .
1*60 = 60
2*30 = 60
3*20 = 60
4*15 = 60
5*12 = 60
6*10 = 60
(-1)*(-60) = 60
(-2)*(-30) = 60
(-3)*(-20) = 60
(-4)*(-15) = 60
(-5)*(-12) = 60
(-6)*(-10) = 60

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

First NumberSecond NumberSum
1601+60=61
2302+30=32
3203+20=23
4154+15=19
5125+12=17
6106+10=16
-1-60-1+(-60)=-61
-2-30-2+(-30)=-32
-3-20-3+(-20)=-23
-4-15-4+(-15)=-19
-5-12-5+(-12)=-17
-6-10-6+(-10)=-16

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).

 sets-and-operations/276775: Find n(A) for the set. A={1/2,1/3,1/4,1/5,...,1/29,1/30}1 solutions Answer 201649 by jim_thompson5910(28504)   on 2010-03-03 17:36:09 (Show Source): You can put this solution on YOUR website!Notice how there are 30 elements in the set {1, 2, 3, 4, 5,...,29, 30} by simply noting that 30-1+1=30 or that the elements are integers, start at 1 and end at 30. Simply invert each element to get {1/1, 1/2, 1/3, 1/4, 1/5, ..., 1/29, 1/30} which is close to what we want, but we have to remove the element 1/1 to get {1/2, 1/3, 1/4, 1/5, ..., 1/29, 1/30}. Since we removed one element, we now have 29 elements in this set. So n(A) = # of elements in set A = 29
 Polynomials-and-rational-expressions/276721: /x-3 Can you please help me solve this? Thank you.1 solutions Answer 201622 by jim_thompson5910(28504)   on 2010-03-03 16:19:52 (Show Source): You can put this solution on YOUR website!In order to simplify this, we can use polynomial long division. So the quotient is and the remainder is 0. This means that or more simply Note: consequently, this means that (just multiply both sides by )
 Geometry_Word_Problems/276730: what is the area of a square whos sides measures 10 centimeters1 solutions Answer 201620 by jim_thompson5910(28504)   on 2010-03-03 16:12:23 (Show Source): You can put this solution on YOUR website!Area: So the area of the square is 100 square cm.
 Inequalities/276649: 5(2k+3)-2(k-8)>3(2k+4)+k-21 solutions Answer 201590 by jim_thompson5910(28504)   on 2010-03-03 13:34:44 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Combine like terms on the right side. Subtract 31 from both sides. Subtract 7k from both sides. Combine like terms on the left side. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the solution is
 Inequalities/276626: plese explain how to solve the inequality 14x +4 <26x +201 solutions Answer 201573 by jim_thompson5910(28504)   on 2010-03-03 12:46:12 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract 4 from both sides. Subtract 26x from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by -12 to isolate x. Remember that the inequality sign flips when you divide by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the solution is
percentage/276400: 11/4 into a percent
1 solutions

Answer 201555 by jim_thompson5910(28504)   on 2010-03-03 12:18:13 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: Converting to and from percents, decimals, and fractions There are two ways to do this Method #1: First, we must convert the given fraction into a decimal number. So use a calculator or long division to convert the given fraction to a decimal number. In this case, Now just multiply the equivalent decimal by 100 to convert it into a percent. So . Take note that we're simply moving the decimal point two spots to the right. So the given fraction is equivalent to 275% -------------------------- Or... Method # 2 Recall that a percent can be represented by the equation  percent part ------------- = ---------------- 100 whole  where 'percent' is the answer we want, the 'part' is the numerator of the given fraction, and 'whole' is the denominator of the given fraction. So let's make 'x' the unknown percentage. Since we're given the fraction , this means that the numerator is and the denominator is . Using the equation above, we see that the 'part' is while the 'whole' is So let's plug these values into the equation given above to get Start with the given equation Multiply both sides by 100 to isolate 'x'. Simplify Multiply 100 and to get Multiply 100 and to get Divide So the given fraction is equivalent to 275% Click here if you need a calculator.

What are the linear factors of 12x^2+7x-12?
The answer given is 4x-3 and 3x+4.
I'm just not too sure how to get to this answer.
1 solutions

Answer 201553 by jim_thompson5910(28504)   on 2010-03-03 12:15:49 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)
In order to factor , first multiply the leading coefficient 12 and the last term -12 to get -144. Now we need to ask ourselves: What two numbers multiply to -144 and add to 7? Lets find out by listing all of the possible factors of -144

Factors:

1,2,3,4,6,8,9,12,16,18,24,36,48,72,144,

-1,-2,-3,-4,-6,-8,-9,-12,-16,-18,-24,-36,-48,-72,-144, List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -144.

(-1)*(144)=-144

(-2)*(72)=-144

(-3)*(48)=-144

(-4)*(36)=-144

(-6)*(24)=-144

(-8)*(18)=-144

(-9)*(16)=-144

(-12)*(12)=-144

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 Number | Second Number | Sum 1 | -144 | 1+(-144)=-143 2 | -72 | 2+(-72)=-70 3 | -48 | 3+(-48)=-45 4 | -36 | 4+(-36)=-32 6 | -24 | 6+(-24)=-18 8 | -18 | 8+(-18)=-10 9 | -16 | 9+(-16)=-7 12 | -12 | 12+(-12)=0 -1 | 144 | (-1)+144=143 -2 | 72 | (-2)+72=70 -3 | 48 | (-3)+48=45 -4 | 36 | (-4)+36=32 -6 | 24 | (-6)+24=18 -8 | 18 | (-8)+18=10 -9 | 16 | (-9)+16=7 -12 | 12 | (-12)+12=0

We can see from the table that -9 and 16 add to 7. So the two numbers that multiply to -144 and add to 7 are: -9 and 16

breaks down to this (just replace with the two numbers that multiply to -144 and add to 7, which are: -9 and 16)

Replace with

Group the first two terms together and the last two terms together like this:

Factor a 3x out of the first group and factor a 4 out of the second group.

Now since we have a common term we can combine the two terms.

Combine like terms.
==============================================================================

Notice how foils back to our original problem . This verifies our answer.

 logarithm/276182: Evaluate the logarithm: log4^1/41 solutions Answer 201366 by jim_thompson5910(28504)   on 2010-03-02 18:08:32 (Show Source): You can put this solution on YOUR website! So
 Linear-equations/276245: need help with this problem y= -1/5x + 4 1 solutions Answer 201364 by jim_thompson5910(28504)   on 2010-03-02 18:06:00 (Show Source): You can put this solution on YOUR website!Are you trying to graph? If so, then... Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is -1 and the run is 5. This means that to go from point to point, we can go down 1 and over 5 So starting at , go down 1 unit and to the right 5 units to get to the next point Now draw a line through these points to graph So this is the graph of through the points and
 Numeric_Fractions/276260: ok..i would like to know how to solve any fraction with an exponent for example: i started one and this is the question:(((6^8/6^6))) this is how far i got:(((6^14))) now what do i do.and what would i do if there was more than one number on the top and bottom of the fraction? thanks for the help! ;)1 solutions Answer 201362 by jim_thompson5910(28504)   on 2010-03-02 18:04:24 (Show Source): You can put this solution on YOUR website! So
Parallelograms/276265: this figure must be a parallelogram and I have to prove that 4x + 20 = x + 26.
I don't understand how to do the algebra.
1 solutions

Answer 201361 by jim_thompson5910(28504)   on 2010-03-02 18:02:53 (Show Source):
You can put this solution on YOUR website!
For more help with solving linear equations, check out this linear equation solver.

 Solved by pluggable solver: Linear Equation Solver Start with the given equation. 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 solution is

 test/276149: When is (11-a)/2 an integer?1 solutions Answer 201301 by jim_thompson5910(28504)   on 2010-03-02 13:31:55 (Show Source): You can put this solution on YOUR website! is an integer when is a divisible by 2 (ie when ) is even).
 Graphs/275934: Give the slope-intercept form of the equation for the line on which these two points lie: (4, -2) and (3, 8)1 solutions Answer 201187 by jim_thompson5910(28504)   on 2010-03-01 21:43:15 (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 . So this means that and . Also, is the second point . So this means that and . 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 Subtract 2 from both sides. Combine like terms. So the equation that goes through the points and is
Equations/275916: can you show me how to solve this prolem?
-(6x-5)-(-5+8)=-3
1 solutions

Answer 201171 by jim_thompson5910(28504)   on 2010-03-01 20:52:56 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: Linear Equation Solver Start with the given equation. Distribute. 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

 Sequences-and-series/275349: List the first six terms of the sequence defined recursively by z0 = 0 z1 = 1 z2 = 2 What exactly, does this imply, and how would I start it? I'm so confused.1 solutions Answer 200853 by jim_thompson5910(28504)   on 2010-02-28 20:02:28 (Show Source): You can put this solution on YOUR website!You would need to know the formula for generating the nth term. Is there more to the problem?
 Exponents/275351: Let 2^a = 5 and 2^b = 9. Using exponent rules, solve the equation in terms of a and/or b. 5^x=32 I really don't even know what the question is asking me to do. Please help! 1 solutions Answer 200851 by jim_thompson5910(28504)   on 2010-02-28 19:51:58 (Show Source): You can put this solution on YOUR website!The goal here is to solve for 'x' in terms of either 'a' or 'b' (or both). In other words, have a solution of x = (something with 'a's and/or 'b's in it) You have to play with it a bit, but it turns out that we never use . So let's just work with First convert into logarithmic form to get . Now use the change of base formula to get Now move onto and convert that into logarithmic form to get . Rewrite 32 as to get Now pull down the exponent to get and use the change of base formula: . Take note how this is very similar to but this just has the reverse of that expression and an extra '5' in there. If we invert 'a', we then get which is the missing piece. So So the solution, in terms of 'a', is
Numbers_Word_Problems/275343: The sum of three consecutive even numbers is 150. Find the numbers. I have tried tried a + b+c = 150. I have also tried. (x+1)+(x+2)+(x+3). I don't think I am doin this problem right. However, I know the consecutive even numbers before 150 are 148, 146, 144..Help.
Dawn
1 solutions

Answer 200844 by jim_thompson5910(28504)   on 2010-02-28 19:22:14 (Show Source):
You can put this solution on YOUR website!
"The sum of three consecutive even numbers is 150" means that or more simply . Let's solve this equation for 'x'.

For more help with solving linear equations, check out this linear equation solver.

 Solved by pluggable solver: Linear Equation Solver 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

Since , this means that the three numbers are 48, 50 and 52

Equations/275344: 3y+2=y-4

1 solutions

Answer 200842 by jim_thompson5910(28504)   on 2010-02-28 19:19:55 (Show Source):
You can put this solution on YOUR website!
For more help with solving linear equations, check out this linear equation solver.

 Solved by pluggable solver: Linear Equation Solver Start with the given equation. 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 solution is

Rational-functions/275270: I have two questions on the equations of lines.
1)Write an equation of a line passing through the points (-3,5) and (2,-7)

2) Write an equation of the line perpendicular to the line 2x-4y=7 and passing through (2,-5)
I am slightly perplexed, thanks in advance.
1 solutions

Answer 200790 by jim_thompson5910(28504)   on 2010-02-28 16:53:46 (Show Source):
You can put this solution on YOUR website!
# 1

First let's find the slope of the line through the points and

Note: is the first point . So this means that and .
Also, is the second point . So this means that and .

Plug in , , , and

Subtract from to get

Subtract from to get

So the slope of the line that goes through the points and is

Now let's use the point slope formula:

Plug in , , and

Rewrite as

Distribute

Multiply

Combine like terms. note: If you need help with fractions, check out this solver.

So the equation that goes through the points and is

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

# 2

Subtract from both sides.

Rearrange the terms.

Divide both sides by to isolate y.

Break up the fraction.

Reduce.

So the slope of and is

 Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of , you can find the perpendicular slope by this formula: where is the perpendicular slope So plug in the given slope to find the perpendicular slope When you divide fractions, you multiply the first fraction (which is really ) by the reciprocal of the second Multiply the fractions. So the perpendicular slope is So now we know the slope of the unknown line is (its the negative reciprocal of from the line ). Also since the unknown line goes through (2,-5), we can find the equation by plugging in this info into the point-slope formula Point-Slope Formula: where m is the slope and (,) is the given point Plug in , , and Distribute Multiply Subtract from both sides to isolate y Combine like terms So the equation of the line that is perpendicular to and goes through (,) is So here are the graphs of the equations and graph of the given equation (red) and graph of the line (green) that is perpendicular to the given graph and goes through (,)

 Equations/275281: Please help me solve this equation.. 3|-8x-9|=1171 solutions Answer 200788 by jim_thompson5910(28504)   on 2010-02-28 16:49:22 (Show Source): You can put this solution on YOUR website! Start with the given equation Divide both sides by 3 Break up the absolute value (remember, if you have , then or ) or Set the expression equal to the original value 39 and it's opposite -39 Now lets focus on the first equation Add 9 to both sides Combine like terms on the right side Divide both sides by -8 to isolate x Reduce Now lets focus on the second equation Add 9 to both sides Combine like terms on the right side Divide both sides by -8 to isolate x Divide So the solutions to are: and