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1 solutions
Answer 386875 by jim_thompson5910(28476)   on 2012-05-26 13:16:01 (Show Source):
You can put this solution on YOUR website! 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.
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Answer:
So the solution is
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Linear-equations/615031: y=1/4x+3
1 solutions
Answer 386873 by jim_thompson5910(28476) on 2012-05-26 13:14:15 (Show Source):
You can put this solution on YOUR website!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 4. This means that to go from point to point, we can go up 1 and over 4
So starting at , go up 1 unit
and to the right 4 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
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Polynomials-and-rational-expressions/614323: factor completely: -36m^2 + 6m + 12
1 solutions
Answer 386502 by jim_thompson5910(28476) on 2012-05-23 21:56:16 (Show Source):
You can put this solution on YOUR website!
 Start with the given expression.
 Factor out the GCF  .
Now let's try to factor the inner expression 
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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) = -12
2*(-6) = -12
3*(-4) = -12
(-1)*(12) = -12
(-2)*(6) = -12
(-3)*(4) = -12
Now let's add up each pair of factors to see if one pair adds to the middle coefficient :
| First Number | Second Number | Sum | | 1 | -12 | 1+(-12)=-11 | | 2 | -6 | 2+(-6)=-4 | | 3 | -4 | 3+(-4)=-1 | | -1 | 12 | -1+12=11 | | -2 | 6 | -2+6=4 | | -3 | 4 | -3+4=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 then factors further to 
===============================================================
Answer:
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).
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If you need more help, email me at jim_thompson5910@hotmail.com
Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you
Jim
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Graphs/614191: Could you graph y= 3x-5.
1 solutions
Answer 386442 by jim_thompson5910(28476) on 2012-05-23 17:31:38 (Show Source):
You can put this solution on YOUR website!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 3 and the run is 1. This means that to go from point to point, we can go up 3 and over 1
So starting at , go up 3 units
and to the right 1 unit 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
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If you need more help, email me at jim_thompson5910@hotmail.com
Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you
Jim
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Equations/613946: Solve for x. 5x - 2 = 9.
1 solutions
Answer 386329 by jim_thompson5910(28476) on 2012-05-22 22:57:44 (Show Source):
You can put this solution on YOUR website! Start with the given equation.
 Add to both sides.
 Combine like terms on the right side.
 Divide both sides by  to isolate  .
----------------------------------------------------------------------
Answer:
So the solution is 
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If you need more help, email me at jim_thompson5910@hotmail.com
Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you
Jim
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Equations/613860: x^2-3x-28=0
work
x^2 - 3x = 28
x^2 - x = 28/3
1 solutions
Answer 386293 by jim_thompson5910(28476) on 2012-05-22 20:16:19 (Show Source):
You can put this solution on YOUR website!
 Start with the given equation.
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
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If you need more help, email me at jim_thompson5910@hotmail.com
Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you
Jim
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Linear-equations/613793: "find the intercepts of the equation"
-4x+2y=8
x-intercept
y-intercept:
1 solutions
Answer 386264 by jim_thompson5910(28476) on 2012-05-22 18:03:58 (Show Source):
You can put this solution on YOUR website!
x-intercept
To find the x-intercept, plug in  and solve for x
 Start with the given equation.
 Plug in .
 Multiply and 0 to get 0.
 Simplify.
 Divide both sides by to isolate .
 Reduce.
So the x-intercept is ) .
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y-intercept
To find the y-intercept, plug in  and solve for y
Start with the given equation.
 Plug in .
 Multiply and 0 to get 0.
 Simplify.
 Divide both sides by to isolate  .
 Reduce.
So the y-intercept is ) .
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If you need more help, email me at jim_thompson5910@hotmail.com
Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you
Jim
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Linear-systems/613778: Find the slope of each line
through (-2,3) & (5,-6)
i think i subtract the y & x1's to the y & x2's but dont know where to go from there.. help please
1 solutions
Answer 386251 by jim_thompson5910(28476) on 2012-05-22 17:27:22 (Show Source):
You can put this solution on YOUR website!
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 
So the slope of the line that goes through the points and is 
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If you need more help, email me at jim_thompson5910@hotmail.com
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Linear-systems/613769: find the intercepts for the equation
3x+y=-7
x-intercept:
y-intercept:
1 solutions
Answer 386244 by jim_thompson5910(28476) on 2012-05-22 16:52:55 (Show Source):
You can put this solution on YOUR website!
x-intercept
To find the x-intercept, plug in and solve for x
 Start with the given equation.
 Plug in .
 Simplify.
 Divide both sides by to isolate .
So the x-intercept is ) .
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y-intercept
To find the y-intercept, plug in and solve for y
Start with the given equation.
 Plug in .
 Multiply and 0 to get 0.
 Simplify.
So the y-intercept is ) .
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Geometry_proofs/613754: Question in geometry about solving proofs. I really have no idea.. I think number 2. is AC/AC and number 3. is triangle CBA = triangle CDA, but can someone help me with the rest? Thank youu (:
http://assets.openstudy.com/updates/attachments/4fbbfe64e4b0556534310054-avieira-1337720440118-photo2.jpg
http://assets.openstudy.com/updates/attachments/4fbbfe64e4b0556534310054-avieira-1337720440340-page25c.gif
1 solutions
Answer 386234 by jim_thompson5910(28476) on 2012-05-22 16:14:18 (Show Source):
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Geometry_proofs/613739: Help with geometry! Solving proofs. I'm not really sure :/ I've filled in a few blanks, but can someone help with the others & explain how you got to that answer? thank youuu! Attached below is the triangle
http://assets.openstudy.com/updates/attachments/4fbbf56ee4b055653430f3e4-avieira-1337718148516-page25c.gif
http://assets.openstudy.com/updates/attachments/4fbbf56ee4b055653430f3e4-avieira-1337718148254-photo21.jpg
1 solutions
Answer 386225 by jim_thompson5910(28476) on 2012-05-22 15:53:22 (Show Source):
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Equations/613736: n^2-10n-24
1 solutions
Answer 386219 by jim_thompson5910(28476) on 2012-05-22 15:26:09 (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 Number | Second Number | Sum | | 1 | -24 | 1+(-24)=-23 | | 2 | -12 | 2+(-12)=-10 | | 3 | -8 | 3+(-8)=-5 | | 4 | -6 | 4+(-6)=-2 | | -1 | 24 | -1+24=23 | | -2 | 12 | -2+12=10 | | -3 | 8 | -3+8=5 | | -4 | 6 | -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 
===============================================================
Answer:
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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Jim
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Graphs/613734: I'm stumped, I've worked on this probably simple problem for two hours and just can't get it, my book doesn't even explain anything like it.
Here it is:
You plan to start taking an aerobics class. Nonmembers pay 5$ power class. Members pay a6$ monthly fee plus an additional 4$ pet class. Three monthly cost, y, of taking x classes can be modeled by the following linear system
Y=5x
Y=4x+6
Using graphing to solve the system.
The solution set is { }
Type an ordered pair. Use integers or decimals for any numbers in the expression.
1 solutions
Answer 386218 by jim_thompson5910(28476) on 2012-05-22 15:25:11 (Show Source):
You can put this solution on YOUR website!Graph y = 5x (shown in green) and y = 4x+6 (shown in blue) to get
Notice how they cross at the point (6,30). If it's hard to see this, use the "intersect" or "trace" feature on your graphing calculator.
So the solutions are x = 6 and y = 30
Answer: The solution set is { (6,30) }
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Jim
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Quadratic_Equations/613730: I am stumped, I just do not know the steps, I would greatly appreciate any help on this. Thank you!
Solve using the quadratic formula. Then use a calculator to approximate, to three decimal places, the solutions as rational numbers.
46.
x^2 + 6x + 4 = 0
1 solutions
Answer 386212 by jim_thompson5910(28476) on 2012-05-22 15:07:04 (Show Source):
You can put this solution on YOUR website!
 Start with the given equation.
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
 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)
 Break up the fraction.
 Reduce.
 or  Break up the expression.
So the exact solutions are or
Then use a calculator to find the approximate solutions to be  or 
Then round those approximate solutions to three places to get  or 
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Jim
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Linear-systems/613728: The question is "Find the slope of the line through each pair of points" (2,-4) & (-3,-4) I need help on figuring it out.
1 solutions
Answer 386210 by jim_thompson5910(28476) on 2012-05-22 15:03:57 (Show Source):
You can put this solution on YOUR website!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
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Miscellaneous_Word_Problems/613726: Mary is swimming in a rectangular pool that is 25 feet wide by 60 feet long.
If she swims diagonally across the pool,about how many feet does Mary swim?
A. 13
B. 55
C. 65
D. 85
Could someone please help!!
1 solutions
Answer 386204 by jim_thompson5910(28476) on 2012-05-22 14:39:53 (Show Source):
You can put this solution on YOUR website!Use the pythagorean theorem to find the length of the diagonal.
a^2 + b^2 = c^2
25^2 + 60^2 = c^2
625 + 3600 = c^2
4225 = c^2
c^2 = 4225
c = sqrt(4225)
c = 65
So the diagonal is 65 feet long.
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Angles/613725: A ramp that is 18 meters long makes an angle of 9º with the ground. What is the height h of the ramp? Round your answer to the nearest tenth of a meter.
1 solutions
Answer 386202 by jim_thompson5910(28476) on 2012-05-22 14:31:23 (Show Source):
You can put this solution on YOUR website!sin(theta) = opposite/hypotenuse
sin(9) = h/18
18*sin(9) = h
h = 18*sin(9)
h = 18*0.156434465040231
h = 2.81582037072416
So the height of the ramp is roughly 2.81582037072416 m which rounds to 2.8 meters
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Jim
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Functions/613723: Solve the system of equations by graphing. Then classfy the system.
x+y=15
X-y=3
1 solutions
Answer 386200 by jim_thompson5910(28476) on 2012-05-22 14:28:56 (Show Source):
You can put this solution on YOUR website!Graph the two equations to get
Note: the first equation x+y=15 is in green and the second equation x-y=3 is in blue
We see that the two lines intersect at the point (9,6). So the solutions are x = 9 and y = 6
So the system is consistent and independent.
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Jim
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Numeric_Fractions/613716: 2-3(t-5)=4+t
1 solutions
Answer 386196 by jim_thompson5910(28476) on 2012-05-22 14:18:18 (Show Source):
You can put this solution on YOUR website! Start with the given equation.
 Distribute.
 Combine like terms on the left 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.
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Answer:
So the solution is
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Equations/613692: i need to solve the equation and my number are not matching up, can you help me please
3x+2(x+4)=5(x+1)+3
1 solutions
Answer 386170 by jim_thompson5910(28476) on 2012-05-22 13:01:54 (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  from both sides.
 Subtract  from both sides.
 Combine like terms on the left side.
 Combine like terms on the right side.
 Simplify.
Since this equation is always true for any x value, this means x can equal any number. So there are an infinite number of solutions.
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Jim
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Probability-and-statistics/613676: What percentage of the area of the standard normal distribution is between z = -2.00 and z = +2.00? How do you know this?
1 solutions
Answer 386148 by jim_thompson5910(28476) on 2012-05-22 12:13:05 (Show Source):
You can put this solution on YOUR website!Using the empirical rule, roughly 68% of the distribution is between z = -1 and z = 1. Also, about 95% of the distribution lies between z = -2 and z = 2. Finally, roughly 99.7% of the distribution is between z = -3 and z = 3
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