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 Equations/614400: -2(5+6m)+16=-901 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. ---------------------------------------------------------------------- Answer: So the solution is
 Equations/615041: 4(4b-5) just to see if we are on the right track1 solutions Answer 386874 by jim_thompson5910(28476)   on 2012-05-26 13:15:30 (Show Source): You can put this solution on YOUR website!4(4b-5) 4(4b)+4(-5) 16b-20 So 4(4b-5) simplifies to 16b-20
 Linear-equations/615031: y=1/4x+31 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
 Equations/615046: 8921=e^5x1 solutions Answer 386871 by jim_thompson5910(28476)   on 2012-05-26 13:12:11 (Show Source): You can put this solution on YOUR website!8921=e^5x ln(8921)=5x ln(8921)/5=x x = ln(8921)/5 So the exact solution is x = ln(8921)/5 The approximate solution is x = 1.81923266538276
 Trigonometry-basics/614584: if the period of a tangent function is 2/3, what is the frequency of the function? 1)2pi/3 2)3pi/2 3)2pi 4)3pi1 solutions Answer 386628 by jim_thompson5910(28476)   on 2012-05-24 17:09:12 (Show Source): You can put this solution on YOUR website!Hint: Frequency = 1/(Period)
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!

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 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 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

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

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 -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 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 -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 Equations/613860: x^2-3x-28=0 work x^2 - 3x = 28 x^2 - x = 28/31 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 -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
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

Plug in .

Multiply and 0 to get 0.

Simplify.

Divide both sides by to isolate .

Reduce.

So the x-intercept is .

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

#### y-intercept

To find the y-intercept, plug in and solve for y

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 please1 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 -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
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

Plug in .

Simplify.

Divide both sides by to isolate .

So the x-intercept is .

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

#### y-intercept

To find the y-intercept, plug in and solve for y

Plug in .

Multiply and 0 to get 0.

Simplify.

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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 Trigonometry-basics/613766: What is the period of the function y = 1/2 sin (x/3 - Pi)? (1) 1/2 (2) 1/3 (3) 2/3 Pi (4) 6 Pi the formula is period = 2pi/b. I tryed to solve it and I got 6/x....1 solutions Answer 386243 by jim_thompson5910(28476)   on 2012-05-22 16:51:10 (Show Source): You can put this solution on YOUR website!T = (2pi)/B T = (2pi)/(1/3) T = 2pi*3 T = 6pi -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 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.gif1 solutions Answer 386234 by jim_thompson5910(28476)   on 2012-05-22 16:14:18 (Show Source): You can put this solution on YOUR website!AC = AC by the reflexive property triangle CBA = triangle CDA by the SAS property AD = CB by the CPCTE property
 Permutations/613749: How many ways can a president and a vice president be selected in a class of 25 students1 solutions Answer 386227 by jim_thompson5910(28476)   on 2012-05-22 15:56:00 (Show Source): You can put this solution on YOUR website!There are 25 choices for the president and 25-1 = 24 choices for the VP. So there are 25*24 = 600 different ways.
 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.jpg1 solutions Answer 386225 by jim_thompson5910(28476)   on 2012-05-22 15:53:22 (Show Source): You can put this solution on YOUR website!Triangle CBA is congruent to triangle CDA due to the SAS Property of Congruence
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 NumberSecond NumberSum
1-241+(-24)=-23
2-122+(-12)=-10
3-83+(-8)=-5
4-64+(-6)=-2
-124-1+24=23
-212-2+12=10
-38-3+8=5
-46-4+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

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

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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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/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) } -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 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 -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 Linear-systems/613729: "Find the slope of each line" y= 4/3x -2 what are the steps to solve the solution?1 solutions Answer 386211 by jim_thompson5910(28476)   on 2012-05-22 15:04:36 (Show Source): You can put this solution on YOUR website!y= 4/3x -2 is in the form y = mx+b where m = 4/3. So the slope is 4/3. -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 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 -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 expressions/613721: simplify 3(5x+5)-12 1 solutions Answer 386208 by jim_thompson5910(28476)   on 2012-05-22 14:56:05 (Show Source): You can put this solution on YOUR website!3(5x+5)-12 3(5x)+3(5)-12 15x+15-12 15x+3 So 3(5x+5)-12 simplifies to 15x+3 -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 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. -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 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 -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 Functions/613723: Solve the system of equations by graphing. Then classfy the system. x+y=15 X-y=31 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. -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 Numeric_Fractions/613716: 2-3(t-5)=4+t1 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. ---------------------------------------------------------------------- Answer: So the solution is -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 absolute-value/613708: EVALUATE: -15 + /5/1 solutions Answer 386187 by jim_thompson5910(28476)   on 2012-05-22 13:53:46 (Show Source): You can put this solution on YOUR website!-15 + |5| -15 + 5 -10 So -15 + |5| = -10 -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 Polynomials-and-rational-expressions/613712: Please help me solve this equuation:x-7>-41 solutions Answer 386186 by jim_thompson5910(28476)   on 2012-05-22 13:53:06 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Add to both sides. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the solution is -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 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)+31 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. -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 expressions/613698: Please simplify and show all work. -2x+3-(-7-x)1 solutions Answer 386169 by jim_thompson5910(28476)   on 2012-05-22 13:00:38 (Show Source): You can put this solution on YOUR website!-2x+3-(-7-x) -2x+3-(-7)-(-x) -2x+3+7+x (-2x+x)+(3+7) -x+10 So -2x+3-(-7-x) simplifies to -x+10 -------------------------------------------------------------------------------------------------------------- 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 --------------------------------------------------------------------------------------------------------------
 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