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Functions/530865: solve and check solution
5x-3=13-3x
1 solutions

Answer 350222 by jim_thompson5910(28476) About Me  on 2011-11-13 16:01:25 (Show Source):
You can put this solution on YOUR website!
5x-3=13-3x Start with the given equation.


5x=13-3x%2B3 Add 3 to both sides.


5x%2B3x=13%2B3 Add 3x to both sides.


8x=13%2B3 Combine like terms on the left side.


8x=16 Combine like terms on the right side.


x=%2816%29%2F%288%29 Divide both sides by 8 to isolate x.


x=2 Reduce.


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

Answer:

So the solution is x=2


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/530868: -4r-11=4r+21 solve and check solution
1 solutions

Answer 350221 by jim_thompson5910(28476) About Me  on 2011-11-13 16:01:03 (Show Source):
You can put this solution on YOUR website!
-4r-11=4r%2B21 Start with the given equation.


-4r=4r%2B21%2B11 Add 11 to both sides.


-4r-4r=21%2B11 Subtract 4r from both sides.


-8r=21%2B11 Combine like terms on the left side.


-8r=32 Combine like terms on the right side.


r=%2832%29%2F%28-8%29 Divide both sides by -8 to isolate r.


r=-4 Reduce.


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

Answer:

So the solution is r=-4


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/530858: hey im doing absoloute value equations...
the question is: "Solve each equation or inequality"
|2d|+3=21
1 solutions

Answer 350219 by jim_thompson5910(28476) About Me  on 2011-11-13 15:52:20 (Show Source):
You can put this solution on YOUR website!
|2d|+3=21


|2d|=21-3


|2d|=18


2d=18 or 2d=-18


d=18/2 or d=-18/2


d=9 or d=-9


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/530857: f(x)=6x find the value f(m)
1 solutions

Answer 350217 by jim_thompson5910(28476) About Me  on 2011-11-13 15:51:22 (Show Source):
You can put this solution on YOUR website!
f(x)=6x


f(m)=6m


Polynomials-and-rational-expressions/530837: find all numbers for which the rational expression is undefined. -17/7y
1 solutions

Answer 350211 by jim_thompson5910(28476) About Me  on 2011-11-13 15:30:22 (Show Source):
You can put this solution on YOUR website!
You cannot divide by zero.


So if the denominator 7y were zero, then y = 0


So y = 0 makes the denominator 0


Therefore, y = 0 makes the expression undefined.


Linear_Algebra/530540: (-10) + 8 =
1 solutions

Answer 350117 by jim_thompson5910(28476) About Me  on 2011-11-12 20:45:34 (Show Source):
You can put this solution on YOUR website!
(-10) + 8 = -2



Subset/530531: Determine whether A = B, A ⊆ B, B ⊆ A, A ⊂ B, B ⊂ A or if none of these answers applies.
A = {x | x is all elements of N and x < 6}
B = {x | x is all elements of N and 1 is less than or equal to x is less than or equal to 5}
I believe that the answer is A=B
Would A ⊆ B and A ⊂ B also be included in my answer as well?

1 solutions

Answer 350109 by jim_thompson5910(28476) About Me  on 2011-11-12 20:28:55 (Show Source):
You can put this solution on YOUR website!
You are correct in saying that A = B since they both equal the set {1, 2, 3, 4, 5}


Note: this is assuming that you've defined the natural numbers to be the set of positive integers.



Also, since A = B, we can say that A ⊆ B, B ⊆ A


This is part of the definition of set equality.


However, we cannot say that A ⊂ B or B ⊂ A since no one set is smaller than the other.


Equations/530533: 2x+2=9
1 solutions

Answer 350107 by jim_thompson5910(28476) About Me  on 2011-11-12 20:26:02 (Show Source):
You can put this solution on YOUR website!
2x%2B2=9 Start with the given equation.


2x=9-2 Subtract 2 from both sides.


2x=7 Combine like terms on the right side.


x=%287%29%2F%282%29 Divide both sides by 2 to isolate x.


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

Answer:

So the solution is x=7%2F2


Polynomials-and-rational-expressions/530498: Essay: Show all work. Find the following quotient: 16x^2 - 9y^2/4x + 3y
1 solutions

Answer 350096 by jim_thompson5910(28476) About Me  on 2011-11-12 19:08:19 (Show Source):
You can put this solution on YOUR website!
%2816x%5E2+-+9y%5E2%29%2F%284x+%2B+3y%29


%28%284x+%2B+3y%29%284x+-+3y%29%29%2F%284x+%2B+3y%29



%28cross%28%284x+%2B+3y%29%29%284x+-+3y%29%29%2Fcross%284x+%2B+3y%29


4x-3y


So %2816x%5E2+-+9y%5E2%29%2F%284x+%2B+3y%29=4x-3y


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


Graphs/530489: I am trying to find the answer for points to do a line graph.
Here is my question.
3x + 4 = 4x =6

I was not sure how to do this.
Thank you for your help.
Sarita
1 solutions

Answer 350074 by jim_thompson5910(28476) About Me  on 2011-11-12 18:07:40 (Show Source):
You can put this solution on YOUR website!
There are too many equal signs. Please repost with correct equation. Thanks.


Permutations/530415: how many sandwiches can you make with 5 meats 4 breads and 4 cheeses
we think the answer is 20 or 80 but book doesn't provide example for a 3 tier choice or 2 so were a lil confused
1 solutions

Answer 350071 by jim_thompson5910(28476) About Me  on 2011-11-12 17:59:51 (Show Source):
You can put this solution on YOUR website!
The answer is 5*4*4 = 20*4 = 80


Functions/530483: Actually some of my problems involve graphs, but maybe I can still get help on a couple other problems.
Find the domain p(x)=x^2+10.
I know all the numbers are real numbers but my question involves whether the solution is equal to or greater than. Like so; {xIx is a real number and x = 10}(with a slash through the equal sign). I chose that as my answer; can someone double check to see if I'm correct. The other options are
{xIx is a real number and x=0} (with a slash through the = sign)
{xIx is a real number and x>0}
and
{xIx is a real number}
Does anyone or whomever I'm writing to understand what the question is asking? This is Algebra 1.
1 solutions

Answer 350069 by jim_thompson5910(28476) About Me  on 2011-11-12 17:50:51 (Show Source):
You can put this solution on YOUR website!
The answer is {xIx is a real number} which is basically saying "The domain is the set of all real numbers"


Equations/530478: 3(x + 2) = 12

1 solutions

Answer 350061 by jim_thompson5910(28476) About Me  on 2011-11-12 17:25:58 (Show Source):
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3%28x%2B2%29=12 Start with the given equation.


3x%2B6=12 Distribute.


3x=12-6 Subtract 6 from both sides.


3x=6 Combine like terms on the right side.


x=%286%29%2F%283%29 Divide both sides by 3 to isolate x.


x=2 Reduce.


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

Answer:

So the solution is x=2


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Coordinate-system/530466: Find the equation of a circle given its center C and one point P.
C(0,4),P(0,0).
Thank You!
1 solutions

Answer 350059 by jim_thompson5910(28476) About Me  on 2011-11-12 17:10:38 (Show Source):
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%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 Start with the general equation of a circle.


%28x-0%29%5E2%2B%28y-4%29%5E2=r%5E2 Plug in h=0 and k=4 (since the center is the point (h,k) ).


%280-0%29%5E2%2B%280-4%29%5E2=r%5E2 Plug in x=0 and y=0 (this is the point that lies on the circle, which is in the form (x,y) ).


%280%29%5E2%2B%28-4%29%5E2=r%5E2 Combine like terms.


0%2B16=r%5E2 Square each term.


16=r%5E2 Add.


So because h=0, k=4, and r%5E2=16, this means that the equation of the circle with center (0,4) that goes through the point (0,0) is


%28x-0%29%5E2%2B%28y-4%29%5E2=16.


which simplifies to


x%5E2%2B%28y-4%29%5E2=16


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Coordinate-system/530469: Find the equation of the circle centered at (4,6) and passing through the point (2,2).
Thank you I'm having a hard time with circle equations!
1 solutions

Answer 350058 by jim_thompson5910(28476) About Me  on 2011-11-12 17:09:34 (Show Source):
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%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 Start with the general equation of a circle.


%28x-4%29%5E2%2B%28y-6%29%5E2=r%5E2 Plug in h=4 and k=6 (since the center is the point (h,k) ).


%282-4%29%5E2%2B%282-6%29%5E2=r%5E2 Plug in x=2 and y=2 (this is the point that lies on the circle, which is in the form (x,y) ).


%28-2%29%5E2%2B%28-4%29%5E2=r%5E2 Combine like terms.


4%2B16=r%5E2 Square each term.


20=r%5E2 Add.


So because h=4, k=6, and r%5E2=20, this means that the equation of the circle with center (4,6) that goes through the point (2,2) is


%28x-4%29%5E2%2B%28y-6%29%5E2=20.


test/530473:
1 solutions

Answer 350057 by jim_thompson5910(28476) About Me  on 2011-11-12 17:07:37 (Show Source):
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There's nothing here. Please enter a problem.


Linear-equations/530472: Graph the following y=3+2x
Find two points on the line to be graphed and enter their coordinates in the boxes below.
A: _______ , ________
B: _______ , _________

1 solutions

Answer 350056 by jim_thompson5910(28476) About Me  on 2011-11-12 17:07:08 (Show Source):
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When x = 0, y = 3+2(0) = 3


So the first answer is

A: ___0___, ___3___

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


When x = 1, y = 3+2(1) = 5

and the second answer is

B: ___1___, ___5___


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Coordinate-system/530470: Find the center and radius of the circle with the given equation:
x^2+y^2-28=0
Thank You : )
1 solutions

Answer 350054 by jim_thompson5910(28476) About Me  on 2011-11-12 17:05:13 (Show Source):
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x%5E2%2By%5E2-28=0


x%5E2%2By%5E2=28


%28x-0%29%5E2%2B%28y-0%29%5E2=%28sqrt%2828%29%29%5E2


The equation is now in %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 form, which is a circle, where h=0, k=0 and r=sqrt%2828%29


Remember that the center is (h,k) and the radius is r.


So the center is (0,0) and the radius is sqrt%2828%29 units.


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Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Numeric_Fractions/530382: (13/15)/(29/30)
1 solutions

Answer 350026 by jim_thompson5910(28476) About Me  on 2011-11-12 14:16:15 (Show Source):
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(13/15)/(29/30)


(13/15)*(30/29)


(13*30)/(15*29)


(390)/(15*29)


(390)/(435)


26/29


So (13/15)/(29/30)=26/29


Equations/530348: my equation problem is 3t+16t-48=2+14t. I simplified it to 5t=-50 when you divide 5 by 5 it drops out when you divied -50 by 5 you get -10 but my choices dont have -10 they have 10 why is that?
1 solutions

Answer 350025 by jim_thompson5910(28476) About Me  on 2011-11-12 14:13:17 (Show Source):
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3t%2B16t-48=2%2B14t Start with the given equation.


-48%2B19t=2%2B14t Combine like terms on the left side.


19t=2%2B14t%2B48 Add 48 to both sides.


19t-14t=2%2B48 Subtract 14t from both sides.


5t=2%2B48 Combine like terms on the left side.


5t=50 Combine like terms on the right side.


t=%2850%29%2F%285%29 Divide both sides by 5 to isolate t.


t=10 Reduce.


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

Answer:

So the solution is t=10


Linear-systems/530362: a^7+a^7+a^7 is equivalent to what?
1 solutions

Answer 350023 by jim_thompson5910(28476) About Me  on 2011-11-12 14:11:54 (Show Source):
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a^7+a^7+a^7 = 3a^7 for all values of 'a'


Linear-equations/530408: How do you write the equation y=2/3x -2 in standard form? I think it is -2/3x + y = -2
1 solutions

Answer 350022 by jim_thompson5910(28476) About Me  on 2011-11-12 14:09:38 (Show Source):
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y=2/3x -2


3y=2x - 6 ... Note: Multiply EVERY term by the LCD 3 to clear out the fraction


-2x + 3y = -6


2x - 3y = 6


So the answer is 2x - 3y = 6


Linear-equations/530409: How do you write the equation y=2/3x -2 in standard form? I think it is -2/3x + y = -2
1 solutions

Answer 350021 by jim_thompson5910(28476) About Me  on 2011-11-12 14:09:12 (Show Source):
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y=2/3x -2


3y=2x - 6 ... Note: Multiply EVERY term by the LCD 3 to clear out the fraction


-2x + 3y = -6


2x - 3y = 6


So the answer is 2x - 3y = 6


Polynomials-and-rational-expressions/530349: please help me to solve 1/3 = 4/n-1
1 solutions

Answer 350019 by jim_thompson5910(28476) About Me  on 2011-11-12 14:06:44 (Show Source):
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1/3 = 4/(n-1)


1(n-1) = 4*3


1(n-1) = 12


n-1 = 12


n = 12+1


n = 13


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Signed-numbers/530357: what is +2 X (+4)=
what is -7 X (+14)=
what is -12 X (+12)=

1 solutions

Answer 350018 by jim_thompson5910(28476) About Me  on 2011-11-12 14:05:32 (Show Source):
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+2 X (+4)= +8
-7 X (+14)= - 98
-12 X (+12)= -144


Equations/530360: factor the following trinomial completely: 3x^2+12x+12

1 solutions

Answer 350017 by jim_thompson5910(28476) About Me  on 2011-11-12 14:04:43 (Show Source):
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3x%5E2%2B12x%2B12 Start with the given expression.


3%28x%5E2%2B4x%2B4%29 Factor out the GCF 3.


Now let's try to factor the inner expression x%5E2%2B4x%2B4


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


Looking at the expression x%5E2%2B4x%2B4, we can see that the first coefficient is 1, the second coefficient is 4, and the last term is 4.


Now multiply the first coefficient 1 by the last term 4 to get %281%29%284%29=4.


Now the question is: what two whole numbers multiply to 4 (the previous product) and add to the second coefficient 4?


To find these two numbers, we need to list all of the factors of 4 (the previous product).


Factors of 4:
1,2,4
-1,-2,-4


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


These factors pair up and multiply to 4.
1*4 = 4
2*2 = 4
(-1)*(-4) = 4
(-2)*(-2) = 4

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 4:


First NumberSecond NumberSum
141+4=5
222+2=4
-1-4-1+(-4)=-5
-2-2-2+(-2)=-4



From the table, we can see that the two numbers 2 and 2 add to 4 (the middle coefficient).


So the two numbers 2 and 2 both multiply to 4 and add to 4


Now replace the middle term 4x with 2x%2B2x. Remember, 2 and 2 add to 4. So this shows us that 2x%2B2x=4x.


x%5E2%2Bhighlight%282x%2B2x%29%2B4 Replace the second term 4x with 2x%2B2x.


%28x%5E2%2B2x%29%2B%282x%2B4%29 Group the terms into two pairs.


x%28x%2B2%29%2B%282x%2B4%29 Factor out the GCF x from the first group.


x%28x%2B2%29%2B2%28x%2B2%29 Factor out 2 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.


%28x%2B2%29%28x%2B2%29 Combine like terms. Or factor out the common term x%2B2


%28x%2B2%29%5E2 Condense the terms.


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


So 3%28x%5E2%2B4x%2B4%29 then factors further to 3%28x%2B2%29%5E2


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


Answer:


So 3x%5E2%2B12x%2B12 completely factors to 3%28x%2B2%29%5E2.


In other words, 3x%5E2%2B12x%2B12=3%28x%2B2%29%5E2.


Note: you can check the answer by expanding 3%28x%2B2%29%5E2 to get 3x%5E2%2B12x%2B12 or by graphing the original expression and the answer (the two graphs should be identical).


If you need more help, email me at jim_thompson5910@hotmail.com

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Jim


Finance/530358: factor the following expression: 9x^4-4y^2
1 solutions

Answer 350016 by jim_thompson5910(28476) About Me  on 2011-11-12 14:03:57 (Show Source):
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9x^4-4y^2


(3x^2)^2-(2y)^2


(3x^2-2y)(3x^2+2y)


So 9x^4-4y^2 completely factors to (3x^2-2y)(3x^2+2y)


Functions/530407: find the zeros of the function given by
f(x)=2x^2-11x+15
1 solutions

Answer 350015 by jim_thompson5910(28476) About Me  on 2011-11-12 14:02:08 (Show Source):
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f(x)=2x^2-11x+15


0=2x^2-11x+15


2x^2-11x+15=0


2x^2-6x-5x+15=0


2x(x-3)-5(x-3)=0


(2x-5)(x-3)=0


2x-5=0 or x-3=0


2x=5 or x=3


x=5/2 or x=3


So the zeros are 5/2 and 3


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Jim


Circles/530393: I'm really lost. Please help.
find the center and radius of the circle with the given equation.
x^2+y^2-28=0
All help is appreciated!
1 solutions

Answer 350014 by jim_thompson5910(28476) About Me  on 2011-11-12 13:59:38 (Show Source):
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x%5E2%2By%5E2-28=0


x%5E2%2By%5E2=28


%28x-0%29%5E2%2B%28y-0%29%5E2=%28sqrt%2828%29%29%5E2


The equation is now in %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 form, which is a circle, where h=0, k=0 and r=sqrt%2828%29


Remember that the center is (h,k) and the radius is r.


So the center is (0,0) and the radius is sqrt%2828%29 units.


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


test/530398:
1 solutions

Answer 350013 by jim_thompson5910(28476) About Me  on 2011-11-12 13:55:36 (Show Source):
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There's nothing here...please post a problem.


Signed-numbers/530401: I am stuck on the answer to this, I know what it is, but how it was solved
How did it get to 33 over 12 (33/12)
26 = -7 + 12p
1 solutions

Answer 350012 by jim_thompson5910(28476) About Me  on 2011-11-12 13:55:09 (Show Source):