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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) 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.
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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) on 2011-11-12 18:07:40 (Show Source):
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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) on 2011-11-12 17:59:51 (Show Source):
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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) on 2011-11-12 17:50:51 (Show Source):
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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) on 2011-11-12 17:10:38 (Show Source):
You can put this solution on YOUR website! Start with the general equation of a circle.
 Plug in  and  (since the center is the point (h,k) ).
 Plug in  and  (this is the point that lies on the circle, which is in the form (x,y) ).
 Combine like terms.
 Square each term.
 Add.
So because  ,  , and  , this means that the equation of the circle with center (0,4) that goes through the point (0,0) is
 .
which simplifies to
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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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) on 2011-11-12 17:09:34 (Show Source):
You can put this solution on YOUR website! Start with the general equation of a circle.
 Plug in  and  (since the center is the point (h,k) ).
 Plug in  and  (this is the point that lies on the circle, which is in the form (x,y) ).
 Combine like terms.
 Square each term.
 Add.
So because  ,  , and  , this means that the equation of the circle with center (4,6) that goes through the point (2,2) is
 .
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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) on 2011-11-12 14:13:17 (Show Source):
You can put this solution on YOUR website! Start with the given equation.
 Combine like terms on the left side.
 Add  to 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/530360: factor the following trinomial completely: 3x^2+12x+12
1 solutions
Answer 350017 by jim_thompson5910(28476) on 2011-11-12 14:04:43 (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  :
1,2,4
-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  .
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  :
| First Number | Second Number | Sum | | 1 | 4 | 1+4=5 | | 2 | 2 | 2+2=4 | | -1 | -4 | -1+(-4)=-5 | | -2 | -2 | -2+(-2)=-4 |
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 the terms.
--------------------------------------------------
So  then factors further to
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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).
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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