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Inequalities/563352: 5x-6+1<-10 1 solutions
Answer 364864 by jim_thompson5910(28598) on 2012-01-26 20:38:15 (Show Source):
You can put this solution on YOUR website!
 Start with the given inequality.
 Combine like terms on the left side.
 Add  to 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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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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Quadratic_Equations/561604: x^2-2x-13=0
I loved algebra, but it's been 30 years since I last used it. 1 solutions
Answer 364308 by jim_thompson5910(28598) on 2012-01-23 22:40:37 (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  .
 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 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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Quadratic_Equations/561415: Factor : x2+21x+54 1 solutions
Answer 364270 by jim_thompson5910(28598) on 2012-01-23 19:37:09 (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  :
1,2,3,6,9,18,27,54
-1,-2,-3,-6,-9,-18,-27,-54
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to  .
1*54 = 54
2*27 = 54
3*18 = 54
6*9 = 54
(-1)*(-54) = 54
(-2)*(-27) = 54
(-3)*(-18) = 54
(-6)*(-9) = 54
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 | 54 | 1+54=55 | | 2 | 27 | 2+27=29 | | 3 | 18 | 3+18=21 | | 6 | 9 | 6+9=15 | | -1 | -54 | -1+(-54)=-55 | | -2 | -27 | -2+(-27)=-29 | | -3 | -18 | -3+(-18)=-21 | | -6 | -9 | -6+(-9)=-15 |
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
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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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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/561375: the question asks to solve: 5t^2-27t+22=0
could t=1 and t=4.4
?? 1 solutions
Answer 364259 by jim_thompson5910(28598) on 2012-01-23 18:01:02 (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 "t":
 Start with the quadratic formula
 Plug in  ,  , and
 Negate  to get  .
 Square  to get  .
 Multiply  to get
 Subtract  from  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
Note: 22/5 = 4.4
So you have the correct answers.
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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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Inequalities/561370: 3x+4 is less than or equal to 31
I have no idea how to solve multi step inequalities I would appeciate a thorough explanation, thank you morgan 1 solutions
Answer 364258 by jim_thompson5910(28598) on 2012-01-23 17:57:25 (Show Source):
You can put this solution on YOUR website!
 Start with the given inequality.
 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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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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Radicals/561329: sqrt(x-6)+3=sqrt(x)
does this have a real solution?
first i subtracted the 3 over, squared both sides and ended up with x=(25/4) but when i plug that in, it was not a true statement.
then i started over and squared both sides like the original problem shows and got the square root equal to a negative so that would be "no real solution".
thank you for looking at this!! 1 solutions
Answer 364245 by jim_thompson5910(28598) on 2012-01-23 17:05:59 (Show Source):
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Triangles/561323: I have a series of problems where i only have the measurements of side C in a right triangle (45, 45, 90 degree triangle) and i have no clue how to find sides a and b??
Let's say side C is 43, how would i find sides A and B?
1 solutions
Answer 364242 by jim_thompson5910(28598) on 2012-01-23 16:56:44 (Show Source):
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Linear_Equations_And_Systems_Word_Problems/561315: Hi! I'm not getting one thing on my math homework, can you help me please?
OK...here's the word problem.
- Dough bought a small tree at the local garden center to plant in his backyard. The employee at the garden center told him that the tree would grow two centimeters per week. The linear equation below represents, h the height of the tree in Doug's backyard. H=2c+61
-What I'm not getting is, what does 61 represent. How tall the tree is when he got it? 1 solutions
Answer 364240 by jim_thompson5910(28598) on 2012-01-23 16:50:54 (Show Source):
You can put this solution on YOUR website!When c = 0, ie when he first got it, H = 2(0)+61 = 61 which means that the height when he got it was 61 cm
So the 61 represents the initial or starting height of the plant.
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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/561305: How many solutions does the system have?
-2x+5y=7
-2x+5y=12 HELP!! 1 solutions
Answer 364234 by jim_thompson5910(28598) on 2012-01-23 16:40:06 (Show Source):
You can put this solution on YOUR website!Let's say that z = -2x+5y
So this would mean that equation 1 would go from -2x+5y = 7 to z = 7
and equation 2 would go from -2x+5y = 12 to z = 12
But z is only ONE number.
So z can't be both 7 and 12 at the same time.
So there are no numbers z which satisfy the system, which means by extension, there are no numbers x and y which satisfy the system
Answer: So there are NO solutions. This means that the system is inconsistent.
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Polynomials-and-rational-expressions/561299: Okay my algebra teacher is teaching us polynomials to a factor, the difference of two squares, and perfect square trinomials. And the problem is I don't understand really. The question is 54k^2 - 24. What I have to do first is 54(x^2-12). And that's where I am stuck, I don't know what to do next so please help me. 1 solutions
Answer 364231 by jim_thompson5910(28598) on 2012-01-23 16:26:45 (Show Source):
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