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Travel_Word_Problems/563418: If “*“ is an operator that transforms a, b according to the rule a*b= a-b, determine the “value” of (a*b)*((a*a)*b).
"*" is supose to be a triangle
1 solutions

Answer 364865 by jim_thompson5910(28598) About Me  on 2012-01-26 20:42:16 (Show Source):
You can put this solution on YOUR website!
(a*b)*((a*a)*b)

(a-b)*((a-a)-b)

(a-b)*(0-b)

(a-b)*(-b)

(a-b)-(-b)

a-b+b

a


So (a*b)*((a*a)*b) = a for all values of a and b




Inequalities/563352: 5x-6+1<-10
1 solutions

Answer 364864 by jim_thompson5910(28598) About Me  on 2012-01-26 20:38:15 (Show Source):
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5x-6%2B1%3C-10 Start with the given inequality.


5x-5%3C-10 Combine like terms on the left side.


5x%3C-10%2B5 Add 5 to both sides.


5x%3C-5 Combine like terms on the right side.


x%3C%28-5%29%2F%285%29 Divide both sides by 5 to isolate x.


x%3C-1 Reduce.


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Answer:

So the solution is x%3C-1
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absolute-value/563118: 3|x|=24
1 solutions

Answer 364771 by jim_thompson5910(28598) About Me  on 2012-01-26 15:26:30 (Show Source):
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3|x|=24


|x|=24/3


|x|=8


x = 8 or x = -8


Distributive-associative-commutative-properties/563159: I'm trying to find the perimeter of a rectangle when the length is x + 25 and the width is 2x
1 solutions

Answer 364770 by jim_thompson5910(28598) About Me  on 2012-01-26 15:24:03 (Show Source):
You can put this solution on YOUR website!
P = 2L + 2W


P = 2(x+25) + 2(2x)


P = 2x+50+4x


P = 6x+50


So the perimeter is 6x+50 units.


Inequalities/561964: 2x-3>x
1 solutions

Answer 364409 by jim_thompson5910(28598) About Me  on 2012-01-24 17:58:01 (Show Source):
You can put this solution on YOUR website!
2x-3>x

-3>x-2x

-3>-x

3 < x

x > 3


So the solution is x > 3


Distributive-associative-commutative-properties/561659: what property is (15+4) + 9 = (4+15) + 9
1 solutions

Answer 364344 by jim_thompson5910(28598) About Me  on 2012-01-24 08:34:33 (Show Source):
You can put this solution on YOUR website!
This is the commutative property of addition.
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Jim

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expressions/561689: -5a^2,a=2
1 solutions

Answer 364342 by jim_thompson5910(28598) About Me  on 2012-01-24 08:31:48 (Show Source):
You can put this solution on YOUR website!
-5a%5E2


-5%282%29%5E2


-5%284%29


-20


So -5a%5E2=-20 when a=2
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Jim

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test/561636:
1 solutions

Answer 364316 by jim_thompson5910(28598) About Me  on 2012-01-24 00:49:32 (Show Source):
You can put this solution on YOUR website!
missing problem


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) About Me  on 2012-01-23 22:40:37 (Show Source):
You can put this solution on YOUR website!

x%5E2-2x-13=0 Start with the given equation.


Notice that the quadratic x%5E2-2x-13 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-2, and C=-13


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-13%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-2, and C=-13


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-13%29+%29%29%2F%282%281%29%29 Negate -2 to get 2.


x+=+%282+%2B-+sqrt%28+4-4%281%29%28-13%29+%29%29%2F%282%281%29%29 Square -2 to get 4.


x+=+%282+%2B-+sqrt%28+4--52+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-13%29 to get -52


x+=+%282+%2B-+sqrt%28+4%2B52+%29%29%2F%282%281%29%29 Rewrite sqrt%284--52%29 as sqrt%284%2B52%29


x+=+%282+%2B-+sqrt%28+56+%29%29%2F%282%281%29%29 Add 4 to 52 to get 56


x+=+%282+%2B-+sqrt%28+56+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%282+%2B-+2%2Asqrt%2814%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%282%29%2F%282%29+%2B-+%282%2Asqrt%2814%29%29%2F%282%29 Break up the fraction.


x+=+1+%2B-+sqrt%2814%29 Reduce.


x+=+1%2Bsqrt%2814%29 or x+=+1-sqrt%2814%29 Break up the expression.


So the solutions are x+=+1%2Bsqrt%2814%29 or x+=+1-sqrt%2814%29
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Inverses/561469: What is the multiplicative inverse of negative one over nine?
1 solutions

Answer 364271 by jim_thompson5910(28598) About Me  on 2012-01-23 19:38:09 (Show Source):
You can put this solution on YOUR website!
The multiplicative inverse of x is 1/x. In this case, x = -1/9. So 1/x = 1/(-1/9) = -9

So the multiplicative inverse of -1/9 is -9
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Jim

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Quadratic_Equations/561415: Factor : x2+21x+54
1 solutions

Answer 364270 by jim_thompson5910(28598) About Me  on 2012-01-23 19:37:09 (Show Source):
You can put this solution on YOUR website!

Looking at the expression x%5E2%2B21x%2B54, we can see that the first coefficient is 1, the second coefficient is 21, and the last term is 54.


Now multiply the first coefficient 1 by the last term 54 to get %281%29%2854%29=54.


Now the question is: what two whole numbers multiply to 54 (the previous product) and add to the second coefficient 21?


To find these two numbers, we need to list all of the factors of 54 (the previous product).


Factors of 54:
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 54.
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 21:


First NumberSecond NumberSum
1541+54=55
2272+27=29
3183+18=21
696+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 3 and 18 add to 21 (the middle coefficient).


So the two numbers 3 and 18 both multiply to 54 and add to 21


Now replace the middle term 21x with 3x%2B18x. Remember, 3 and 18 add to 21. So this shows us that 3x%2B18x=21x.


x%5E2%2Bhighlight%283x%2B18x%29%2B54 Replace the second term 21x with 3x%2B18x.


%28x%5E2%2B3x%29%2B%2818x%2B54%29 Group the terms into two pairs.


x%28x%2B3%29%2B%2818x%2B54%29 Factor out the GCF x from the first group.


x%28x%2B3%29%2B18%28x%2B3%29 Factor out 18 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%2B18%29%28x%2B3%29 Combine like terms. Or factor out the common term x%2B3


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


Answer:


So x%5E2%2B21x%2B54 factors to %28x%2B18%29%28x%2B3%29.


In other words, x%5E2%2B21x%2B54=%28x%2B18%29%28x%2B3%29.


Note: you can check the answer by expanding %28x%2B18%29%28x%2B3%29 to get x%5E2%2B21x%2B54 or by graphing the original expression and the answer (the two graphs should be identical).
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test/561393: evalute absolute -5
1 solutions

Answer 364262 by jim_thompson5910(28598) About Me  on 2012-01-23 18:17:08 (Show Source):


test/561384:
1 solutions

Answer 364260 by jim_thompson5910(28598) About Me  on 2012-01-23 18:07:00 (Show Source):
You can put this solution on YOUR website!
blank page, please post the full problem + full instructions. Thanks.


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) About Me  on 2012-01-23 18:01:02 (Show Source):
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5t%5E2-27t%2B22=0 Start with the given equation.


Notice that the quadratic 5t%5E2-27t%2B22 is in the form of At%5E2%2BBt%2BC where A=5, B=-27, and C=22


Let's use the quadratic formula to solve for "t":


t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


t+=+%28-%28-27%29+%2B-+sqrt%28+%28-27%29%5E2-4%285%29%2822%29+%29%29%2F%282%285%29%29 Plug in A=5, B=-27, and C=22


t+=+%2827+%2B-+sqrt%28+%28-27%29%5E2-4%285%29%2822%29+%29%29%2F%282%285%29%29 Negate -27 to get 27.


t+=+%2827+%2B-+sqrt%28+729-4%285%29%2822%29+%29%29%2F%282%285%29%29 Square -27 to get 729.


t+=+%2827+%2B-+sqrt%28+729-440+%29%29%2F%282%285%29%29 Multiply 4%285%29%2822%29 to get 440


t+=+%2827+%2B-+sqrt%28+289+%29%29%2F%282%285%29%29 Subtract 440 from 729 to get 289


t+=+%2827+%2B-+sqrt%28+289+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


t+=+%2827+%2B-+17%29%2F%2810%29 Take the square root of 289 to get 17.


t+=+%2827+%2B+17%29%2F%2810%29 or t+=+%2827+-+17%29%2F%2810%29 Break up the expression.


t+=+%2844%29%2F%2810%29 or t+=++%2810%29%2F%2810%29 Combine like terms.


t+=+22%2F5 or t+=+1 Simplify.


So the solutions are t+=+22%2F5 or t+=+1


Note: 22/5 = 4.4


So you have the correct answers.
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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) About Me  on 2012-01-23 17:57:25 (Show Source):
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3x%2B4%3C=31 Start with the given inequality.


3x%3C=31-4 Subtract 4 from both sides.


3x%3C=27 Combine like terms on the right side.


x%3C=%2827%29%2F%283%29 Divide both sides by 3 to isolate x.


x%3C=9 Reduce.


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

Answer:

So the solution is x%3C=9
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Linear-equations/561366: Is the linear equation 3x-2=y in standard form ? If yes then how ?
1 solutions

Answer 364256 by jim_thompson5910(28598) About Me  on 2012-01-23 17:45:17 (Show Source):
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No it is not in standard form since Ax+By = C is standard form.


Quadratic-relations-and-conic-sections/561358: 162x^4-2y^4

how do i factor this? with work
1 solutions

Answer 364255 by jim_thompson5910(28598) About Me  on 2012-01-23 17:38:45 (Show Source):
You can put this solution on YOUR website!
162x^4-2y^4

2(81x^4-y^4)

2((9x^2)^2-(y^2)^2)

2(9x^2-y^2)(9x^2+y^2)

2((3x)^2-y^2)(9x^2+y^2)

2(3x-y)(3x+y)(9x^2+y^2)


So 162x^4-2y^4 completely factors to 2(3x-y)(3x+y)(9x^2+y^2)

In other words, 162x^4-2y^4 = 2(3x-y)(3x+y)(9x^2+y^2)
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test/561357:
1 solutions

Answer 364254 by jim_thompson5910(28598) About Me  on 2012-01-23 17:36:16 (Show Source):
You can put this solution on YOUR website!
missing problem


test/561345: 26•54
1 solutions

Answer 364253 by jim_thompson5910(28598) About Me  on 2012-01-23 17:31:33 (Show Source):


Polynomials-and-rational-expressions/561338: Hello! How do I solve for B in y=(-9/2)+b

1 solutions

Answer 364250 by jim_thompson5910(28598) About Me  on 2012-01-23 17:15:45 (Show Source):
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y=%28-9%2F2%29%2Bb

y=-9%2F2%2Bb

y%2B9%2F2=b

b+=+y%2B9%2F2
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Linear_Equations_And_Systems_Word_Problems/561339: Hi! Ok, I'm not really getting this question is says..
-P=3.25c-780
- If the above equation were to be graphed, what would be the slope of this graph?
-I know the slope is 3.25 and since that's positive, so would the slope be positive?
Thanks! I really appreciate it!
1 solutions

Answer 364249 by jim_thompson5910(28598) About Me  on 2012-01-23 17:14:43 (Show Source):
You can put this solution on YOUR website!
You are correct, the slope is 3.25, which is positive.


test/561335: 8(k+8)
1 solutions

Answer 364248 by jim_thompson5910(28598) About Me  on 2012-01-23 17:10:31 (Show Source):
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8(k+8) = 8k+64


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) About Me  on 2012-01-23 17:05:59 (Show Source):
You can put this solution on YOUR website!
You are correct. No real solutions exist.


Travel_Word_Problems/561328: if you ride a bike at 3 mph for 4 hours, how far will you travel?
1 solutions

Answer 364244 by jim_thompson5910(28598) About Me  on 2012-01-23 17:04:06 (Show Source):
You can put this solution on YOUR website!
d = rt

d = 3*4

d = 12

So you've traveled 12 miles.
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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) About Me  on 2012-01-23 16:56:44 (Show Source):
You can put this solution on YOUR website!
Using the pythagorean theorem, a%5E2%2Bb%5E2=c%5E2, we can say that if side A = x, B = x (note: A = B because this is an isosceles triangle) and C = 43, then


a%5E2%2Bb%5E2=c%5E2

x%5E2%2Bx%5E2=43%5E2

2x%5E2=1849

x%5E2=1849%2F2

x%5E2=924.5

x=sqrt%28924.5%29

x=30.4055915910216

So A and B are roughly 30.4055915910216 units long
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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) About Me  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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Polynomials-and-rational-expressions/561314: Create a data set that contains three values and has a mode of 1/3
1 solutions

Answer 364238 by jim_thompson5910(28598) About Me  on 2012-01-23 16:49:27 (Show Source):
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{1/3, 1/3, 5} is one such set or {1/3, 1/3, 1/3} is another


Subset/561312: WHAT ARE THE SUBSETS OF THE SET (-1,9)
1 solutions

Answer 364236 by jim_thompson5910(28598) About Me  on 2012-01-23 16:47:45 (Show Source):
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There are 4 Subsets, and they are:
{}, {-1}, {9}, {-1, 9}
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Probability-and-statistics/561310: create a data set that contains four values and has a mean of 24
1 solutions

Answer 364235 by jim_thompson5910(28598) About Me  on 2012-01-23 16:46:53 (Show Source):
You can put this solution on YOUR website!
The set {24, 24, 24, 24} is a very simple example (since adding them will get 96 and then divide that by 4 to get 24 again)

also, the set {22, 23, 25, 26} works as well (same reason as above)
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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) About Me  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) About Me  on 2012-01-23 16:26:45 (Show Source):
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54k^2 - 24

6(9k^2 - 4)

6( (3k)^2 - 2^2 )

6(3k-2)(3k+2)


So 54k^2 - 24 completely factors to 6(3k-2)(3k+2)
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