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Probability-and-statistics/531479: In how many ways can the letters in "laser" be arranged?
1 solutions

Answer 350494 by jim_thompson5910(28598) About Me  on 2011-11-14 18:12:48 (Show Source):
You can put this solution on YOUR website!
There are 5! = 5*4*3*2*1 = 120 ways to arrange the letters.


Inequalities/531493: Solve the inequality: 8b>32
1 solutions

Answer 350493 by jim_thompson5910(28598) About Me  on 2011-11-14 18:12:16 (Show Source):
You can put this solution on YOUR website!
8b > 32


b > 32/8


b > 4


Equations/531535: How to solve 3w - 65 = 8w
1 solutions

Answer 350491 by jim_thompson5910(28598) About Me  on 2011-11-14 18:11:36 (Show Source):
You can put this solution on YOUR website!
3w-65=8w Start with the given equation.


3w=8w%2B65 Add 65 to both sides.


3w-8w=65 Subtract 8w from both sides.


-5w=65 Combine like terms on the left side.


w=%2865%29%2F%28-5%29 Divide both sides by -5 to isolate w.


w=-13 Reduce.


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

Answer:

So the solution is w=-13


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Jim


Equations/531539: 6=1-2n + 5
1 solutions

Answer 350490 by jim_thompson5910(28598) About Me  on 2011-11-14 18:10:59 (Show Source):
You can put this solution on YOUR website!
6=1-2n%2B5 Start with the given equation.


6=-2n%2B6 Combine like terms on the right side.


0=-2n%2B6-6 Subtract 6 from both sides.


2n=6-6 Add 2n to both sides.


2n=0 Combine like terms on the right side.


n=%280%29%2F%282%29 Divide both sides by 2 to isolate n.


n=0 Reduce.


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

Answer:

So the solution is n=0


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


Coordinate-system/531546: Find the x- intercept and y -intercept of the line given by the equation.
8x-3y=-6

1 solutions

Answer 350488 by jim_thompson5910(28598) About Me  on 2011-11-14 18:09:53 (Show Source):
You can put this solution on YOUR website!

x-intercept


To find the x-intercept, plug in y=0 and solve for x


8x-3y=-6 Start with the given equation.


8x-3%280%29=-6 Plug in y=0.


8x-0=-6 Multiply -3 and 0 to get 0.


8x=-6 Simplify.


x=%28-6%29%2F%288%29 Divide both sides by 8 to isolate x.


x=-3%2F4 Reduce.


So the x-intercept is .


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


y-intercept


To find the y-intercept, plug in x=0 and solve for y


8x-3y=-6 Start with the given equation.


8%280%29-3y=-6 Plug in x=0.


0-3y=-6 Multiply 8 and 0 to get 0.


-3y=-6 Simplify.


y=%28-6%29%2F%28-3%29 Divide both sides by -3 to isolate y.


y=2 Reduce.


So the y-intercept is .


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

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Jim


Equations/531547: Please help me with the following(Make sure to include the steps)
1. -11-5a=6(5a+4)
2. -5(4x-2=-2(3+6x)
3. 5(2x+6)=-4(-5-2x)+3x
1 solutions

Answer 350486 by jim_thompson5910(28598) About Me  on 2011-11-14 18:09:05 (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started.

# 1

-11-5a=6%285a%2B4%29 Start with the given equation.


-11-5a=30a%2B24 Distribute.


-5a=30a%2B24%2B11 Add 11 to both sides.


-5a-30a=24%2B11 Subtract 30a from both sides.


-35a=24%2B11 Combine like terms on the left side.


-35a=35 Combine like terms on the right side.


a=%2835%29%2F%28-35%29 Divide both sides by -35 to isolate a.


a=-1 Reduce.


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

Answer:

So the solution is a=-1


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/531057: c2+11c+18/c+9 the quotient is_____
(c to the 2nd power)
1 solutions

Answer 350318 by jim_thompson5910(28598) About Me  on 2011-11-13 20:07:33 (Show Source):
You can put this solution on YOUR website!
%28c%5E2%2B11c%2B18%29%2F%28c%2B9%29


%28%28c%2B9%29%28c%2B2%29%29%2F%28c%2B9%29


%28highlight%28%28c%2B9%29%29%28c%2B2%29%29%2F%28highlight%28%28c%2B9%29%29%29


%28cross%28%28c%2B9%29%29%28c%2B2%29%29%2F%28cross%28%28c%2B9%29%29%29


c%2B2


So %28c%5E2%2B11c%2B18%29%2F%28c%2B9%29=c%2B2


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Jim


logarithm/531058: How do i express 27^-2/3 = 1/9 in logarithmic form
1 solutions

Answer 350316 by jim_thompson5910(28598) About Me  on 2011-11-13 20:06:02 (Show Source):


Numeric_Fractions/531052: 12n-7-3n=11
1 solutions

Answer 350312 by jim_thompson5910(28598) About Me  on 2011-11-13 20:00:49 (Show Source):
You can put this solution on YOUR website!
12n-7-3n=11 Start with the given equation.


9n-7=11 Combine like terms on the left side.


9n=11%2B7 Add 7 to both sides.


9n=18 Combine like terms on the right side.


n=%2818%29%2F%289%29 Divide both sides by 9 to isolate n.


n=2 Reduce.


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

Answer:

So the solution is n=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


Square-cubic-other-roots/531015: I need to simplify radical 176a^3b^5 but I am having trouble knowing exactly where to begin.
1 solutions

Answer 350302 by jim_thompson5910(28598) About Me  on 2011-11-13 19:30:29 (Show Source):
You can put this solution on YOUR website!

sqrt%28176%2Aa%5E3%2Ab%5E5%29 Start with the given expression.


sqrt%2816%2A11%2Aa%5E3%2Ab%5E5%29 Factor 176 into 16%2A11


sqrt%2816%2A11%2Aa%5E2%2Aa%2Ab%5E5%29 Factor a%5E3 into a%5E2%2Aa


sqrt%2816%2A11%2Aa%5E2%2Aa%2Ab%5E2%2Ab%5E2%2Ab%29 Factor b%5E5 into b%5E2%2Ab%5E2%2Ab


Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


Take the square root of 16 to get 4.


4%2Asqrt%2811%29%2Aa%2Asqrt%28a%29%2Asqrt%28b%5E2%29%2Asqrt%28b%5E2%29%2Asqrt%28b%29 Take the square root of a%5E2 to get a.


4%2Asqrt%2811%29%2Aa%2Asqrt%28a%29%2Ab%2Ab%2Asqrt%28b%29 Take the square root of b%5E2 to get b.


4ab%5E2%2Asqrt%2811ab%29 Rearrange and multiply the terms.

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

Answer:


So sqrt%28176%2Aa%5E3%2Ab%5E5%29 simplifies to 4ab%5E2%2Asqrt%2811ab%29


In other words, sqrt%28176%2Aa%5E3%2Ab%5E5%29=4ab%5E2%2Asqrt%2811ab%29 where every variable is non-negative.



Polynomials-and-rational-expressions/531014: I only have a few hours left to turn in my assignment and really need help with these problems. I have already completed over 50 problems and keep getting things confused so I'm not even sure if those are correct. Please help! I would greatly appreciate being shown how to solve these problems. Thanks in advance!


1. Find the following. 12^sqrt(-5)^12
2. Multiply (-3x)^2(2x^8)^2
3. Use the foil method to find the product (3x^3-4)(x^6-1)
4. Divide and simplify 3x-27/14 divide by x-9/6x
5. Find all numbers for which the rational expression is undefined. q^3-2q/q^2-16
6. Multiply (5x+4)(7x^2+9x+4)
7. Factor completely 3x^5-27x^4+9x^3
8. Subtract. Simplify, if possible. (4-v/v-7)-(6v-5/7-v)
9. Perform the indicated operations and simplify (y-6/y-8) – (y+1/y+8 )+(y-40/y^2-64)
10. Simplify by taking roots of the numerator and the denominator 3^sqrt 8x^14/y^3
11. Multiply and simplify. (4b^2/4b^2-24b+36)(4b-12/2b)
12. Solve. 2/v=6/v-1/3
13. Add. Simplify if possible. (3w/w^2-25) + (w/w-5)

1 solutions

Answer 350301 by jim_thompson5910(28598) About Me  on 2011-11-13 19:29:15 (Show Source):
You can put this solution on YOUR website!
I'll do the first three to get you started

# 1

Use the idea that root%28n%2Cx%5En%29=abs%28x%29 where n is even


So

root%2812%2C+%28-5%29%5E12%29+=+abs%28-5%29+=+5


or simply


root%2812%2C+%28-5%29%5E12%29+=+5

-------------------------------------------------------
# 2


(-3x)^2(2x^8)^2


(-3)^2*(x^2)(2)^2*(x^8)^2


9x^2*4*x^16


36x^18


So (-3x)^2(2x^8)^2 = 36x^18

-------------------------------------------------------
# 3

(3x^3-4)(x^6-1)


(3x^3)(x^6)+(3x^3)(-1)+(-4)(x^6)+(-4)(-1)


3x^9-3x^3-4x^6+4


So (3x^3-4)(x^6-1)=3x^9-3x^3-4x^6+4


Inverses/531013: Solve: 2 + 5x > 2x - 13. > can also be equal to
1 solutions

Answer 350296 by jim_thompson5910(28598) About Me  on 2011-11-13 19:21:26 (Show Source):
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2%2B5x%3E2x-13 Start with the given inequality.


5x%3E2x-13-2 Subtract 2 from both sides.


5x-2x%3E-13-2 Subtract 2x from both sides.


3x%3E-13-2 Combine like terms on the left side.


3x%3E-15 Combine like terms on the right side.


x%3E%28-15%29%2F%283%29 Divide both sides by 3 to isolate x.


x%3E-5 Reduce.


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

Answer:

So the solution is x%3E-5


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Jim


Triangles/531004: The sides of an equilateral triangle measure (2x+4) units. What is the perimeter
1 solutions

Answer 350291 by jim_thompson5910(28598) About Me  on 2011-11-13 19:08:41 (Show Source):
You can put this solution on YOUR website!
Perimeter is 3(2x+4) = 6x+12


Linear_Algebra/530986: Solve the system of equations
x + y = 6
x - y = -9
1 solutions

Answer 350290 by jim_thompson5910(28598) About Me  on 2011-11-13 19:06:37 (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%28x%2By=6%2Cx-y=-9%29


Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28x%2By%29%2B%28x-1y%29=%286%29%2B%28-9%29


%281x%2B1x%29%2B%281y%2B-1y%29=6%2B-9 Group like terms.


2x%2B0y=-3 Combine like terms.


2x=-3 Simplify.


x=%28-3%29%2F%282%29 Divide both sides by 2 to isolate x.


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


x%2By=6 Now go back to the first equation.


-3%2F2%2By=6 Plug in x=-3%2F2.


2%28-3%2Fcross%282%29%2By%29=2%286%29 Multiply both sides by the LCD 2 to clear any fractions.


-3%2B2y=12 Distribute and multiply.


2y=12%2B3 Add 3 to both sides.


2y=15 Combine like terms on the right side.


y=%2815%29%2F%282%29 Divide both sides by 2 to isolate y.


So the solutions are x=-3%2F2 and y=15%2F2.


Which form the ordered pair .


This means that the system is consistent and independent.


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Inverses/530998: 1/x + 1/y = 5, can you solve for x without ending up with an xy
1 solutions

Answer 350287 by jim_thompson5910(28598) About Me  on 2011-11-13 19:04:38 (Show Source):


Rectangles/530993: what is the different between 79 and 105
1 solutions

Answer 350286 by jim_thompson5910(28598) About Me  on 2011-11-13 18:59:50 (Show Source):
You can put this solution on YOUR website!
105 - 79 = 26


Numbers_Word_Problems/530987: What would be the algebraic expression for twice a number is added to fifteen.
1 solutions

Answer 350285 by jim_thompson5910(28598) About Me  on 2011-11-13 18:58:39 (Show Source):
You can put this solution on YOUR website!
"twice a number is added to fifteen" translates to 2x%2B15 where x is the unknown number.


Radicals/530980: Need help to solve this one, please!
√(y+5) - 4 = 1

1 solutions

Answer 350279 by jim_thompson5910(28598) About Me  on 2011-11-13 18:46:30 (Show Source):
You can put this solution on YOUR website!
sqrt%28y%2B5%29+-+4+=+1


sqrt%28y%2B5%29++=+1%2B4


sqrt%28y%2B5%29++=+5


y%2B5++=+5%5E2


y%2B5+=+25


y+=+25-5


y+=+20


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Jim


Inverses/530975: Write a problem with the equation r divided by 6 = 14. Topic: algebra
1 solutions

Answer 350277 by jim_thompson5910(28598) About Me  on 2011-11-13 18:42:28 (Show Source):
You can put this solution on YOUR website!
"r divided by 6 = 14" means r%2F6=14


Exponents/530967: not sure if answer is negative or positive.
-4+3
divided by
-4*3
1 solutions

Answer 350276 by jim_thompson5910(28598) About Me  on 2011-11-13 18:38:58 (Show Source):
You can put this solution on YOUR website!
-4+3 = -1

and

-4*3 = -12


So -4+3 divided by -4*3 is -1/(-12) = 1/12


So the answer is 1/12


Equations/530965: using numbers 2,3,7,5,6 solve to get 31
1 solutions

Answer 350274 by jim_thompson5910(28598) About Me  on 2011-11-13 18:35:00 (Show Source):
You can put this solution on YOUR website!
2*3*7-5-6 = 31


Numeric_Fractions/530921: what is 5n-9 = 11
1 solutions

Answer 350251 by jim_thompson5910(28598) About Me  on 2011-11-13 17:38:11 (Show Source):
You can put this solution on YOUR website!
5n-9=11 Start with the given equation.


5n=11%2B9 Add 9 to both sides.


5n=20 Combine like terms on the right side.


n=%2820%29%2F%285%29 Divide both sides by 5 to isolate n.


n=4 Reduce.


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

Answer:

So the solution is n=4


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Jim


Exponents/530922: what is 9-6/7) to the zero power
1 solutions

Answer 350250 by jim_thompson5910(28598) About Me  on 2011-11-13 17:37:45 (Show Source):
You can put this solution on YOUR website!
Anything to the zeroth power (except 0) is 1


So the answer is 1


Note: I'm assuming that everything is raised to the zeroth power.


Polynomials-and-rational-expressions/530914: 25y^2-10y+1
1 solutions

Answer 350246 by jim_thompson5910(28598) About Me  on 2011-11-13 17:18:59 (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor.

Looking at the expression 25y%5E2-10y%2B1, we can see that the first coefficient is 25, the second coefficient is -10, and the last term is 1.


Now multiply the first coefficient 25 by the last term 1 to get %2825%29%281%29=25.


Now the question is: what two whole numbers multiply to 25 (the previous product) and add to the second coefficient -10?


To find these two numbers, we need to list all of the factors of 25 (the previous product).


Factors of 25:
1,5,25
-1,-5,-25


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


These factors pair up and multiply to 25.
1*25 = 25
5*5 = 25
(-1)*(-25) = 25
(-5)*(-5) = 25

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -10:


First NumberSecond NumberSum
1251+25=26
555+5=10
-1-25-1+(-25)=-26
-5-5-5+(-5)=-10



From the table, we can see that the two numbers -5 and -5 add to -10 (the middle coefficient).


So the two numbers -5 and -5 both multiply to 25 and add to -10


Now replace the middle term -10y with -5y-5y. Remember, -5 and -5 add to -10. So this shows us that -5y-5y=-10y.


25y%5E2%2Bhighlight%28-5y-5y%29%2B1 Replace the second term -10y with -5y-5y.


%2825y%5E2-5y%29%2B%28-5y%2B1%29 Group the terms into two pairs.


5y%285y-1%29%2B%28-5y%2B1%29 Factor out the GCF 5y from the first group.


5y%285y-1%29-1%285y-1%29 Factor out 1 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.


%285y-1%29%285y-1%29 Combine like terms. Or factor out the common term 5y-1


%285y-1%29%5E2 Condense the terms.


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


Answer:


So 25y%5E2-10y%2B1 factors to %285y-1%29%5E2.


In other words, 25y%5E2-10y%2B1=%285y-1%29%5E2.


Note: you can check the answer by expanding %285y-1%29%5E2 to get 25y%5E2-10y%2B1 or by graphing the original expression and the answer (the two graphs should be identical).


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Jim


Equations/530910: what is 9x-5x=7
1 solutions

Answer 350245 by jim_thompson5910(28598) About Me  on 2011-11-13 17:13:47 (Show Source):
You can put this solution on YOUR website!
The previous poster meant to write x = 7/4 for the final answer.


Circles/530880: If the diameter of a circle is 27 meters, what is the area? Round to the nearest tenth
1 solutions

Answer 350237 by jim_thompson5910(28598) About Me  on 2011-11-13 16:22:15 (Show Source):
You can put this solution on YOUR website!
If the diameter of a circle is 27 meters, then the radius is 27/2 = 13.5 meters


So r = 13.5


A=pi%2Ar%5E2 Start with the area of a circle formula.


A=pi%2A%2813.5%29%5E2 Plug in r=13.5.


A=%283.14159265%29%2A%2813.5%29%5E2 Replace pi with 3.14159265 (note: Use more digits of pi to get better accuracy).


A=%283.14159265%29%2A%28182.25%29 Square 13.5 to get 182.25.


A=572.5552604625 Multiply 3.14159265 and 182.25 to get 572.5552604625 (this figure is approximate).


A=572.6 Round to the nearest tenth.


So the area is roughly 572.6 square meters.


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Jim


Functions/530881: What is the missing value for (3,2) and (6,y) ?
1 solutions

Answer 350235 by jim_thompson5910(28598) About Me  on 2011-11-13 16:20:34 (Show Source):
You can put this solution on YOUR website!
Do you know the slope of the line that passes through these points?


Polynomials-and-rational-expressions/530878: perform the indicated operation
8n-[9n-(4n+5)
1 solutions

Answer 350234 by jim_thompson5910(28598) About Me  on 2011-11-13 16:16:54 (Show Source):
You can put this solution on YOUR website!
8n-[9n-(4n+5)]


8n-[9n-4n-5]


8n-9n+4n+5


3n+5


Complex_Numbers/530877: 3^2*3^-3
1 solutions

Answer 350232 by jim_thompson5910(28598) About Me  on 2011-11-13 16:14:39 (Show Source):
You can put this solution on YOUR website!
3^2*3^-3 = 3^(2+(-3)) = 3^(-1) = 1/(3^1) = 1/3


So 3^2*3^-3 = 1/3


Sequences-and-series/530874: what is the answer to (1\9)^4 with the answer left in fractional form.

1 solutions

Answer 350230 by jim_thompson5910(28598) About Me  on 2011-11-13 16:13:07 (Show Source):


Functions/530873: 1-m=6-6m solve and check solution
1 solutions

Answer 350227 by jim_thompson5910(28598) About Me  on 2011-11-13 16:09:33 (Show Source):
You can put this solution on YOUR website!
1-m=6-6m Start with the given equation.


-m=6-6m-1 Subtract 1 from both sides.


-m%2B6m=6-1 Add 6m to both sides.


5m=6-1 Combine like terms on the left side.


5m=5 Combine like terms on the right side.


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


m=1 Reduce.


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

Answer:

So the solution is m=1


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