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Polynomials-and-rational-expressions/353584: Perform the indicated operations and simplify:
z-7/z-9 - z+1/z+9 + z-45/z^2-81
I came up with 3/z+9
Multiply.
(5sqrt2 - 10sqrt5)(3sqrt2 + 6sqrt5)
Multiply and simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers.
^3sqrtY^7 ^3sqrt16Y^8
Any help is very much appreciated. Thank you in advance.

1 solutions

Answer 252641 by Fombitz(13828) About Me  on 2010-10-08 09:53:48 (Show Source):
You can put this solution on YOUR website!
First one: You have an addition error somewhere. The answer should be highlight_green%2811%2F%28z%2B9%29%29.
Check your work to see if you can spot the error.
.
.
.
%285%2Asqrt%282%29+-+10%2Asqrt%285%29%29%283%2Asqrt%282%29+%2B+6%2Asqrt%285%29%29
Use the FOIL method,

%285%2Asqrt%282%29+-+10%2Asqrt%285%29%29%283%2Asqrt%282%29+%2B+6%2Asqrt%285%29%29=30-300

.
.
.







Functions/353549: find the derivative of the function using the chain rule
y = cos (a^3 + x^3)
1 solutions

Answer 252637 by Fombitz(13828) About Me  on 2010-10-08 09:43:57 (Show Source):


Exponents/353582: find the derivative of the function
y+=+2+%5E+%28sin%28pi%2Ax%29%29
1 solutions

Answer 252636 by Fombitz(13828) About Me  on 2010-10-08 09:40:29 (Show Source):
You can put this solution on YOUR website!
Use the chain rule,
Let u=sin%28pi%2Ax%29
dy%2Fdx=%28dy%2Fdu%29%2A%28du%2Fdx%29
dy%2Fdu=ln%282%29%2A2%5Eu
du%2Fdx=cos%28pi%2Ax%29%2Api
Put it all together,
dy%2Fdx=ln%282%29%2A2%5E%28u%29%2Api%2Acos%28pi%2Ax%29
dy%2Fdx=ln%282%29%2Api%2A2%5E%28sin%28pi%2Ax%29%29%2Acos%28pi%2Ax%29


Exponents/353583: find the derivative of the function
y = 2^3^x^2
1 solutions

Answer 252630 by Fombitz(13828) About Me  on 2010-10-08 09:26:29 (Show Source):
You can put this solution on YOUR website!
y+=+2%5E%283%5E%28x%5E2%29%29
Use the chain rule,
Let u=3%5E%28x%5E2%29, let v=x%5E2,
dy%2Fdx=%28dy%2Fdu%29%2A%28du%2Fdx%29
du%2Fdx=%28du%2Fdv%29%2A%28dv%2Fdx%29
dy%2Fdx=%28dy%2Fdu%29%2A%28du%2Fdv%29%2A%28dv%2Fdx%29
dy%2Fdu=2%5Eu%2Aln%282%29
du%2Fdv=3%5Ev%2Aln%283%29
dv%2Fdx=2x
Putting it all together,
dy%2Fdx=2%5E%28u%29%2Alog%282%29%2A3%5E%28v%29%2Aln%283%29%2A2x
dy%2Fdx=ln%282%29%2Aln%283%29%2A2%5E%28u%2B1%29%2A3%5E%28v%29%2Ax
dy%2Fdx=ln%282%29%2Aln%283%29%2A2%5E%283%5E%28x%5E2%29%2B1%29%2A3%5E%28x%5E2%29%2Ax


Finance/353579: I am trying to solve for the unknown profit margin (PM) but I don't understand how to properly work the equation. Below, I have copied the equation as it is written in my text book:
.10 = PM(1.5)(.6)/ [1 - PM(1.5)(.6)
PM = .1/ .99 = 10.1%
Please advise the steps.
Thank you.
DW


1 solutions

Answer 252629 by Fombitz(13828) About Me  on 2010-10-08 09:25:46 (Show Source):
You can put this solution on YOUR website!
.10+=+%28PM%281.5%29%28.6%29%29%2F+%281+-+PM%281.5%29%28.6%29%29
.
.
.10+=+%280.9%2APM%29%2F+%281+-+0.9%2APM%29
.
.
0.1%281-0.9%2APM%29=0.9%2APM
.
.
0.1-0.09%2APM=0.9%2APM
.
.
0.99PM=0.1
.
.
PM=0.1%2F0.99
.
.
highlight%28PM=0.101%29


Linear-equations/353525: graph the fuction f(x)=|x+1|+|x-1|.show the steps, please, thanks.
1 solutions

Answer 252628 by Fombitz(13828) About Me  on 2010-10-08 09:21:18 (Show Source):
You can put this solution on YOUR website!
abs%28x%2B1%29=x%2B1 when x%2B1%3E0
abs%28x%2B1%29=-%28x%2B1%29 when x%2B1%3C0
x%3C-1
.
abs%28x%2B1%29=x%2B1 when x%3E-1
abs%28x%2B1%29=-x-1%29 when x%3C-1
.
.
.
abs%28x-1%29=x-1 when x-1%3E0
abs%28x-1%29=-%28x-1%29 when x-1%3C0
x%3C1
.
abs%28x%2B1%29=x-1 when x%3E1
abs%28x%2B1%29=-x%2B1%29 when x%3C1
.
.
.
So now build the function and use the two critical points x=-1 and x=1.
When x%3C-1
f%28x%29=-x-1%2B%28-x%2B1%29=-2x
When -1%3Cx%3C1
f%28x%29=x%2B1%2B%28-x%2B1%29=2
When x%3E1
f%28x%29=x%2B1%2B%28x-1%29=2x
.
.
Now graph it.
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.



Length-and-distance/353516: the measure of an angle is one fourth the measure of it supplament. Find the measure of the angle
1 solutions

Answer 252625 by Fombitz(13828) About Me  on 2010-10-08 09:13:31 (Show Source):
You can put this solution on YOUR website!
A%2BS=180
.
.
A=%281%2F4%29S
Substitute,
%281%2F4%29S%2BS=180
%285%2F4%29S=180
S=%284%2F5%29180
highlight%28S=144%29degrees
.
.
A=%281%2F4%29%28144%29
highlight%28A=36%29degrees


Number-Line/353511: how would this be answered on a number line A=(-9,7), B=(0,8)
1 solutions

Answer 252624 by Fombitz(13828) About Me  on 2010-10-08 09:11:44 (Show Source):
You can put this solution on YOUR website!
I'm not sure what you mean by answered but the two points can be plotted on a coordinate plane.
First Point A:(-9,7),
.
.
.

.
.
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Then Point B:(0,8),
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.
.


expressions/353482: Need help badly on these two questions!!!!
2/3 x -7 =x
8(5-n)=2n
1 solutions

Answer 252623 by Fombitz(13828) About Me  on 2010-10-08 09:07:07 (Show Source):
You can put this solution on YOUR website!
%282%2F3%29x+-7+=x
Multiply both sides by 3.
2x-21=3x
Now solve for x.
.
.
.
8%285-n%29=2n
40-8n=2n
10n=40
Now solve for n.


test/353490: Well I was wondering with a problem like ummm say 8(12m/3)-2(3m) now how could u simplify that step by step?? THANK YOU
1 solutions

Answer 252621 by Fombitz(13828) About Me  on 2010-10-08 09:04:59 (Show Source):
You can put this solution on YOUR website!
Since both terms in the expression have an m in common factor the m out.
8%28%2812m%29%2F3%29-2%283%29=m%288%2812%2F3%29-2%283%29%29
Now simplify.
8%28%2812m%29%2F3%29-2%283%29=m%288%284%29-6%29
8%28%2812m%29%2F3%29-2%283%29=m%2832-6%29
8%28%2812m%29%2F3%29-2%283%29=m%2826%29
8%28%2812m%29%2F3%29-2%283%29=highlight%2826m%29


Inequalities/353487: 3x-1/x-7 is less than or equal to 4 inequality problem using infinity
1 solutions

Answer 252619 by Fombitz(13828) About Me  on 2010-10-08 09:01:53 (Show Source):
You can put this solution on YOUR website!
%283x-1%29%2F%28x-7%29%3C=4
%283x-1%29%2F%28x-7%29-4%3C=0
%283x-1%29%2F%28x-7%29-%284%28x-7%29%29%2F%28x-7%29%3C=0
%283x-1-4%28x-7%29%29%2F%28x-7%29%3C=0
%283x-1-4x%2B28%29%2F%28x-7%29%3C=0
%2827-x%29%2F%28x-7%29%3C=0
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.
.
Break up the number line into 3 regions using the critical points from the equation.
Region 1:(-infinity,7)
Region 2:(7,27)
Region 3:(27,infinity)
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.
For each region pick a test point (not an endpoint).
Test the inequality.
If the inequality is satisfied, the region is part of the solution region.
Region 1:x=0
%2827-x%29%2F%28x-7%29%3C=0
%2827%29%2F%28-7%29%3C=0
-27%2F7%3C=0
True, this region is part of the solution.
.
.
Region 2:x=10
%2827-10%29%2F%2810-7%29%3C=0
17%2F3%3C=0
False, this region is not part of the solution.
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.
Region 1:x=30
%2827-30%29%2F%2830-7%29%3C=0
-3%2F23%3C=0
True, this region is part of the solution.
.
.
Solution region: (-infinity,7) U (27,infinity)


Numeric_Fractions/353569: what is the decimal and percent of 13 over 12

1 solutions

Answer 252616 by Fombitz(13828) About Me  on 2010-10-08 08:51:16 (Show Source):
You can put this solution on YOUR website!
13%2F12=1.083333, with the 3 repeating.
108.3%


test/353555: Which equation goes through these points: (2,-3),(-4,6),and (0,0)
A. 4x+y^2/4=8
B. 3xy^2/16=6
C. 3x+2y=0
D. 4x+y=8
Please help me and thank you
1 solutions

Answer 252615 by Fombitz(13828) About Me  on 2010-10-08 08:49:23 (Show Source):
You can put this solution on YOUR website!

The three points lie on a straight line so only C and D are possible choices.
The line goes through the origin so D is eliminated since it leads to an inconsistency.
4%280%29%2B0=8
0=8
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.
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By elimination, it's C.


Average/353567: The mean of four numbers is 83. If three of the numbers 82, 75, and 85, what is the fourth number?
1 solutions

Answer 252612 by Fombitz(13828) About Me  on 2010-10-08 08:43:52 (Show Source):
You can put this solution on YOUR website!
%2882%2B75%2B85%2BX%29%2F4=84
242%2BX=336
Now solve for X.


Numbers_Word_Problems/353502: prove that the sum of a positive real number and its reciprocal is at least two.
1 solutions

Answer 252568 by Fombitz(13828) About Me  on 2010-10-08 00:02:05 (Show Source):
You can put this solution on YOUR website!
n%2B1%2Fn=M
n%5E2%2B1=Mn
n%5E2-Mn%2B1=0
In order for the quadratic equation to have a real solution, the discriminant must be greater than or equal to 0.
b%5E2-4ac=M%5E2-4%281%29%281%29=M%5E2-4%3E=0
M%5E2%3E=4
highlight%28M%3E=2%29


Trigonometry-basics/353499: Find all solutions of the following equation on the interval [0, 2pi)
-csc^2(x)+2=0 Thanks
1 solutions

Answer 252567 by Fombitz(13828) About Me  on 2010-10-07 23:57:11 (Show Source):


Travel_Word_Problems/353279: 2 trains 360 miles apart, their speeds differ by 20mph. What speed is each train traveling for them to meet in three hours. Need to know how to set this up thanks
1 solutions

Answer 252446 by Fombitz(13828) About Me  on 2010-10-07 16:36:21 (Show Source):
You can put this solution on YOUR website!
Rate*Time=Distance
.
.
.
R%5B1%5D%2At=D%5B1%5D
R%5B2%5D%2At=D%5B2%5D
You also know that,
t=3
R%5B2%5D=R%5B1%5D%2B20
.
.
D%5B1%5D%2BD%5B2%5D=360
Substitute for D%5B1%5D and D%5B2%5D with known value and only R%5B1%5D as a variable.
Then solve for R%5B1%5D and then go back and find R%5B2%5D.


Graphs/353178: graph the inequality on a plane 3x+4yless than or equal to 12
1 solutions

Answer 252444 by Fombitz(13828) About Me  on 2010-10-07 16:32:25 (Show Source):
You can put this solution on YOUR website!
Plot the line 3x%2B4y=12 using the intercepts, (4,0) and (0,3).
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.
.

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.
.
Choose a point not on the line.
(0,0) is a convenient choice.
Test the inequality.
3x%2B4y%3C=12
3%280%29%2B4%280%29%3C=12
0%3C=12
True, so shade the region containing (0,0).
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.
.
Solved by pluggable solver: Plot Any Inequality
Graphing function 3x%2B4y%3C=12:

graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+3x%2B4y%3C=12+%29




Polynomials-and-rational-expressions/353192: I'm trying to find a polynomial for the perimeter and area of a rectangle. n+6 is on the top and n is on the right side..
1 solutions

Answer 252441 by Fombitz(13828) About Me  on 2010-10-07 16:26:41 (Show Source):
You can put this solution on YOUR website!
The area of a rectangle is,
A=L%2AW
The perimeter of a rectangle is,
P=2L%2B2W
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.
.
You also know that,
L=n%2B6
W=n
Substitute,
highlight%28A=%28n%2B6%29n=n%5E2%2B6n%29
I'll leave you to finish the perimeter by subsituting just like I did in the area equation.
Substitute and simplify.


Linear-equations/353205: please help
use the method of addition or method of elimination to solve the system of linear equations.
5x+2y=70;15x+6y=20
the answer i got is 0=190
but i'm told the correct answer is 0=-190
will you please explain how you come up with the answer
thank you
1 solutions

Answer 252439 by Fombitz(13828) About Me  on 2010-10-07 16:24:39 (Show Source):
You can put this solution on YOUR website!
Those answers are identical.
0=190
Multiply both sides by (-1).
0=-190
Either way, this is an inconsistent system which means your two lines are parallel and never meet, hence no solution.


Exponents-negative-and-fractional/353252: what is -18 / (-6)=
1 solutions

Answer 252437 by Fombitz(13828) About Me  on 2010-10-07 16:22:31 (Show Source):


Exponential-and-logarithmic-functions/353208: Please solve:
6 to the power 18
------------------------------------------
6 to the 7th (6 to the 4th x 6 to the 4th
1 solutions

Answer 252436 by Fombitz(13828) About Me  on 2010-10-07 16:21:30 (Show Source):


Numbers_Word_Problems/353275: is 230 odd
1 solutions

Answer 252434 by Fombitz(13828) About Me  on 2010-10-07 16:20:09 (Show Source):
You can put this solution on YOUR website!
No, numbers ending in 0,2,4,6,8 are even;
numbers ending in 1,3,5,7,9 are odd.


Linear_Algebra/353239: y=1/3x+11 y=3x-9
1 solutions

Answer 252433 by Fombitz(13828) About Me  on 2010-10-07 16:19:19 (Show Source):
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1.y=%281%2F3%29x%2B11
2.y=3x-9
Since they both equal y, set them equal to each other and solve for x.
%281%2F3%29x%2B11=3x-9
x%2B33=9x-27
8x=60
highlight%28x=15%2F2%29
Then from eq. 2,
y=3%2815%2F2%29-9
y=45%2F2-18%2F2
highlight%28y=27%2F2%29


Circles/352975: AP = X+7 and CP = 2x-11 Find BP
1 solutions

Answer 252430 by Fombitz(13828) About Me  on 2010-10-07 16:15:08 (Show Source):
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Explain the relationship of A,B, C, and P or provide a diagram if you have one.


Mixture_Word_Problems/353272: how many liters of a 14% alcohol solution must be mixed with 20 L of a 50% solution to get a 30% solution?
1 solutions

Answer 252429 by Fombitz(13828) About Me  on 2010-10-07 16:14:22 (Show Source):
You can put this solution on YOUR website!
Let A+be the number of liters of 14% alcohol.
14A%2B50%2820%29=30%28A%2B20%29
14A%2B50%2820%29=30A%2B30%2820%29
16A=20%2820%29=400
highlight%28A=25%29 liters



Miscellaneous_Word_Problems/353196: A rock is tossed into the air at t = 0 seconds from a building 30 feet above the ground. Its height, in feet above the ground, as a function of time is given by .
1 solutions

Answer 252426 by Fombitz(13828) About Me  on 2010-10-07 16:11:26 (Show Source):
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By thrown into the air, I'm assuming you gave it a velocity in the opposite direction of gravity.
I'll call that velocity, v%5B0%5D.
At time, t=0, the rock is at 30 feet elevation.
The ground is at 0 feet.
.
.
.
y%28t%29=30%2Bv%5B0%5D%2At-%281%2F2%29gt%5E2


Linear-systems/353267: Write equation in slope-intercept form.
3x + 2y = 10
1 solutions

Answer 252422 by Fombitz(13828) About Me  on 2010-10-07 16:06:41 (Show Source):


Surface-area/353183: if an arc with length of 12 phi is 3/4 the circumference of a circle. what is the shortest distance between the end points of the arc?
1 solutions

Answer 252421 by Fombitz(13828) About Me  on 2010-10-07 16:05:34 (Show Source):
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The circumference of a circle is,
C=pi%2AD
pi%2AD=12%2Api
D=12
If we looked at the circle on a coordinate system, the one endpoint would be at (R,0) and the other would be at (0,R), where R is the radius of the circle.
The shortest distance between two points in Euclidean geometry is a straight line.
The two points and the origin also desribe an isoceles right triangle with equals length sides of R.
You can use the Pythaogorean theorem to find the hypotenuse.
R%5E2%2BR%5E2=H%5E2
H%5E2=2R%5E2
H=sqrt%282%29%2AR
H=sqrt%282%29%2A%28D%2F2%29
H=sqrt%282%29%2A6
highlight%28H=6%2Asqrt%282%29%29


Polynomials-and-rational-expressions/353245: -9x1/4 + x1/2 +20=0
solve equation after making appropriate substitution
1 solutions

Answer 252417 by Fombitz(13828) About Me  on 2010-10-07 15:44:19 (Show Source):
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-9%2Aroot%284%2Cx%29+%2B+sqrt%28x%29+%2B20=0
Let u=root%284%2Cx%29, u%5E2=sqrt%28x%29
u%5E2-9u%2B20=0
%28u-4%29%28u-5%29=0
Two solutions,
u-4=0
u=4
highlight%28x=4%5E4=256%29
.
.
.
u-5=0
u=5
highlight%28x=5%5E4=625%29


Trigonometry-basics/353254: an for a radar station is located at the origin of a coordinate system. for each of the points find the bearing of an airplane located at that point.(5,0)
1 solutions

Answer 252416 by Fombitz(13828) About Me  on 2010-10-07 15:37:46 (Show Source):
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I'm assuming East is 0 degrees and North is 90 degrees.
(5,0) is 5 miles (or whatever proper units) due East (0 degrees).