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Quadratic_Equations/357964: Hi guys,
Struggeling with the following partial fractions:
1/(x+1)(x^2-1)
1/x^3+2x
Any Help To Show Me Steps Of How To Complete The Equations Would Be Much Help,
Thank you
1 solutions

Answer 255530 by Fombitz(13828) on 2010-10-18 13:50:33 (Show Source):

You can put this solution on YOUR website!
1%2F%28%28x%2B1%29%28x%5E2-1%29%29=1%2F%28%28x%2B1%29%28x-1%29%28x%2B1%29%29

1%2F%28%28x%2B1%29%28x%5E2-1%29%29=1%2F%28%28x%2B1%29%5E2%28x-1%29%29

1%2F%28%28x%2B1%29%28x%5E2-1%29%29=A%2F%28x%2B1%29%2BB%2F%28x%2B1%29%5E2%2BC%2F%28x-1%29

Multiply by the denominator,
1=A%28x%2B1%29%28x-1%29%2BB%28x-1%29%2BC%28x%2B1%29%5E2

A%28x%5E2-1%29%2BB%28x-1%29%2BC%28x%5E2%2B2x%2B1%29=1

From eq. 1,
A=-C

From eq. 2,
B=-2C

Then substituting into eq. 3,
C%2B2C%2BC=1

Now back substitute and find A and B.
.
.
.
1%2F%28x%5E3%2B2x%29=1%2F%28x%28x%5E2%2B2%29%29

1%2F%28x%5E3%2B2x%29=A%2Fx%2B%28Bx%29%2F%28x%5E2%2B2%29

Multiply by the denominator,
1=A%28x%5E2%2B2%29%2BBx%5E2

From eq. 2,
highlight%28A=1%2F2%29

Then from eq. 1,
B=A

.
.
.

highlight_green%281%2F%28x%5E3%2B2x%29=1%2F%282x%29-%28x%29%2F%282%28x%5E2%2B2%29%29%29

Polynomials-and-rational-expressions/357927: (a + 3)(a - 2)
1 solutions

Answer 255527 by Fombitz(13828) on 2010-10-18 13:41:33 (Show Source):

You can put this solution on YOUR website!
Use the FOIL Method,
%28a%2B3%29%28a-2%29=a%5E2-2a%2B3a-6

%28a%2B3%29%28a-2%29=highlight%28a%5E2%2Ba-6%29

Angles/357935: The measure of ∠A is 8° more than three times the measure of ∠B. If A and B are supplementary angles, find the measure of ∠A.
1 solutions

Answer 255518 by Fombitz(13828) on 2010-10-18 13:21:12 (Show Source):

You can put this solution on YOUR website!
By definition,
A%2BB=180

.
.
.

Substitute,
8%2BB%2BB=180

degrees
Then
A=8%2B86

degrees

Angles/357945: How do i find the measure of a complement angle of 27 degrees?
1 solutions

Answer 255516 by Fombitz(13828) on 2010-10-18 13:19:38 (Show Source):

You can put this solution on YOUR website!
By definition,
A%2BC=90

degrees

Linear-equations/357944: Find the slope and the y-intercept of each line. y = -4 + 12 another problem is y = 5x and another problem is y = 1/2x + 6

1 solutions

Answer 255515 by Fombitz(13828) on 2010-10-18 13:18:01 (Show Source):

You can put this solution on YOUR website!
Each line is in slope-intercept form, y=mx%2Bb

, where

is the slope and

is the y-intercept.
Example: y=%281%2F2%29x%2B6

, the slope is m=1%2F2

, the y-intercept is b=6

Systems-of-equations/357947: Perform the indicated operations:
Simplify
(-3a^4b^8/6a^3b^12)^4
1 solutions

Answer 255514 by Fombitz(13828) on 2010-10-18 13:17:02 (Show Source):

You can put this solution on YOUR website!

%28%28-3a%5E4b%5E8%29%2F%286a%5E3b%5E12%29%29%5E4=%281%2F16%29a%5E%2816-12%29b%5E%2832-48%29

%28%28-3a%5E4b%5E8%29%2F%286a%5E3b%5E12%29%29%5E4=%281%2F16%29a%5E%284%29b%5E%28-16%29

Linear_Equations_And_Systems_Word_Problems/357948: Set up an equation in one variable and solve it.
Abner has 4 liters of a 40% solution of alcohol. How much pure alcohol must he add to have an 80% solution?
1 solutions

Answer 255513 by Fombitz(13828) on 2010-10-18 13:14:09 (Show Source):

You can put this solution on YOUR website!
Let A be the amount of 100% alcohol added.
Concentration equation:
100%28A%29%2B40%284%29=80%28A%2B4%29

liters.

Permutations/357967: How many 5 digit license plates can be formed allowing repetition of letters and numbers?
1 solutions

Answer 255511 by Fombitz(13828) on 2010-10-18 13:12:31 (Show Source):

You can put this solution on YOUR website!
If numbers and letters can be used in each place, then 36 possible values for each of the 5 positions.
N=36%5E5=60466176

plates

Polynomials-and-rational-expressions/357963: Multiply. (5-2x^7)^2
1 solutions

Answer 255509 by Fombitz(13828) on 2010-10-18 13:10:50 (Show Source):

You can put this solution on YOUR website!
Use the FOIL Method,
%285-2x%5E7%29%5E2=+%285-2x%5E7%29%285-2x%5E7%29

%285-2x%5E7%29%5E2=+25-5%282x%5E7%29-2x%5E7%285%29%2B4x%5E14

highlight%28%285-2x%5E7%29%5E2=4x%5E14-20x%5E7%2B25%29

Systems-of-equations/357966: : Perform the indicated operations:
Expand the expression: (2a – 3)3

1 solutions

Answer 255508 by Fombitz(13828) on 2010-10-18 13:08:01 (Show Source):

You can put this solution on YOUR website!
%282a+-+3%29%5E2=%282a-3%29%282a-3%29%282a-3%29

%282a+-+3%29%5E2=%282a-3%29%284a%5E2-6a-6a%2B9%29

%282a+-+3%29%5E2=%282a-3%29%284a%5E2-12a%2B9%29

%282a+-+3%29%5E2=%282a%29%284a%5E2-12a%2B9%29%2B%28-3%29%284a%5E2-12a%2B9%29

%282a+-+3%29%5E2=%288a%5E3-24a%5E2%2B18a%29%2B%28-12a%5E2%2B36a-27%29

%282a+-+3%29%5E2=highlight%288a%5E3-36a%5E2%2B54a-27%29

Sequences-and-series/357898: Hi,
having some problems with the following question any chance some one could step by step walk me though it please
Q. find a formula for the sum of
x^2+x^6+x^10+...+x^2+4n+...+x^42
What will be the sum of the series when x = 1?
Also finding this one tricky to:
Q. obtain the sum of the infinite geometric progression
2-2/3+2/9-2/27+...
Any help would be very helpful
Thanks :)
1 solutions

Answer 255483 by Fombitz(13828) on 2010-10-18 11:18:39 (Show Source):

You can put this solution on YOUR website!
T=sum%28x%5E%282%2B4i%29%2Ci=0%2CN%29

Find the number of terms.
2%2B4N=42

Since the terms start at 0 and not 1, then there are 11 terms altogether.
Eleven terms, each having a value of 1.
S=11%281%29

.
.
.

S=2%2B2%2Asum%28%28-1%2F3%29%5En%2Cn=1%2Cinfinity%29

S=2%2B2%2A%28-%28%281%2F3%29%2F%281%2B1%2F3%29%29%29

S=2%2B2%2A%28-%28%281%2F3%29%2F%284%2F3%29%29%29

Equations/357897: Divide
(30b^3 + 3b^2 + 36b +30) / (6b + 3)
1 solutions

Answer 255480 by Fombitz(13828) on 2010-10-18 11:09:05 (Show Source):

You can put this solution on YOUR website!
Use polynomial long division.
.
.
.


          5b^2 + (-2b) +   7
        __________________________
6b + 3 | 30b^3 +  3b^2 +  36b + 30
      - (30b^3 + 15b^2)
       ---------------
                -12b^2 +  36b
             - (-12b^2 + (-6b))
                --------------
                          42b + 30
                      -  (42b + 21)
                          --------
                                 9

.
.
.

Numbers_Word_Problems/357911: find the sum of 2+4+6+.......+120=
1 solutions

Answer 255477 by Fombitz(13828) on 2010-10-18 11:03:58 (Show Source):

You can put this solution on YOUR website!
a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad

.
.

.
.

.
.

Polynomials-and-rational-expressions/357907: Multiply. (9-2x)(2-8x)
1 solutions

Answer 255475 by Fombitz(13828) on 2010-10-18 11:00:17 (Show Source):

You can put this solution on YOUR website!
Use the FOIL Method,
%289-2x%29%282-8x%29=9%2A2%2B9%28-8x%29%2B%28-2x%29%282%29%2B%28-2x%29%28-8x%29

%289-2x%29%282-8x%29=18-72x-4x%2B16x%5E2

test/357909: Solve the following system by the addition method.
8x+3y=8
8x-5y=8
x=
y=
1 solutions

Answer 255474 by Fombitz(13828) on 2010-10-18 10:58:46 (Show Source):

You can put this solution on YOUR website!
1. 8x%2B3y=8

Multiply eq. 1 by -1 and add to eq. 2,
-8x-3y%2B8x-5y=-8%2B8

Then use either equation to solve for

Functions/357821: Write your answers in the form of a+bi, where a and b are real
numbers.
2-7i/1-6i + 3-5i/1-6i
1 solutions

Answer 255472 by Fombitz(13828) on 2010-10-18 10:57:03 (Show Source):

You can put this solution on YOUR website!
%282-7i%29%2F%281-6i%29+%2B+%283-5i%29%2F%281-6i%29=%282-7i%2B3-5i%29%2F%281-6i%29

%282-7i%29%2F%281-6i%29+%2B+%283-5i%29%2F%281-6i%29=%285-12i%29%2F%281-6i%29

%282-7i%29%2F%281-6i%29+%2B+%283-5i%29%2F%281-6i%29=%2877%2B18i%29%2F%2837%29

test/357903: Solve the following system by the addition method.
1/2x-1/3y= -4
-1/12x+1/10y= 2
x=
y=
1 solutions

Answer 255471 by Fombitz(13828) on 2010-10-18 10:52:08 (Show Source):

You can put this solution on YOUR website!
1. %281%2F2%29x-%281%2F3%29y=+-4

Multiply eq. 1 by ( 1%2F6

) and add to eq. 2 to eliminate

%281%2F12%29x-%281%2F18%29y-%281%2F12%29x%2B%281%2F10%29y=-%282%2F3%29%2B2

-%281%2F18%29y%2B%281%2F10%29y=-%282%2F3%29%2B6%2F3

-%2810%2F180%29y%2B%2818%2F180%29y=4%2F3

Then use either equation to solve for

Exponents/357905: Simplify by removing factors of 1

m^2-1 /(m+1)^2

the simplified form is ???
1 solutions

Answer 255470 by Fombitz(13828) on 2010-10-18 10:48:05 (Show Source):

You can put this solution on YOUR website!
%28m%5E2-1%29+%2F%28m%2B1%29%5E2=%28%28m%2B1%29%28m-1%29%29%2F%28m%2B1%29%5E2

%28m%5E2-1%29+%2F%28m%2B1%29%5E2=highlight%28%28m-1%29%2F%28m%2B1%29%29

Linear_Equations_And_Systems_Word_Problems/357822: Determine whether there is a maximum or minimum value for the given
function, and find that value.
f(x) = x2 – 5x + 12
1 solutions

Answer 255469 by Fombitz(13828) on 2010-10-18 10:47:11 (Show Source):

You can put this solution on YOUR website!
Convert to vertex form, y=a%28x-h%29%5E2%2Bk

Since

, then the value at the vertex is a minimum.
y%5Bmin%5D=23%2F4

.
.
.

Quadratic_Equations/357902: Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard ax^2 + bx + c = 0

Solution 6, only solution.

The equation is ????? = 0
1 solutions

Answer 255468 by Fombitz(13828) on 2010-10-18 10:43:39 (Show Source):

You can put this solution on YOUR website!
%28x-6%29%5E2=0

Exponents/357899: Add, simplify if possible
2r/r^2-16 + r/r-4
1 solutions

Answer 255467 by Fombitz(13828) on 2010-10-18 10:42:41 (Show Source):

You can put this solution on YOUR website!
Use the common denominator, r%5E2-16=%28r%2B4%29%28r-4%29

%282r%29%2F%28r%5E2-16%29%2Br%2F%28r-4%29=%282r%2Br%5E2%2B4r%29%2F%28%28r-4%29%28r%2B4%29%29

%282r%29%2F%28r%5E2-16%29%2Br%2F%28r-4%29=%28r%5E2%2B6r%29%2F%28%28r-4%29%28r%2B4%29%29

Finance/357892: Find all the complex solutions of:

x^4+3x^2-4=0
1 solutions

Answer 255466 by Fombitz(13828) on 2010-10-18 10:39:07 (Show Source):

You can put this solution on YOUR website!
x%5E4%2B3x%5E2-4=0

Use a substitution,
u=x%5E2

.
.
.

Probability-and-statistics/357893: You are given the following data. Number of Absences
Final
Grade

0
91

1
89

2
84

3
76

4
67

5
49

- Find the correlation coefficient for the data.
- Find the equation for the regression line for the data, and predict the final grade of a student who misses 3.5 days.
1 solutions

Answer 255464 by Fombitz(13828) on 2010-10-18 10:35:06 (Show Source):

You can put this solution on YOUR website!

.
.
.

highlight_green%28r%5E2=b1%2Ab2=0.909%29

.
.
.

Probability-and-statistics/357696: Find the probability of getting at least three defective items in a batch of ten items if the overall percentage of defects is 40%
1 solutions

Answer 255463 by Fombitz(13828) on 2010-10-18 10:26:18 (Show Source):

You can put this solution on YOUR website!
Find the probability for