Resolve into partial fractions

Resolve Into Partial Fractions

Answers

Answer 1

Answer:

See below

Step-by-step explanation:

1)

[tex] \frac{11 + x}{(2 - x)(x - 3)} = \frac{A}{2 - x} + \frac{B}{x - 3} \\ \\ \therefore \: \frac{11 + x}{(2 - x)(x - 3)} = \frac{A(x - 3) +B(2 - x) }{(2 - x)(x - 3)} \\ \\ \therefore \: 11 + x = Ax - 3A + 2B - Bx \\ \\ \therefore \: 11 + x = - 3A + 2B + Ax - Bx\\ \\ \therefore \: 11 + x = - 3A + 2B + (A - B)x \\ \\ equating \: the \: like \: terms \: on \: both \: sides \\ A - B = 1 \\ \therefore \: A = B + 1.....(1) \\ \\ - 3A + 2B = 11....(2) \\ from \: eq \: (1) \: and \: (2) \\ - 3(B + 1) + + 2B = 11 \\ \\ - 3B - 3 + 2B = 11 \\ \\ - B = 11 + 3 \\ \\ B = - 14 \\ A = - 14 + 1 = - 13 \\ \\ \frac{11 + x}{(2 - x)(x - 3)} = \frac{ - 13}{2 - x} + \frac{ - 14}{x - 3} \\ \\ \frac{11 + x}{(2 - x)(x - 3)} = - \frac{ 13}{2 - x} - \frac{ 14}{x - 3}[/tex]

2)

[tex] \frac{12x + 11}{x^2 +x - 6}[/tex]

[tex] =\frac{12x + 11}{x^2 +3x-2x - 6}[/tex]

[tex] =\frac{12x + 11}{x(x +3) -2(x +3)}[/tex]

[tex] \therefore \frac{12x + 11}{x^2 +x - 6}=\frac{12x + 11}{(x +3) (x - 2)}[/tex]

[tex] \therefore \frac{12x + 11}{x^2 +x - 6}=\frac{A}{(x +3)}+\frac{B}{(x - 2)}[/tex]

[tex] \therefore \frac{12x + 11}{x^2 +x - 6}=\frac{A(x-2)+B(x+3)}{(x-2)(x+3)}[/tex]

[tex] \therefore 12x + 11 = A(x-2)+B(x+3)[/tex]

[tex] \therefore 12x + 11 = Ax-2A+Bx+3B[/tex]

[tex] \therefore 12x + 11 = Ax+Bx-2A+3B[/tex]

[tex] \therefore 12x + 11 = (A+B) x-2A+3B[/tex]

Equating like terms on both sides:

[tex] A + B = 12\implies A = 12-B... (1)[/tex]

[tex] - 2A + 3B = 11... (2)[/tex]

Solving equations (1) & (2), we find:

A = 5, B = 7

[tex] \therefore \frac{12x + 11}{x^2 +x - 6}=\frac{5}{(x +3)}+\frac{7}{(x - 2)}[/tex]


Related Questions

The list below shows the number of train tickets sold each
week during an eight-week period.
2945, 4572, 3560, 3359, 4089, 2841, 3283,
4266
What is the range of the data?

Answers

Answer: The range is 1731

Step-by-step explanation: lowest number 4572- 2841 highest

Find the measure of the missing angle.

Answer: a= ______

(NO FILES) IF YOU ANSWER YOU WILL BE MARKED BRAINLIEST :)

Answers

Answer:

a= 32

Step-by-step explanation:

Since "a" is a part of a supplementary angle (An angle that adds up to 180º)

What you would need to do is add 58º and 90º (90º because the right angle = 90)

so 58+90 = 148

Then you would subtract 148 from the total of the angle (Which is 180)

so 180 - 148 = 32, And that shows that a = 32

(P.S. THE BOTS THAT POST THE LINKS TO THE FILES ARE POSTING MALWARE AND VIRUSES, DO NOT DOWNLOAD ANYTHING FROM THEM THEY ARE VIRUSES. IF YOU HAVE DOWNLOADED ANYTHING, GET A RELIABLE ANTIVIRUS SOFTWARE AND SCAN YOUR COMPUTER)

For the first four days of a five day vacation, the mean temperature was 80 degrees. What must the temperature be on the fifth day in order for the mean temperature to be 82 degrees?

Answers

Answer:

The 5th day must be 90

Step-by-step explanation:

The first 4 days averaged out to 80

You can find their total just by multiplying by 4. That won't tell you the exact values, but it will tell you their total when you add the 4 of them together.

80*4 = 320

Now you need to add another day into the mix. Call it x

320 + x

Now there are 5 days, not 4, and the new total is 82.

(320 + x) / 5 = 82          Multiply both sides by 5

5*(320 + x) / 5 = 82 *5

320 + x = 410                 Subtract 320

-320        -320

x = 90

Which of the following rational functions is graphed below?

Answers

Answer:C
Explanation:just solving in a website by a graphing calculator and I find the answer specifically to “C”.

Can some one help me out my grades are bad

Answers

Answer:

Go to the bottom of that problem and click save for later

A rectangle has a length of
381
and a width of 33 inches. Find the area of the rectangle. (2 points)

Answers

Length times width equals area.
381*33=12,575

Answer: 12,573 sq inches

A rectangle is formed by placing two identical squares side by side. The area of the rectangle is 162 cm2

Answers

Answer:

a) The area of each square is 81 square centimeters.

b) The side length of the square is 9 centimeters.

c) The perimeter of the rectangle is 54 centimeters.

Step-by-step explanation:

Statement is incomplete. After some web research we conclude that the complete statement is the following:

A rectangle is formed by placing two identical squares side by side. The area of the rectangle is 162 square centimeters. Find:

a) The area of each square.

b) The side length of each square.

c) The perimeter of the rectangle.

a) The area of the each square is half the area of the rectangle. Hence, the area of each square is 81 square centimeters.

b) The area formula for squares ([tex]A[/tex]), in square centimeters, is:

[tex]A = l^{2}[/tex] (1)

Where [tex]l[/tex] is the side length of the square, in centimeters.

If we know that [tex]A = 81\,cm^{2}[/tex], then the side length of the square is:

[tex]l = \sqrt{A}[/tex]

[tex]l = \sqrt{81\,cm^{2}}[/tex]

[tex]l = 9\,cm[/tex]

The side length of the square is 9 centimeters.

c) The perimeter formula of the rectangle ([tex]p[/tex]), in centimeters, is presented below:

[tex]p = 6\cdot l[/tex]

[tex]p = 6\cdot (9\,cm)[/tex]

[tex]p = 54\,cm[/tex]

The perimeter of the rectangle is 54 centimeters.

find the value of x pls help

Answers

mwahahahahauauauhahauaha i love you hahaha

What is the best description of the relationship in the scatterplot below?
Chose 1 answer
A- positive linear association
B- negative linear association
C-Nonlinear association
D- no association

Answers

Answer:

a becuase it is just a so if you get that wroung dont blem me lol

Step-by-step explanation:

Answer:

A - Positive linear association

Step-by-step explanation:

You can see that the overall direction of the graph is going up, therefore, this graph has a postivie association.

I MEEED HELPPP PLEASEEEEEE HELPPPPP PLEASE SOMEONE IM BEGGING UUUUU

Answers

Answer:

x= 10°

Step-by-step explanation:

BWN = BRN (W=R)

56+ (5x-16) +90 =180 {triangle BNW} [angles in a triangle add up to 180] ( properties of a kite)

5x = 180 - (56 + 90 - 16)

5x = 180 - 130

5x = 50

x =50/5

x = 10°

Find the missing measure angle

Answers

Answer:

Step-by-step explanation:

x+90+90+78=360(sum of 4 angles is always 360 degree)

x+258=360

x=360-258

x=102

Answer:

[tex] {x}^{o} = {102}^{o} [/tex]

Step-by-step explanation:

Hint:

sum of angles = 360°

Simplify:

[tex] {x}^{o} + {78}^{o} + {90}^{o} + {90}^{o} = {360}^{o} \\ {x }^{o} + 258^{o} = {360}^{o} \\ {x}^{o} = {360}^{o} - {258}^{o} \\ {x}^{o} = {102}^{o} [/tex]

Hope it is helpful....

Find the value of that makes ADEFAXYZ.
18
24
E
5
8
6
D
F
X
Z
6x + 6
30

Answers

Answer:

x = 2/3

DF = 10

scale factor of ΔDEF to ΔXYX is 1:3

Step-by-step explanation:

DF corresponds to XZ and DE corresponds to XY so we can set up a proportion:

6x+6/30 = 8/24

simplify 8/24 to be 1/3

6x+6/30 = 1/3

cross-multiply:

3(6x+6) = 30

18x + 18 = 30

18x = 12

x = 12/18 or 2/3

If you don’t help me your a criminal

Answers

Answer:

take angle U as reference angle

using sine rule

sin U=opposite/hypotenuse

sinU=42/42

sin U=1

sin 90=1

therefore the value of U is 90 degree

Step-by-step explanation:

5) A qué % anual se prestó un capital de 1700 soles que en 1 año y 3 meses ha producido 255 soles de interés?

Answers

Answer:

12%

Step-by-step explanation:

Interés simple = Principal × Tasa × Tiempo

Tasa = Interés simple / Principal × Tiempo

Principal = 1700 soles

Tiempo = 1 año y 3 meses

12 meses = 1 año

3 meses = 3/12 = 1/4 = 0.25

Tiempo = 1.25 años

Tasa = 255 /1700 × 1.25

= 0.12

= 0.12 × 100

= 12%

What is the measure of ZP
609
x 80°
F
40°
H
100
80
90°
40°

Answers

Answer:

100 degrees

Step-by-step explanation:

angle x is next to 80. the sum of angles that form a straight line = 180 degrees. So, 180-80 =100 degrees

If a right triangle has side lengths that measure 4 and 9, what is the length of the hypotenuse to the nearest hundredth (2 decimal places)?

Answers

The length of the hypotenuse will be 9.85.

Question 5:Solve for a Side
Find the missing side. Round to the nearest tenth.

Answers

34

5 divided by 9 = ans

sin^-1(ans) = 33.7 which rounds to 34

Solve the following quadratic function
by utilizing the square root method.
y = 9x2 - 36
X =
= + [?]

Answers

Answer:

x=2 or -2

Step-by-step explanation:

You can refer to the photo I attached


simplify by using the law of indices:
y^a(b+c)×y^b(c-a)×y^c(a-b)​

Answers

Answer:

[tex]y^{2ac}[/tex]

Step-by-step explanation:

Using the law if indices

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

Thus to simplify the expression add the 3 exponents

a(b + c) + b(c - a) + c(a - b) ← distribute parenthesis

= ab + ac + bc - ab + ac - bc ← collect like terms

= 2ac

Then the expression simplifies to

[tex]y^{2ac}[/tex]

DEFG is an isosceles trapezoid with bases FE and
GD. DE = 5x -2, and FG = 4x + 2. Find FG.

Answers

Answer:

FG is 18 units

Step-by-step explanation:

if the trapezoid is isosceles then DE = GF so we can create this equation:

4x + 2 = 5x - 2

4x = 5x - 4

-x = -4

x = 4

FG = 4(4)+2 which is 18

Can someone please help mweeeeeee

Answers

Answer:

D

Step-by-step explanation:

180 degrees in a triangle

102+(x+6)+(x+15)=180

remove parenthesis and combine like terms

123+2x=180

subtract 123 from both sides

2x=57

divide

x=28.5

substitute x for its actual value

28.5+6

angle A= 34.5

28.5+15

angle B= 43.5

Can I get a answer for all of it?

Answers

Answer:

R'=(-3,6)

Q'=(-3,-3)

S'=(7,6)

T'=(7,-3)

Answer:

see explanation

Step-by-step explanation:

A translation of 7 units right means adding 7 to the x- coordinate. The y- coordinate remains unchanged, then

Q (- 10, - 3 ) → Q' (- 10 + 7, - 3 ) → Q' (- 3, - 3 )

R (- 10, 6 ) → R' (- 10 + 7, 6 ) → R' (- 3, 6 )

S (0, 6 ) → S' (0 + 7, 6 ) → S' (7, 6 )

T (0, - 3 ) → T' (0 + 7, - 3 ) → T' (7, - 3 )

Please help if you can

Answers

Answer:

9x-6=84(being vertically opposite angle )

9x=84+6

x=90/9

x=10

Step-by-step explanation:

note: vertically opposite angles are always equal.

Choose the best description of an irregular polygon
1. a polygon with equal sides.
2. a polygon with unequal sides and angles
3.a polygon with unequal sides
4.a polygon with unequal angles

Answers

Answer: A polygon that does not have all sides equal and all angles equal.

Step-by-step explanation:A polygon that does not have all sides equal and all angles equal. (A polygon is "regular" only when all angles are equal and all sides are equal, otherwise it is irregular.)

if u subtract 12 from a number and multiply the result by 12 you get 18. what is the number​

Answers

Answer:

27/2 is the value of the number.

Let the number be x.

According to the question,

12(x-12)=18

x-12=18/12

x-12=3/2

x=3/2+12

x=3/2+24/2

x=27/2

HOPE IT HELP :)

Answer:

13.5    27/2      13 (1/2)   all the same

Step-by-step explanation:

(x-12)x12  = 18

12x-144 = 18

12x = 162

x = 162/12 = 27/2  = 13(1/2) = 13.5

When a biological researcher arrived on Wombat Island, there were about 1000 wombats on the island. Their population grew quickly. Estimated Wombat Population Year 1 2 3 4 5 Wombats 1000 2000 4000 8000 16,000 The researcher decided that the population growth followed a geometric sequence. He wrote the explicit formula an = 1000(2)n – 1 to model the growth, and used this formula to predict the populations for years 6, 10, and 50.

Answers

Answer:

Yes

Step-by-step explanation: The explicit formula used: An = 1000(2)n - 1 is the correct formula. This is modeled as exponential growth with a common ratio of 2; which is correct based on the data given in the table.

The predicted population for year 50 is approximately [tex]1.1259[/tex] x [tex]10^18[/tex] wombats.

To predict the populations for years 6, 10, and 50 using the given explicit formula an = [tex]1000(2)^n[/tex] – 1, we can substitute the respective values of n and calculate the population.

For year 6 (n = 6):

a6 =  [tex]1000(2)^6[/tex] – 1

a6 = 1000(64) – 1

a6 = 64,000 – 1

a6 ≈ 63,999

The predicted population for year 6 is approximately 63,999 wombats.

For year 10 (n = 10):

a10 = [tex]1000(2)^ 10[/tex]

a10 = 1000(1,024) – 1

a10 = 1,024,000 – 1

a10 = 1,023,999

The predicted population for year 10 is 1,023,999 wombats.

For year 50 (n = 50):

a50 = [tex]1000(2)^50[/tex] – 1

a50 = 1000(1.1259 x 10¹⁵ ) – 1

a50 = 1.1259 x 10¹⁸ – 1

a50 ≈ 1.1259 x 10¹⁸

The predicted population for year 50 is approximately 1.1259 x 10^18 wombats.

To know more about geometric sequence. here

https://brainly.com/question/29632351

#SPJ2

HELLLLLLPPP URGENT HEEELLPPPP

Answers

Answer:

The answer is "0.1245", "1245 out of 10,000", and "12.45 out of 100"

Step-by-step explanation:

wrong - 0.001245 in percent is 1245%

wrong - 0.1245 out of 100 is 0.1245/100 which is 0.001245%

don't know - pretty close to one-eight means 1/8 which = 0.125, as a % = 12.5%

wrong - 1245 out of 1,000 is 1.245 and in percent = 0.01245%

wrong - 1245 out of 100,000 is 0.01245 and in percent = 1.245%

RIGHT - 0.1245 as percent is 12.45%

RIGHT - 1245 out of 10,000 is 0.1245 and in percent = 12.45%

wrong - 1245 as a percent is 124500%

RIGHT - 12.45 out of 100 is 12.45/100 which is 0.1245 and as a percent is 12.45%

(please give me brainliest :)

What is the value of the expression 1/3x - 3/4 when x = 1/4

Answers

Answer:

-2/3

Step-by-step explanation:


At the end of January, Garrett had $176 in his
savings account. By the end of February, he
had $217. To the nearest percent, what is the
percent change in the amount of money in
Garrett's savings account?

Answers

Answer:

bank account cant give me 5 bank name

Help pleaseee?? Yuhh

Answers

Answer : Copy the question into brainly search bar and get youre answer.

The last one because x/y (4x/1) flips to (1/4x)
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