Help needed to solve this ​

Help Needed To Solve This

Answers

Answer 1

Given:

The expression is:

[tex]\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^7+4a^3b^4}{b^8-a^8}[/tex]

To find:

The simplified form of the given expression

Solution:

Formula used:

[tex]x^2-y^2=(x-y)(x+y)[/tex]

We have,

[tex]\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^7+4a^3b^4}{b^8-a^8}[/tex]

It can be written as:

[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3(a^4+b^4)}{(b^4)^2-(a^4)^2}[/tex]

[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3(a^4+b^4)}{(b^4-a^4)(b^4+a^4)}[/tex]

[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3}{(b^2-a^2)(b^2+a^2)}[/tex]

[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]

Taking LCM, we get

[tex]=\dfrac{1(b-a)(b^2+a^2)+2a(b-a)(b+a)+4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]

[tex]=\dfrac{b^3+a^2b-ab^2-a^3+2a(b^2-a^2)+4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]

[tex]=\dfrac{b^3+a^2b-ab^2-a^3+2ab^2-2a^3+4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]

[tex]=\dfrac{b^3+a^2b+ab^2+a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]

Using the grouping method factories the numerator.

[tex]=\dfrac{b(b^2+a^2)+a(b^2+a^2)}{(b-a)(b+a)(b^2+a^2)}[/tex]

[tex]=\dfrac{(b+a)(b^2+a^2)}{(b-a)(b+a)(b^2+a^2)}[/tex]

Cancel out the common factors.

[tex]=\dfrac{1}{b-a}[/tex]

Therefore, the value of the given expression is [tex]\dfrac{1}{b-a}[/tex].


Related Questions

Please help test tomorrow everything you need is in the photo below

Answers

Answer:

yes

Step-by-step explanation:

write the set of natural numbers that is less than or equal to 6 in both the notations​

Answers

Answer:

Step-by-step explanation:

Builder :

X = { x ∈ N : x ≤ 6}

Roster :

X = { 1, 2 , 3 , 4 , 5 , 6}

evaluate the function for x = -8.
f(x) = -2x - 12

Answers

Answer:

4

Step-by-step explanation:

f(-8)=-2(-8)-12

f(-8)=16-12

=4

Yes the correct answer is 4

At a pet store, Rhonda paid $55 for 8 dog bowls and 6 bones. Kelly paid $32.50 for 2 dog bowls and 9 bones. Determine the cost of one dog bowl (x) and one bone (y). Write a system of linear equations that models this situation.

Answers

Answer:

8d + 6b = 55

2d + 9b = 32.50

Step-by-step explanation:

let 'd' = # dog bowls

let 'b' + # bones

Rhonda:  8d + 6b = 55

Kelly:  2d + 9b = 32.50

we can multiply Kelly's equation by -4 to eliminate the 'd' terms:

Kelly: -4(2d + 9b) = 32.5(-4)

-8d - 36b = -130

now add the above equation to Rhonda's equation:

  -8d - 36b = -130

+  8d + 6b = 55

-30b = -75

b = 2.50

now we can use either equation and substitute 2.5 for 'b' to find 'd'

2d + 9(2.5) = 32.5

2d + 22.5 = 32.5

2d = 10

d = 5

Find the interest rate if £6400 has a final value of £8334 in 3 years. Give your answer to 1 d.p​

Answers

Answer:

Step-by-step explanation:

6400(1+i)³=8334

(1+i)³=1.3021875

∛(1+i)³=∛(1.3021875)

1+i= 1.092

i= .092

I guess if you were to round to 1 decimal point it'd be .1

What is the median for this set of data?
28, 32, 15, 19, 24, 26, 22, 32, 30

Answers

Step-by-step explanation:

according order 15 , 19,22, 24,26,28,30,32,32. answer is 26

Answer:

Hello There!!

Step-by-step explanation:

26 is the median as you order the numbers smallest to largest.Therefore,it is 15,19,22, 24, 26,28,30,32,32 and the amount of numbers are odd so the median is the middle number.If it was even the two middle numbers would be added together and then divided by 2.

hope this helps,have a great day!!

~Pinky~

Write the following number in standard decimal form
seven and fifty-two thousandths

Please help

Answers

Answer:

seven and fifty-two thousandths as a decimal

Step-by-step explanation:

7.52

Your answer should be 7.052

The and represents the decimal point, meaning that 7 is in the ones places, and the decimals go in the following order:

tenths, hundredths, thousandths, and so on. Because the 52 was in the thousandths place, that’s where the 2 goes, and the 5 is in the hundredths place. I hope this helped you

*BRAINLIEST**

Would anyone be willing to give a quick sketch of what this should look like?

Answers

Answer:

There is your answer. Hope this helps

What is the length of b?

Answers

with a 45,45,90 right triangle, the hypotenuse is always the length of one of the other side times the square root of 2, so divide by that and you get 8

Please answer properly.

Answers

Answer:

Step-by-step explanation:

$15 is a constant value while $5 change depending by the hours.

We can write this expression to find the total cost:

5r + 15

part b

1) substitute r with 3

5 * 3 + 15

2) solve the expression

15 + 15 = $30

Please help? I really need it

Answers

Answer:

216 in²

Step-by-step explanation:

a = bh

a = 18 * 12

a = 216

216 in2 this is because you are finding the area meaning you multiple your two sides

what is



0.05
+0.82
——————-

Answers

Answer:

0.87

Step-by-step explanation:

Answer:

0.87

Step-by-step explanation:

0.05

+0.82

—0—.8—7———-

just add like regularly but i think you have to line up the decimals

What is the value of
4/3 divided by 2/5 ?

Answers

Answer: (10/3)

Explanation:

(4/3)/(2/5) = (10/3)
Multiply by reciprocal
And solve

Answer:

4/3 ÷ 2/5

= 4/3 × 5/2

= 4×5/3×2

= 20/6

= 10/3 = 3  1/3 or 3.3333

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

Answers

1/3 x 1/4 - 3/4
it should be -2/3

Enriques bathroom measures 6 ft. Long by 5 ft. Wide His shower is 3 feet square The title he wants to buy for the floor is sold in square feet. What is the area of the floor that he has to title

Answers

Answer:

Area of the floor is 30 square ft.

Step-by-step explanation:

Length of the floor, L = 6 ft

width of the floor, W = 5 ft  

The floor is in the shape of rectangle.

The area of the rectangle is

A = Length x width

So, the area of the floor is

A = L x W

A = 6 x 5

A = 30 ft^2

For consumers making purchases online, 60% have devices made by Apple, 85% own a smartphone, and 75% use Venmo. Also, out of the smartphone users, 80% use Venmo. Assume that having a device made by Apple and owning a smartphone are independent. A consumer who makes purchases online is selected at random, what is the probability they have an Apple device or own a smartphone (or both)? Enter your answer as a decimal to two places, and include the leading zero. For example, 0.12 would be a valid format.

Answers

Answer:

The probability that a customer selected at random has an Apple device or own a smartphone or both is 0.94

Step-by-step explanation:

The percentage of costumers that have a device made by Apple = 60%

The percentage of customers that own a smartphone = 85%

The percentage of customers that use Venmo = 80%

The percentage out of the smartphone users that use Venmo = 80%

The probability both independent events A and B occurring = P(A) × P(B)

The exclusive probability of A or B occurring P(A XOR B) = P(A) + P(B) - 2 × P(A ∩ B)

Therefore, the probability of A or B or both occurring is given as follows;

P(A or B or Both) = P(A) + P(B) - 2 × P(A ∩ B) + P(A) × P(B)

Where A represent the percentage of costumers that have a device made by Apple and let B represent the percentage of users that have a smartphone, we have;

P(A or B or Both) = 0.6 + 0.85 - 2×0.6×0.85 + 0.6 × 0.85 = 0.94

Therefore, the probability that a customer selected at random has an Apple device or own a smartphone (or both), P(A or B or Both) = 0.94

Triangle PQR is similar to triangle XYZ. The length of PQ is one-half the length of XY. THe length of RP is 2 cm. Which proportion can be used to find the length of ZX?

Answers

Answer:

[tex]ZX = 4cm[/tex]

Step-by-step explanation:

Given

[tex]\triangle PQR[/tex] similar to [tex]\triangle XYZ[/tex]

[tex]PQ = \frac{1}{2}XY[/tex]

[tex]RP = 2cm[/tex]

Required

Find ZX

[tex]\triangle PQR[/tex] similar to [tex]\triangle XYZ[/tex] implies that, the following sides are similar

[tex]PQ \to XY[/tex]

[tex]QR \to YZ[/tex]

[tex]RP \to ZX[/tex]

To find ZX, we make use of the following equivalent ratio

[tex]PQ : XY = RP : ZX[/tex]

Where

[tex]PQ = \frac{1}{2}XY[/tex]

[tex]RP = 2cm[/tex]

So, we have:

[tex]\frac{1}{2}XY : XY = 2cm : ZX[/tex]

Express as fraction

[tex]\frac{\frac{1}{2}XY }{ XY }= \frac{2cm }{ ZX}[/tex]

[tex]\frac{1}{2}= \frac{2cm }{ ZX}[/tex]

Make ZX the subject

[tex]ZX = 2 * 2cm[/tex]

[tex]ZX = 4cm[/tex]

Acri invested $500 for 3 years at the rate of 2.8% per year compound interest. Calculate the final amount he has after 3 years

Answers

Answer:

[tex]A=P (1 + \frac{r}n)} ^{nt}[/tex]

A = 500(1 + .028/1)^ (3*1)

$543.19

Step-by-step explanation:

Given that ABCD is a rhombus, what is the value of x?

Answers

Your answer is 30 i guess you understood
Keep learning : )

Answer:20.75

Step-by-step explanation:

Trust me gangsta

What is the sum of the fractions? Use the number line and equivalent fractions to help find the answer.
-12-1
-3
-11
2
2
-1
2
х
-1
DO
o
-13
من ال۔
ला

Answers

Answer:  -3/4  (choice C)

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

Explanation:

Think of a whole cake or pizza. Now slice it into 4 equal pieces. This represents 1 is the same as 4/4.

Adding on another quarter slice gets us 4/4+1/4 = 5/4

In other words, the mixed number 1 & 1/4 is the same as the improper fraction 5/4.

So 1 & 1/4 = 5/4

This then means -1 & 1/4 = -5/4 because we multiply both sides by -1.

Now we'll add on 1/2, which is the same as 2/4, like so

(-1 & 1/4) + 1/2

-(1 & 1/4) + 2/4

-(1 + 1/4) + 2/4

-1 - 1/4 + 2/4

-1 + (-1/4 + 2/4)

-1 + 1/4

-4/4 + 1/4

-3/4

which points us to choice C as our final answer

Notice how if we started at -5/4, and moved to the right 2 tickmarks, we arrive at -3/4. Each tickmark represents 1/4 of a unit, so two of them is 2/4 = 1/2.

Side note: -3/4 converts to the decimal -0.75

Find mAC.

Pls help me



Answers

Answer:

Measure of Arc AC is 30 degrees

Step-by-step explanation:

To find the value of the marked arc, we are going to use the arc-angle relationship

from the type of given diagram, we can figure out the relationship to use

Mathematically, we have this as;

Measure of Arc AC = 2 * angle ABC

So we have arc AC as 2 * 15

Arc AC = 30 degrees

NEED HELP ASAP PLS
10. Jimmy was a busboy and makes 7.15 per hour. Ashley is a server and makes 3.40 per hour plus about $105 in tips per week. how many hours would they have to work to make the same amount?​

Answers

Answer: 28 hours

Step-by-step explanation:

1. Write original equation: 7.15x=3.40x+105

2. Combine like terms to isolate x: 3.75x=105

3. Divide both sides by same amount to find x: x=28

They would have to work 28 hours to earn the same amount of money.

13 14 14 17 18 20 20 what's the mode?

Answers

Answer:

mode is 14,20

if you dont know mode is the frequency of the numbers

Step-by-step explanation:

Answer:

14 & 20

Step-by-step explanation:

the number that appears the most

the expression (x^2-1)^-2/3 is equivalent to

Answers

Answer:it’s x

Step-by-step explanation:

Sry if I’m wrong

does anyone know how to do this ?

Answers

Answer:

i^85 = i

A way you can solve this is divide 85 by4

The remainder is one right? that means i^85 is the same as i^1. remember, i^1 = i.

I think it B it’s like simplifying imaginary numbers

Type in the value of y.



If x = 7, then y =

Answers

Answer:  8

Explanation:

The rule says "whatever x is, add 1 to it to get y"

So for instance, if x = 3, then y = x+1 = 3+1 = 4

Now if x = 7, then y = x+1 = 7+1 = 8

Answer:

[tex]\huge\boxed{Answer\hookleftarrow}[/tex]

Given that,

[tex]1 + 1 = 2 \\ 2 + 1 = 3 \\ 3 + 1 = 4 \\ 4 + 1 = 5...[/tex]

So from this we can infer that, [tex]\large\bold{ x + 1 = y}[/tex]

Now,

[tex]x = 7 \\ y= \: ?[/tex]

Use the rule [tex]\large\bold{ x + 1 = y}[/tex]

[tex]x + 1 = y \\ 7 + 1 = y \\ 8 = y[/tex]

The value of y is 8.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

# ꧁❣ RainbowSalt2²2² ࿐

The graph of f(x) is the solid black graph below. Which function represents the
dotted graph?

Answers

Answer: The answer is y= f(x+1)+5

Step-by-step explanation: The reason is that when you are translating the graph, the information in the parenthesis (In this case: (x+1)) is always on the x axis moving either left or right. You just go one in the opposite direction of what the sign is, so since the sign in the parenthesis is "+" you would go left in the opposite direction. Then, for the upward translation, you would have to move 5 units upward and this is done by just adding five to the end of it.

Suppose your mother can clean your kitchen in 30 minutes. You can clean the kitchen in 45 minutes. How long will it take you and your mother to clean the kitchen working together? (write equation and show work to solve)

Answers

Answer:

it will take 18 min

Step-by-step explanation:

1/45+1/30=2/90+4/90=5/90=90 divided by 5 is 18

Select the number line model that matches the expression
|8 - 1|

Answers

Answer:

B

Step-by-step explanation:

Trust

PLEASE HELP ME PLEASE AS SOON AS YOU CAN

EXPLAINATION = BRAINLIEST

THANK YOU SO MUCH

Answers

Answer:

35.18576

Step-by-step explanation:

use eqation E

Answer:

If the angle is in radians...

Area of sector =½r²¢

Where ¢ is theta.

Since Our angle is degree

We use

Area of Sector = ¢/360 x πr²

¢=theta

radius = Diameter/2

radius = 16/2 = 8m

Area = 126/360 x π x 8²

= 112π/5

=70.37

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