Your friends asks you to bring a couple of bags of chips to his party. There are several brands of chips, each a different size and price.

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].

Answer:

50%

Step-by-step explanation:

To solve this you would do 1350/2700 which is 50%

Hope this answer helps you :)

Have a great day

Mark brainliest

We need to solve this question using Algebraic expressions. The answer for the given question is x-6.

A mathematical expression with variables and/or numbers is called an algebraic expression. It can be simplified even if it cannot be solved since it lacks an equals sign (=). Algebraic equations, which have algebraic expressions divided by an equals sign, can be solved. Recognize the distinction between an algebraic equation and an algebraic expression. A mathematical expression called an algebraic expression can have variables or integers in it. be able to combine similar phrases. Adding up (or removing) the terms with the same degree is all that is required to combine related terms. All x2 terms can be mixed with other x2 terms, and all x3 terms can be coupled with x3 terms, according to this.

x students are trying in a chorus concert.

Only 6 students will be chosen.

        so the answer for the given question=x-6

We need to solve this question using Algebraic expressions. The answer for the given question is x-6.

To  refer more about Algebraic expressions, visit:

https://brainly.com/question/4344214

#SPJ1

Answer:

x = - [tex]\frac{3}{2}[/tex], x = 3

Step-by-step explanation:

To find the zeros let p(x) = 0 , that is

2x² - 3x - 9 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 9 = - 18 and sum = - 3

The factors are - 6 and + 3

Use these factors to split the x- term

2x² - 6x + 3x - 9 = 0 ( factor the first/second and third/fourth terms)

2x(x - 3) + 3(x - 3) = 0 ← factor out (x - 3) from each term

(x - 3)(2x + 3) = 0

Equate each factor to zero and solve for x

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex]

x - 3 = 0 ⇒ x = 3

Answer:

b

Step-by-step explanation:

8×19= 152  

1 : 4.5  

152×4.5=684  

Answer:

Step-bLet X be the number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM.

In mathematical terms,  

X

∼

P

o

i

s

s

o

n

(

2

)

.

The PMF of the random variable X is given as,

P

(

X

=

x

)

=

e

−

2

×

2

x

x

!

f

o

r

x

=

0

,

1

,

2

,

.

.

.

.

.

=

0

E

l

s

e

w

h

e

r

e

The probability of getting no more than 3 calls between eight and nine in the morning is obtained by the following way,

P

(

X

≤

3

)

=

P

(

X

=

0

)

+

P

(

X

=

1

)

+

P

(

X

=

2

)

+

P

(

X

=

3

)

=

e

−

2

×

2

0

0

!

+

e

−

2

×

2

1

1

!

+

e

−

2

×

2

2

2

!

+

e

−

2

×

2

3

3

!

=

0

.13534

+

0

.27067

+

0

.27067

+

0

.18045

=

0

.85712

Hence the probability of getting no more than 3 calls between eight and nine in the morning is 0.85712.y-step explanation:

Step-by-step explanation:

the (A) formula is preferable to use and is the correct one

Answer:

35,691

Step-by-step explanation:

First step, look at the diagram and you see that you have a sphere and a cone.

The total surface area of a sphere is

[tex]A = 4\pi r^{2} \\A = 4\pi 39^{2} \\A = 19,113[/tex]

Since you only have half of a sphere, the surface area is 9,556.5

The surface area of the cone is

[tex]A = pi r(r+\sqrt{h^{2}+r^{2} }) A = \pi39(39+\sqrt{42^{2} +39^{2} } \\A=11,800[/tex]

You don't need the bottom of the cone however as it is connected to the half sphere.

So substract the area of a circle with a radius of 39 from the product of 19,113 + 11,800

The area of the circle is 4,778

Answer:

manz I think u would need like a ruler or something

Answer:

79°

Step-by-step explanation:

Remember, the sum of all the angles in a triangle is 180

So 180-RST-RTS=180-53-48=79

Answer:

130°

Step-by-step explanation:

Angle 3 and 7 are the same so angle 7 is 50°

180° is the angle of a straight line so we take 50 away from 180 giving us 130°.

Hope this helps! :)

Answer:

√85

Step-by-step explanation:

A (-3 , 4)    B (4 , -2)

AB² = (4 - -3)² + (-2 -4)² = 49 + 36 = 85

AB = √85

Answer:

hello

3x = 1/81

x = 1/ 81*3

x = 1/243

Step-by-step explanation:

Answer:

x=(1/81)/3

x=1/243

Step-by-step explanation:

Answer:

The input for the method is a continuous function f, an interval [a, b], and the function values f(a) and f(b). The function values are of opposite sign (there is at least one zero crossing within the interval). Each iteration performs these steps: Calculate c, the midpoint of the interval, c = a + b2.

Step-by-step explanation:

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

Answer:

60 bacteria

Step-by-step explanation:

c on edge 2022

Answer:

I hope the above attachment helps you mate

Have a great day

[tex]#Liliflim[/tex]

Answer:

Solution given;

a⁴-23a²b²+b⁴

making in the form of a²+2ab+b²

a⁴+2a²b²+b⁴-2a²b²-23a²b²

(a²+b²)²-(5ab)²

factoring by using formula

x²-y²=(x+y)(x-y)

(a²+5ab+b²)(a²-5ab+b²)

Answer:

C

Step-by-step explanation:

f(-2) = 4(-2) + 5

f(-2) = -8 + 5

f(-2) = -3

Answer:

-3

Step-by-step explanation:

f(x) = 4x + 5

Let x = -2

f(-2) = 4(-2) + 5

        =-8+5

           -3

Answer:

3/4

Step-by-step explanation:

2 problems consist 8 choices of answers.

the events for the correct answer are 2

and the events for incorrect answer are 6

so, the probability that she answered neither of the problems correctly = 6/8 = 3/4

hb=10in

b Base

7

in

A Area

35

in²

Using the formula

A=hbb

2

Solving forhb

hb=2A

b=2·35

7=10in

Answer:

the arc length is

[tex]2\pi.14. \frac{45}{360} = \frac{7\pi}{2} [/tex]

=> B

Answer:

D answer

Step-by-step explanation:

x=- 1/ 2 answer is d.

Answer:

Step-by-step explanation:

m = - 2

b = 4

x - intercept = 2

Answer:

Step-by-step explanation:

If we draw radii from the center of this 18-gon to each vertex, we end up with 18 triangles that are all congruent to each other. If we divide 360 by 18 we get the measure of the vertex angle of each of these 18 triangles. 360/18 = 20. So we take one of these triangles and pull it out and use it as a representative triangle from which we use trig to find its height and its base length.

The formula for the area for a regular polygon is

[tex]A=\frac{1}{2}ap[/tex] where a is the apothem (the height of our triangle) and p is the perimeter (found from the base of our triangle).

If we split this triangle we extracted right down the center vertically, we get 2 right triangles. Pull one of those out and this is the triangle we work with. The vertex angle is split in half and it now measures 10. The one base angle is the right angle and, by the Triangle Angle-Sum Theorem, the other base angle is 80. To find the height (or the apothem) of this right triangle that has a hypotenuse of 1 (the radius of the polygon is the hypotenuse of the right triangle), we use the sin or cos ratio. I used cos:

[tex]cos10=\frac{a}{1}[/tex] so

a = .9848

To find the base of this right triangle, I used the sin ratio:

[tex]sin10=\frac{p}{1}[/tex] so

p = .1736. But this is only half the length of one of the sides of the polygon, so multiply it by 2 to get the length of the whole side.

.1736 * 2 = .3473

Now, in order to find the perimeter, we multiply that one side by 18 to get

p = 6.2514

Now we're ready to find the area:

[tex]A=\frac{1}{2}(.9848)(6.2514)[/tex] so

A = 3.078 square feet

Answer:

KQ = 11.5 units

Step-by-step explanation:

In triangle ABC,

K is the point of intersection of medians AP and BQ.

Therefore, point K will be the centroid of the triangle.

Property of the centroid of a triangle,

" Centroid of a triangle divides the median in the ratio of 2 : 1"

Ratio of BK and KQ = 2 : 1

[tex]\frac{BK}{KQ}=\frac{2}{1}[/tex]

[tex]\frac{23}{KQ}= \frac{2}{1}[/tex]

[tex]KQ = \frac{23}{2}[/tex]

KQ = 11.5

Therefore, length of segment KQ = 11.5 units

Answer:

0.25 (or [tex]\frac{1}{4}[/tex])

Step-by-step explanation:

As the coin is fair, there is an equal chance the coin lands on heads or tails, therefore:

Probability of heads = 0.5 (or [tex]\frac{1}{2}[/tex])

Probability of tails = 0.5 (or [tex]\frac{1}{2}[/tex])

For Bob to win, the coin must land on heads twice, To work this out, we multiply the two events together.

Probability of 2 heads = 0.5 (probability of landing heads up) x 0.5 (probability of landing heads up) = 0.25 (or [tex]\frac{1}{4}[/tex])

Answer:

Something that's in your budget.

Answer:

Start at zero, then go to the left two times, then go down eight more. The new location would be negative ten.

Step-by-step explanation: