-2/3 + 5/7 Write your answer in simplest form

(x +y)^5<br> Complete the polynomial operation

Vesna [10]

Answer:

Please check the explanation!

Step-by-step explanation:

Given the polynomial

$\left(x+y\right)^5$

$\mathrm{Apply\:binomial\:theorem}:\quad \left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i$

$a=x,\:\:b=y$

$=\sum _{i=0}^5\binom{5}{i}x^{\left(5-i\right)}y^i$

so expanding summation

$=\frac{5!}{0!\left(5-0\right)!}x^5y^0+\frac{5!}{1!\left(5-1\right)!}x^4y^1+\frac{5!}{2!\left(5-2\right)!}x^3y^2+\frac{5!}{3!\left(5-3\right)!}x^2y^3+\frac{5!}{4!\left(5-4\right)!}x^1y^4+\frac{5!}{5!\left(5-5\right)!}x^0y^5$

solving

$\frac{5!}{0!\left(5-0\right)!}x^5y^0$

$=1\cdot \frac{5!}{0!\left(5-0\right)!}x^5$

$=1\cdot \:1\cdot \:x^5$

$=x^5$

also solving

$=\frac{5!}{1!\left(5-1\right)!}x^4y$

$=\frac{5}{1!}x^4y$

$=\frac{5x^4y}{1}$

$=5x^4y$

similarly, the result of the remaining terms can be solved such as

$\frac{5!}{2!\left(5-2\right)!}x^3y^2=10x^3y^2$

$\frac{5!}{3!\left(5-3\right)!}x^2y^3=10x^2y^3$

$\frac{5!}{4!\left(5-4\right)!}x^1y^4=5xy^4$

$\frac{5!}{5!\left(5-5\right)!}x^0y^5=y^5$

so substituting all the solved results in the expression

$=\frac{5!}{0!\left(5-0\right)!}x^5y^0+\frac{5!}{1!\left(5-1\right)!}x^4y^1+\frac{5!}{2!\left(5-2\right)!}x^3y^2+\frac{5!}{3!\left(5-3\right)!}x^2y^3+\frac{5!}{4!\left(5-4\right)!}x^1y^4+\frac{5!}{5!\left(5-5\right)!}x^0y^5$

$=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5$

Therefore,

$\left(x\:+y\right)^5=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5$

6 0

3 years ago

Find KL<br><br> step by step

stich3 [128]

Answer:

7x-2 = 12x-22

-7x

-2=5x-22

+22

20=5x

÷5

x=4

KL is 7x-2, so substitute the value of x.

7 x 4 - 2 = 26

KL = 26

Hope this helps!

3 0

3 years ago

What is the probability of rolling a die and having it land on a factor of 30?

Daniel [21]

Answer:

So, since there is an equal chance to roll any number on a six sided die, that means the chance of rolling any one number is one out of 6 or 1/6. You can see that with a diagram. Now, rolling two different numbers in a specific order you can tell with a diagram is 1/36.

Step-by-step explanation:

8 0

3 years ago

which equation represents a line that is parallel to the line whose equation is 3x-2y=7; which equation represents a line parall

aleksley [76]

The equation of the line that is parallel to the line whose equation is 3x-2y=7 would be y = 3/2x + b, in which b can be any real number.

How are parallel straight lines related?

Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.

We have been given a parallel line with has equation

3x-2y=7

In order to solve this, the slope of the original line.

3x - 2y = 7

-2y = -3x + 7

y = 3/2x - 7/2

thus its slope is 3/2.

thus, the slope of the needed line is 3/2 too.

we know that any line that is parallel to that would have this slope.

So anything is written in the form:

y = 3/2x + b

The equation of the line that is parallel to the line whose equation is 3x-2y=7 would be y = 3/2x + b, in which b can be any real number.

Learn more about parallel lines here:

brainly.com/question/13857011

#SPJ4

3 0

1 year ago

To solve 4÷13, Matthew thinks about blocks that each weigh 13 pound and how many blocks he would need to put on a scale so that

Katarina [22]

3.25 if you round it it’ll be 3.3

4 0

2 years ago