3/5x-5+x-4=-1 A. –5 B. 5 C. 7 D.

(x +y)^5 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

2 years ago

Convert 15/50 into a fraction

Lunna [17]

It already is a fraction though. I assume you mean to simplify it. You can simplify fraction by taking out the greatest common factor(that they share) in the denominator and numerator. In this case the denominator and numerator share the factor 5. So you if you divide the numerator and denominator by 5 you get 3/10 or the simplest form of the fraction.
The answer is $\frac{3}{10}$

8 0

3 years ago

Helpppppppppppppppppppppppppppppppppppppppppppp

ahrayia [7]

Answer:

I think it should be $24x^{2}$

Step-by-step explanation:

When the question said area of the cube, I think it was supposed to be surface area, which would $6a^{2}$ where a is the length of one edge. Given that the length of one edge is 2x, we would plug in 2x to the equation to get $6*(2x)^{2}$ which would become $24x^{2}$ .

8 0

2 years ago

A class of 32 students earned

Yuliya22 [10]

Answer:

5/16 Got a C

Step-by-step explanation:

A = 1/4 x 32

B = (32 - A)/2

D = 2

A = 8

B = (32 - 8)/2

B = 24/2

B = 12

D = 2

8 + 12 + 2 = 22

22/32 did not get a C

32/32 - 22/32 = 10/32

10/32 - > 5/16

3 0

2 years ago

Britney is solving a quadratic equation. Her first

Liula [17]

Britney used commutative property of addition and distributive property of multiplication over addition to get to step

The answer is II and IV ⇒ answer 4

Step-by-step explanation:

The quadratic equation is:

3x² - 8 - 10x = 3(2x + 3)

Britney's step is:

3x² - 10 x - 8 = 6x + 9

Lets explain the meaning of:

1. Commutative property of addition is: you can add a and b or b and a

both give the same answer

2. Distributive property of multiplication over addition is: when the

number a is multiplied by the sum of two numbers (b + c), the

first number a can be distributed to both b and c and multiplied

by each of them separately, then adding the two products ab and

ac together for the same result as multiplying the first number a by

the sum (b + c) ⇒ a(b + c) = ab + ac

3. Addition property of equality is: the property that states if you

add the same number to both sides of an equation, the sides

remain equal

4. Multiplication property of equality is: The property that states if

you multiply both sides of an equation by the same number, the

sides remain equal

Now let us explain Britney's step

∵ She change the places of the terms - 10x and - 8

- She arranges the terms of the left hand side from greatest power

of x to the numerical term

∴ She used the commutative property of addition

∵ She multiplied 3 by 2x and multiplied 3 by 3

- She multiplied the number out side the bracket by each of the

two terms in the bracket

∴ She used the distributive property of multiplication over addition

Britney used commutative property of addition and distributive property of multiplication over addition to get to step

The answer is number 4) II and IV

Learn more:

You can learn more about quadratic equation in brainly.com/question/8196933

#Learn withBrainly

8 0

3 years ago

Read 2 more answers

3/5x-5+x-4=-1 A. –5 B. 5 C. 7 D. –7