Is 10 pounds greater or 10 kilograms

What is the factored form of the expression? 4x^2-81y^2

Tasya [4]

$4x^2-81y^2$

$(2x)^2-(9y)^2
$

$(2x+9y)(2x-9y)$

4 0

3 years ago

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(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

Jordan went shopping last weekend and bought a pair of shoes. The shoes were originally priced at $124.00, but are now on sale f

forsale [732]

Answer:

8.68

Step-by-step explanation:

just multiply 124.00 times 0.07 and that's it

6 0

2 years ago

4x-5+3m-2x ; x=5 and m=7

Viefleur [7K]

Answer:

7

Step-by-step explanation:

7 0

3 years ago

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If Lisa’s gross pay was $1204.89 and her net pay was $818.44, about what percent of her pay was deducted?

Amanda [17]

Answer:

About 32% of her pay was deducted ⇒ 2nd answer

Step-by-step explanation:

Lisa’s gross pay was $1204.89

Her net pay was $818.44

We need to find the percentage of the amount deducted from her pay

Lets calculate the deduction amount

The deduction amount is the difference between the gross pay and

the net pay

∵ The amount deducted = gross pay - net pay

∵ Gross pay = $1204.89

∵ Net pay = $818.44

∴ The amount deducted = 1204.89 - 818.44 = $386.45

Now lets find the percentage of the amount deducted

∵ Percent of deducted = [amount deducted/gross pay] × 100%

∵ The amount deducted = $386.45

∵ Gross pay = 1204.89

∴ Percent of deducted = $\frac{386.45}{1204.89}$ × 100%

∴ Percent of deducted = 32.07%

About 32% of her pay was deducted

8 0

3 years ago