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3 years ago

6

Triangle PQR is a right triangle. if PQ= 8 , what is PR?

1 answer:

Norma-Jean [14]3 years ago

5 0

It is 30-60-90 triangle, so:

$PR=\dfrac{PQ\cdot\sqrt{3}}{2}=\dfrac{8\cdot\sqrt{3}}{2}=\boxed{4\sqrt{3}}$

Answer B.

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11 family members are going on a trip together. They have cars that only fit 4 people how many cars will they need to take?

Shalnov [3]

They will need 3 cars, but one of the cars will be having 3 passengers instead of 4. :)

6 0

2 years ago

(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

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

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

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

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

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

$=5x^4y$

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

SOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!

NARA [144]

ANSWER

Step 3

EXPLANATION

The given polynomial expression is:

$2 {p}^{2} - 3p - 7 - (3 {p}^{2} + p - 5)$

Fatau correctly expanded the parenthesis in the first step.

$2 {p}^{2} - 3p - 7 - 3 {p}^{2} - p + 5$

Fatau also correctly grouped the like terms to obtain:

$(2- 3) {p}^{2} + (- 3 - 1)p + (- 7 + 5)$

Fatau committed a mistake at the third step.

Instead of obtaining,

$- {p}^{2} - 4p - 2$

He mistakenly got:

${p}^{2} - 2p +2$

3 0

3 years ago

Dilating a triangle changes the size of the triangle but does not change its shape. true or false?

____ [38]

<h3><u>Answer;</u></h3>

The correct answer<em> </em><em><u>is true</u></em>

<h3><u>Explanation;</u></h3>

<u>Dilation</u> is a type of transformation which stretches and reduces the size of the original figure.

A dilation has a center of dilation and a dilation scale factor. If the scale factor is less than one then the original size will shrink, and if the scale factor is greater than one then the figure will increase in size.

Dilation transformation does not alter the shape of a figure but alters the size by making it bigger or smaller.

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