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3 years ago

Please help!!! (link attached)

Mathematics

1 answer:

Softa [21]3 years ago

8 0

The slope is -5!

Explanation:
Start from the top point and you count down until you’re on the same line as the other dot. You should have counted down 5 and over 1. 5/1. The line is negative, therefore it’s -5!

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WILL MARK BRAINLIEST!!! 40 POINTS!! ACTUAL ANSWERS, PLZZZ

steposvetlana [31]

Answer:

Part A:

$\left(x + 7\right)^{5}=x^{5} + 35 x^{4} + 490 x^{3} + 3430 x^{2} + 12005 x + 16807$

Part B:

The closure property describes cases when mathematical operations are CLOSED. It means that if you apply certain mathematical operations in a polynomial it will still be a polynomial. Polynomials are closed for sum, subtraction, and multiplication.

It means:

$\text{Sum of polynomials } \Rightarrow \text{ It will always be a polynomial}$

$\text{Subtraction of polynomials } \Rightarrow \text{ It will always be a polynomial}$

$\text{Multiplication of polynomials } \Rightarrow \text{ It will always be a polynomial}$

But when it is about division:

$\text{Division of polynomials } \Rightarrow \text{ It will not always/sometimes be a polynomial}$

Example of subtraction of polynomials:

$(2x^2+2x+3) - (x^2+5x+2)$

$x^2-3x+1$

Step-by-step explanation:

First, it is very important to define what is a polynomial in standard form:

It is when the terms are ordered from the highest degree to the lowest degree.

Therefore I can give:

$x^5-5x^4+3x^3-3x^2+7x+20$

but,

$x^5+3x^3-3x^2+7x+20-5x^4$ is not in standard form.

For this question, I can simply give the answer: $x^5-5x^4+3x^3-3x^2+7x+20$ and it is correct.

But I will create a fifth-degree polynomial using this formula

$(a+b)^n=\sum_{k=0}^n \binom{n}{k} a^{n-k} b^k$

Also, note that

$\binom{n}{k}=\frac{n!}{(n-k)!k!}$

For $a=x \text{ and } b=7$

$\left(x + 7\right)^{5}=\sum_{k=0}^{5} \binom{5}{k} \left(x\right)^{5-k} \left(7\right)^k$

$\text{Solving for } k \text{ values: } 0, 1, 2, 3, 4 \text{ and } 5$

Sorry but I will not type every step for each value of $k$

The first one is enough.

For $k=0$

$\binom{5}{0} \left(x\right)^{5-0} \left(7\right)^{0}=\frac{5!}{(5-0)! 0!}\left(x\right)^{5} \left(7\right)^{0}=\frac{5!}{5!} \cdot x^5= x^{5}$

Doing that for $k$ values:

$\left(x + 7\right)^{5}=x^{5} + 35 x^{4} + 490 x^{3} + 3430 x^{2} + 12005 x + 16807$

8 0

3 years ago

How many loads of laundry can you wash if you work 3 shifts? express your answer numerically as an integer?

Likurg_2 [28]

Given that number of working shifts = 3

Let number of loads of laundry that you can wash in 1 shift = x

Then number of loads of laundry that you can wash in 3 shift = 3x

Numerical value of the number of loads of laundry that you can wash in 1 shift is not given so it's not possible to convert "3x" into integer.

But whatever be the value say 5 loads of laundry is washed in 1 shift then the answer is given by 3x= 3*5= 15

3 0

3 years ago

There are 8 red, 4 green and 12 yellow balls in a box. If you choose one ball from the box, what is the probability that it will

rusak2 [61]

Answer:

50% percent chance the ball will be yellow

Step-by-step explanation:

Find the amount of all the balls-24 and the amount of yellow balls-12

Then divide the number of yellow balls by the number of total balls.

12÷24=0.5

0.5=50%

8 0

3 years ago

Simplify: (p-q)^2 + 2pq

lorasvet [3.4K]

Answer:

(p-q)^2+2pq

= p^2-2pq+q^2+2pq

= p^2+q^2

Step-by-step explanation:

Please mark me the brainliest :-)

7 0

3 years ago

Write out the series given by:

omeli [17]

When $n=1$ , we have

$\dfrac n{2n+1}=\dfrac1{2\cdot1+1}=\dfrac13$

When $n=2$ , we have

$\dfrac n{2n+1}=\dfrac2{2\cdot2+1}=\dfrac25$

and so on. The series is then

$\displaystyle\sum_{n=1}^6\frac n{2n+1}=\frac13+\frac25+\frac37+\frac49+\frac5{11}+\frac6{13}$

3 0

3 years ago