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marysya [2.9K]
3 years ago
10

What us the average rate of change

Mathematics
1 answer:
Pepsi [2]3 years ago
6 0

the rate of change is -2 for every set shown in the chart on the right

 so 6 to 7 would be -11 -2 = -13

7 to 8 would be -13-2 = -15

8 to 9 = -15-2 = -17

 B is the answer

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Given that the expression 2x^3 + mx^2 + nx + c leaves the same remainder when divided by x -2 or by x+1 I prove that m+n =-6
Alla [95]

Given:

The expression is:

2x^3+mx^2+nx+c

It leaves the same remainder when divided by x -2 or by x+1.

To prove:

m+n=-6

Solution:

Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).

Let the given polynomial is:

P(x)=2x^3+mx^2+nx+c

It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that

P(2)=P(-1)              ...(i)

Substituting x=-1 in the given polynomial.

P(-1)=2(-1)^3+m(-1)^2+n(-1)+c

P(-1)=-2+m-n+c

Substituting x=2 in the given polynomial.

P(2)=2(2)^3+m(2)^2+n(2)+c

P(2)=2(8)+m(4)+2n+c

P(2)=16+4m+2n+c

Now, substitute the values of P(2) and P(-1) in (i), we get

16+4m+2n+c=-2+m-n+c

16+4m+2n+c+2-m+n-c=0

18+3m+3n=0

3m+3n=-18

Divide both sides by 3.

\dfrac{3m+3n}{3}=\dfrac{-18}{3}

m+n=-6

Hence proved.

7 0
2 years ago
Please help ill mark brainliest
ella [17]

<u>Answer</u>:

Equation  :    y = 6

<u>Explanation</u>:

It is a straight line, cuts y axis and does not meet x axis.

Equation of the line is y = 6

3 0
2 years ago
Y=-2x+2 Y=-2x-2 state the solution
Arisa [49]

Answer:

Step-by-step explanation:

Y=-2x+2.....(1)

Y=-2x-2.....(2)

Subtracting (1) from (2)

Y - Y = -2x - (-2x) -2 - 2

O = -2x + 2x - 4

O = 0 - 4

Hence it as no solution the the two variables tend to zero

4 0
3 years ago
Read 2 more answers
Determine whether the equation is always sometimes or never true 2(5x+4)=10x+6
Usimov [2.4K]
This equation is NEVER true. Let's solve the equations algebraically by applying the Distributive Property of Multiplication and transposing the terms across the equality sign. The solution is as follows:

<span>2(5x+4)=10x+6
10x + 8 = 10x + 6
10x - 10x = 6 - 8
0 = -2

Therefore, it is not true.</span>
3 0
2 years ago
Mrs O’maley ran 2 2/3 miles today.she plans to run the same distance every day this week. How many total miles wil she run this
natulia [17]
Okay, so we multiply..

And we know that a week = 7 days..

So..

2 * 2/3 * 7 = ???

We change the 2 into 2/1
THEN we multiply..

2/1 * 2/3 = 4/3

Then we change the 7 into 1/7.. ( Which is still a whole )

Then multiply again..

4/3 * 1/7 = 4/21

You can correct me if I'm wrong...
I hope this helps you!
7 0
3 years ago
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