Given that x = 7.3 m and θ = 52°, work out AB rounded to 3 SF.

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

Use properties to compare expression 5 x ( 6 x 3 )and ( 5 x 6) x 3

nadya68 [22]

5(6*3) = 5(18) = 90

(5*6)3 = (30)3 = 90

The answer is the same by the associative law.

6 0

2 years ago

Evaluate (x + y)0 for x = 4 and y = 3.

Ksju [112]

Sice you are multiply by zero the answer is 0 because any number time 0 is 0. 3+4 =7 then times 0

6 0

3 years ago

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What is x? And what are the steps to get x?

gregori [183]

Answer:

x is the variable

Step-by-step explanation:

do area = base times height

5 0

3 years ago

PLEASE HELP BEEN STUCK FOR HOURS WILL MARK THE BRAINLIEST HAVE TO ANSWER A,B, and C

zaharov [31]

Answer:

A. 1)5.5 2)4.5 3)5.75 4)6.25 B. 1.75 C. A correct B incorrect C incorrect D correct

Step-by-step explanation:

Mean is a fancy way of saying Average , when calculating average you add all the numbers and divide by how many numbers there are:

A

1.

8+6+3+5=22/4=5.5

2.

5+7+4+2=18/4=4.5

3.

8+7+5+3=23/4=5.75

4.

6+8+4+5=25/4=6.25

B

largest mean is 6.25, smallest mean is 4.5:

Subtract lowest mean from highest mean:

6.25-4.5=1.75

C

A)

this is correct because averaging your average gives an overall average,

B)

if a is correct b has to be incorrect

C)

if D is correct C must be incorrect

D)

The closer they are together, that means more likely to be accurate because they are almost the same

I hope this helps u!

pls pls PLS give a brainliest and a thx ;)

8 0

2 years ago

Read 2 more answers