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1 year ago

A paragraph proof

Mathematics

1 answer:

Butoxors [25]1 year ago

4 0

A paragraph proof D. contains a set of sentences explaining the steps needed to reach a conclusion.

<h3>What is a paragraph proof?</h3>

It should be noted that a paragraph proof simply means a way of presenting a mathematical proof.

In this case, it contains a set of sentences explaining the steps needed to reach a conclusion.

In conclusion, the correct option is D.

Learn more about proof on:

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What is the cube root of 64i

Rus_ich [418]

Answer:

Step-by-step explanation:

3 0

3 years ago

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

3 years ago

Find the value of x in the triangle shown below.<br> x =<br> 98°<br> 27°

Levart [38]

Answer: 55

Step-by-step explanation: There is one simple theorem we need to know in order to solve for this.

Triangle Angle-Sum Property: All three angles interior angles of a triangle add up to 180°.

Thus, we could label the points A, B, and C, and set up an algebraic expression.

Let A = 27, B = 98, and C = x.

A + B + C = 180°.

Substituting A, B, and C we get:

27 + 98 + x = 180°.

Adding, we get:

125 + x = 180°

Subtracting 125 by 180, we get:

x = 55°

Thus, the angle X is 55°.

We could have simply solved this by just doing 180 - 98 - 27 = 55 in the first place, but I wanted to show you how I got such results.

5 0

2 years ago

A=1/2bh for b<img src="https://tex.z-dn.net/?f=a%3D1%2F2bh%20for%20b" id="TexFormula1" title="a=1/2bh for b" alt="a=1/2bh for b"

valkas [14]

Times both sides by 2
$2A=bh$
divide both sides b h
$\frac{2A}{h}=b$
$b=\frac{2A}{h}$

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3 years ago

Arrange the pennies into a complete rectangular array and then into a different rectangular array that has a reminder of 1

Inessa [10]

I'm guessing the answer would be 141 pennies in a rectangular array I think I'm right but i might be wrong

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3 years ago