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3 years ago

Which statement shows how two polynomials 3x + 6 and 5x2 − 4x demonstrate the closure property when multiplied?

Mathematics

2 answers:

Ira Lisetskai [31]3 years ago

8 0

Answer:

15x^3+18x^2-24x

Step-by-step explanation:

it is a polynomial

Novosadov [1.4K]3 years ago

5 0

Answer:

$15x^3+18x^2-24x$ is a polynomial.

B is correct

Step-by-step explanation:

Given: $3x+6$ and $5x^2-4x$

There are two polynomial with each has two term.

Using closure property multiplied both polynomial.

If multiply two polynomial then result must be a polynomial with higher degree of previous two.

Product of $3x+6$ and $5x^2-4x$

$\Rightarrow (3x+6)(5x^2-4x)$

$\Rightarrow 3x\cdot 5x^2-3x\cdot 4x+6\cdot 5x^2-4x\cdot 6$

$\Rightarrow 15x^3-12x^2+30x^2-24x$

Combine the like terms

$\Rightarrow 15x^3+18x^2-24x$

This is a polynomial with degree 3

Hence, The product of $3x+6$ and $5x^2-4x$ is a polynomial.

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4 years ago

The frequency f of vibration of a violin string is inversely proportional to its length L. The constant of proportionality k is

Natali5045456 [20]

Answer:

(A) $f=\frac{k}{L}$

(B) Frequency becomes half.

Step-by-step explanation:

We have been given that the frequency f of vibration of a violin string is inversely proportional to its length L. The constant of proportionality k is positive and depends on the tension and density of the string.

(A) We know that two inversely proportional quantities are in form $y=\frac{k}{x}$ , where y is inversely proportional to x and k is constant of proportionality.

Upon substituting our given values, we will get:

$f=\frac{k}{L}$

Therefore, our required equation would be $f=\frac{k}{L}$ .

(B) For part, we have been given that length is twice, so our new frequency will be $f_n$ and new length $L_n$ is $2L$ .

Upon substituting $2L$ in our equation as:

$f_n=\frac{k}{L_n}$

$f_n=\frac{k}{2L}$

$f_n=\frac{1}{2}\cdot \frac{k}{L}$

$f_n=\frac{1}{2}\cdot f$

Upon comparing $f_n$ with $f$ , we can see that $f_n$ is half the value of $f$ .

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3 years ago

Ronnie is scheduling a chess tournament in which each player plays every other player once. He created a table and found that ea

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2) And what about the recursive rule for the original sequence, the approrpiate one is an = an-1 + n - 1, so the answer is lying in the second option from the scale.
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I am sure it's clear now!

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4 years ago

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