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3 years ago

9

If a trend line has a slope of -3, what is true about the data? Select all that apply.

1 answer:

jeka57 [31]3 years ago

5 0

Answer: Choice B and choice D

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A negative slope indicates that the line moves downward as you move from left to right. As x increases, y decreases (and vice versa). There's this opposite relationship going on.

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Find the fourth-degree polynomial function with zeros 4, -4, 4i , and -4i . Write the function in factored form.

Iteru [2.4K]

Given:

A fourth-degree polynomial function has zeros 4, -4, 4i , and -4i .

To find:

The fourth-degree polynomial function in factored form.

Solution:

The factor for of nth degree polynomial is:

$P(x)=(x-a_1)(x-a_2)...(x-a_n)$

Where, $a_1,a_2,...,a_n$ are n zeros of the polynomial.

It is given that a fourth-degree polynomial function has zeros 4, -4, 4i , and -4i. So, the factor form of given polynomial is:

$P(x)=(x-4)(x-(-4))(x-4i)(x-(-4i))$

$P(x)=(x-4)(x+4)(x-4i)(x+4i)$

$P(x)=(x-4)(x+4)(x^2-(4i)^2)$ $[\because a^2-b^2=(a-b)(a+b)]$

On further simplification, we get

$P(x)=(x-4)(x+4)(x^2-4^2i^2)$

$P(x)=(x-4)(x+4)(x^2+16)$ $[\because i^2=-1]$

Therefore, the required fourth degree polynomial is $P(x)=(x-4)(x+4)(x^2+16)$ .

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2 years ago

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