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Gennadij [26K]
3 years ago
8

Can you help me plz

Mathematics
1 answer:
Zielflug [23.3K]3 years ago
8 0

Answer:

area is always length times width times height

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y = 2/5x - 5

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y = 2/5x - 5

(If you go to desmos.com you can graph any equation. It really helps. I'm doing similar things in class, I use it all the time.)

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Write a polynomial function with the given zeros. multiply the terms (write in standard form).
ryzh [129]

1) \ f(x)=x^3-3x-2 \\ \\ 2) \ g(x)=x^3-x^2-6x

<h2>Explanation:</h2>

A \ \mathbf{polynomial \ function} \ of \ x \ with \ degree \ n \ is \ given \ by:\\ \\ f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\ldots +a_{2}x^{2}+a_{1}x+a_{0} \\ \\ where \ n \ is \ a \ nonnegative \ integer \ and \ a_{n}, a_{n-1}, \ldots a_{2}, a_{1}, a_{0} \\ with \ a_{n}\neq 0

In this exercise, we have two cases and both will be polynomial functions with degree 3 because we have three real roots in each case. So:

<h3>First.</h3>

The roots are:

x= -1, -1, 2

So we can write this polynomial functions as the product of linear factors:

f(x)=(x-(-1))(x-(-1))(x-2) \\ \\ f(x)=(x+1)^2(x-2)

Since we have to write it in standard form, let's expand:

f(x)=(x+1)^2(x-2) \\ \\ \\ By \ property: \\ \\ (a+b)^2=a^2+2ab+b^2 \\ \\ \\ f(x)=(x^2+2x+1)(x-2) \\ \\ f(x)=x^3+2x^2+x-2x^2-4x-2 \\ \\ \\ Combine \ like \ terms: \\ \\ x^3+(2x^2-2x^2)+(x-4x)-2 \\ \\ \\ \boxed{f(x)=x^3-3x-2}

<h3>Second.</h3>

The roots are:

x= -2, 0, 3

Writing the polynomial function as the product of linear factors:

g(x)=(x-(-2))(x-0)(x-3) \\ \\ g(x)=(x+2)x(x-3) \\ \\ g(x)=x(x+2)(x-3) \\ \\ \\ Distributive \property: \\ \\ g(x)=x(x^2-3x+2x-6) \\ \\ g(x)=x(x^2-x-6) \\ \\ \\ Distributive \ property \ again: \\ \\ \boxed{g(x)=x^3-x^2-6x}

<h2>Learn more:</h2>

Degree of polynomial functions: brainly.com/question/5451252

#LearnWithBrainly

7 0
3 years ago
Read 2 more answers
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