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3 years ago

8

Over the course of 4 days the price of stock at Acme corporation fell $28. What was the average change in stock price per day?

1 answer:

densk [106]3 years ago

6 0

28 / 4 = 7
So every day, an average $7 fell.

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Part A: Create a third-degree polynomial in standard form. How do you know it is in standard form? (5 points)

Svetlanka [38]

Answer:

(See explanation for further details)

Step-by-step explanation:

a) Let consider the polynomial $p(x) = 5\cdot x^{3} +2\cdot x^{2} - 6 \cdot x +17$ . The polynomial is in standards when has the form $p(x) = \Sigma \limit_{i=0}^{n} \,a_{i}\cdot x^{i}$ , where $n$ is the order of the polynomial. The example has the following information:

$n = 3$ , $a_{0} = 17$ , $a_{1} = -6$ , $a_{2} = 2$ , $a_{3} = 5$ .

b) The closure property means that polynomials must be closed with respect to addition and multiplication, which is demonstrated hereafter:

Closure with respect to addition:

Let consider polynomials $p_{1}$ and $p_{2}$ such that:

$p_{1} = \Sigma \limits_{i=0}^{m} \,a_{i}\cdot x^{i}$ and $p_{2} = \Sigma \limits_{i=0}^{n}\,b_{i}\cdot x^{i}$ , where $m \geq n$

$p_{1}+p_{2} = \Sigma \limits_{i=0}^{n}\,(a_{i}+b_{i})\cdot x^{i} + \Sigma_{i=n+1}^{m}\,a_{i} \cdot x^{i}$

Hence, polynomials are closed with respect to addition.

Closure with respect to multiplication:

Let be $p_{1}$ a polynomial such that:

$p_{1} = \Sigma \limits_{i=0}^{m} \,a_{i}\cdot x^{i}$

And $\alpha$ an scalar. If the polynomial is multiplied by the scalar number, then:

$\alpha \cdot p_{1} = \alpha \cdot \Sigma \limits_{i = 0}^{m}\,a_{i}\cdot x^{i}$

Lastly, the following expression is constructed by distributive property:

$\alpha \cdot p_{1} = \Sigma \limits_{i=0}^{m}\,(\alpha\cdot a_{i})\cdot x^{i}$

Hence, polynomials are closed with respect to multiplication.

4 0

3 years ago

F(x-3)=f(x)-f(3)<br>Prove:<br>f(0)=0

Sergio039 [100]

Step-by-step explanation:

Let x=3.

So, f(3-3)=f(3)-f(3), and thus f(0)=0.

8 0

2 years ago

Which numbers are factors of 4? Select all that apply.<br><br> 1<br> 4<br> 2<br> 3

brilliants [131]

Answer:

1,2,4

Step-by-step explanation:

Factors are the numbers that we can multiply together to make 4

1*4 = 4

2*2 = 4

The factors are 1,2 and 4

4 0

3 years ago

Read 2 more answers

Please Help me solve this (Who ever answers correctly will get brainlest)

o-na [289]

Answer:

1.52

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5 0

2 years ago

Read 2 more answers

What is the product of (r + 4) and (r - 3)

dlinn [17]

r + 4(r - 3)

<em><u>We'll use the distributive property to simplify this.</u></em>

r^2 - 3r + 4r - 12

<u><em>Combine like terms</em></u>

r^2 + r - 12 is the simplified form.

6 0

3 years ago