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andrey2020 [161]

2 years ago

14

Which of the following below is a function?

1 answer:

ohaa [14]2 years ago

6 0

Answer:

i don't know sorry

Step-by-step explanation:

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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

How do i graph -7x-2y=-21???

ExtremeBDS [4]

Answer:

-7/2 is the slope. -10.5 is your starting point on the y-axis. You go from -10.5, up 7 and over to the left 2 times because it's negative.

Step-by-step explanation:

-7x-2y=-21

-2y=7x-21

y=-7/2x-21/2

y=-7/2x-10.5

Hope this helps!

7 0

3 years ago

Read 2 more answers

Good Stuff is giving away free pens to each of the first 200 people who come in the store today. In the first hour, they gave aw

AnnyKZ [126]

Answer:

50 pens

Step-by-step explanation:

x= 25 percent of 200

25/100 times X/200

Cross multiply them and you get

100x=5000

X=5000/100

X=50

25 percent of 200 is 50.

Which means they have away 50 pens

7 0

3 years ago

Read 2 more answers

Find the perimeter or circumference and area

Romashka [77]

Answer:

Step-by-step explanation:

The diameter is just the radius times two, so divide the diameter by two and you will have the radius of the circle.

4 0

3 years ago

Luis has three than dimes in his pocket, for a total of 1.80. which equation could be used to determine the number of dimes

Oksi-84 [34.3K]

X= 1.80/10 . x is the number of dimes. 1.80 is your total and 10 represents the worth of the dime

4 0

3 years ago