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lubasha [3.4K]
3 years ago
5

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

Mathematics
1 answer:
Svetlanka [38]3 years ago
4 0

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.

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UkoKoshka [18]
C.

This is because the x vale is clearly after the 6 and the y value is right on 5 
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Jose unlocks his cellphone by placing his right thumb on a square of 1 centimeter by 1 centimeter at the center of the screen. U
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Answer:

Step-by-step explanation:

We can solve this question using proportion

Perimeter of the square/Time is takes to unlock

We are told in the question that:

The cellphone unlocks when the perimeter reaches 32 centimeters, taking a total of 2.5 seconds.

Hence, the perimeter of the square after 1.5 seconds is:.x = unknown

32/2.5 = x/1.5

Cross Multiply

2.5x = 32 × 1.5

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4 0
3 years ago
What is 42 divided into 84 + 8 - 676 ???
puteri [66]

Answer: -5


Step-by-step explanation:

84 +  8 -676

3 0
3 years ago
Can somebody please help m eits 9th grade math im so confused !
prisoha [69]

Answer:

Option 3: (5, 1)

Step-by-step explanation:

There are several ways of solving for systems of linear equations, either through graphing, substitution, or elimination.  

The graphing method is the easiest, as you only need to plot points on the graph using the y-intercepts and the slopes.  

I will be demonstrating the <u>graphing method</u>.  

Given the systems of linear equations:  

Equation 1:  y = x - 4

where the <u>slope</u>, <em>m</em> = 1, and <u>y-intercept </u>(0, -4).

Equation2: y = -x + 6

where the <u>slope</u>, <em>m </em>= -1, and <u>y-intercept</u> (0, 6).

The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b).

<h3>Graphing Instructions:</h3>

For Equation 1, plot the y-intercept, (0, -4) on the graph. Then use the <u>slope</u>, m = 1 (rise 1 unit, run 1 unit) to plot other points on the graph. Repeat this process until you have enough points to connect a line with.  

Repeat these same procedures for graphing Equation 2, start by plotting its y-intercept at (0, 6), and its slope, m = -1 (down 1 unit, run 1 unit).

<h3>Solution: </h3>

The intersection of both lines occurs at point, (5, 1), which is solution to the given systems of linear equations.  Therefore, the correct answer is the third option, (5, 1).

Attached is the screenshot of the graphed systems of linear equations, where it shows the point of intersection at (5, 1).  

5 0
3 years ago
Evaluate the expression for m=4 n=5 p=-2<br> mn^p
Serga [27]

Answer:

<h2>mn^p = 4×(5^-2)</h2><h2> =4×0.04</h2><h2> =0.16</h2>

7 0
3 years ago
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