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vitfil [10]
3 years ago
14

The side of a square measures (3x − 6) units. Part A: What is the expression that represents the area of the square? Show your w

ork to receive full credit. (4 points) Part B: What are the degree and classification of the expression obtained in Part A? (3 points) Part C: How does Part A demonstrate the closure property for polynomials? (3 points)
Mathematics
2 answers:
Nastasia [14]3 years ago
6 0
Given: The side of a square is (3x - 6) units.
Note that (a + b)² = a² + 2ab + b².

Part A
The area of the square is
A = (3x - 6)(3x - 6)
    = (3x)² + 2(3x)(-6) + (-6)²
    = 9x² - 36x + 36

Part B
The area is a 2nd-degree polynomial, or a quadratic function, or parabola.

Part C
A 2nd-degree polynomial is of the form
f(x) = ax² + bx¹ + cx⁰ = ax² + bx + c
where a,b,c are constants (coefficients of the polynomial).
The area obtained in Part A has the coefficients
a = 9, b = -36, c = 36.

The polynomial is closed because it is completely defined by multiply and addition operations.

Daniel [21]3 years ago
6 0

Answer:

Given: Side of the Square = ( 3x - 6 ) units

Part A).

Area of the Square = Side × Side = ( 3x - 6 )( 3x - 6 ) = ( 3x - 6 )²

                                = ( 3x )² + 6² - 2 × 3x × 6

                                = 9x² + 36 - 36x

Part B).

Degree of a polynomial is the height power of the polynomial.

Degree of the 9x² + 36 - 36x is 2.

Since Polynomial representing Area of the square has 3 terms and degree = 2.

So the Polynomial is a Trinomial polynomial and Quadratic polynomial.

Part C).

Closure Property of polynomial is always under multiplication means when two polynomials are multiplies then the resulting product is also a polynomial.

Here, Also two linear polynomial are multiplied and we get a quadratic polynomial.

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Answer:

Choice B: BD/DA = CE/EA

Step-by-step explanation:

Slope is rise over run. For the two slopes to be equal, the rise over run of the two triangles must be equal.

The rise over run for triangle ABD is BD/DA.

The rise over run of triangle ACE is CE/EA.

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Mr.lucido purchases a new video game system that is on sale for 35% off the regular retail price. if the retail price is $429, w
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Answer:

Regular price: $429

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Step-by-step explanation:

regular price=$429

0.35(429)=150.15

429-150.15=278.85

35% discount amount: $278.85

278.85(0.05)=13.94

278.85+13.94=292.79

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2 years ago
What is the quality of 4x+27x=5
Nadya [2.5K]

Answer:

<h3>X=5/31=0.16</h3>

Step-by-step explanation:

Isolate x on one side of the equation.

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31x=5

31x/31=5/31 (Divide by 31 from both sides.)

5/31=0.16

x=5/31=0.16

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