Answer: A) Justification 1
<u>Step-by-step explanation:</u>
The student did not match the angles correctly.
∠ABC = 90° and ∠BCD = 60° so they cannot state that the angles are congruent. The other statement on that line is wrong also, but is irrelevant since there is already an error in that line.
Answer:
Eight pieces
Step-by-step explanation:
Create a number line running from 0 to 4/6.
Label the divisions as 1/6, 2/6, 3/6, and 4/6.
Divide each section in half to get small pieces of length 1/12.
Starting at zero, move to 4/6 on the number line and count the number of pieces as you go.
You count eight pieces, so Dario has eight pieces of rope.
Using the Factor Theorem, the polynomials are given as follows:
1. 
2. 
3. P(x) = -0.1(x³ - 4x² - 3x + 18)
<h3>What is the Factor Theorem?</h3>
The Factor Theorem states that a polynomial function with roots
is given by:

In which a is the leading coefficient.
Item a:
The parameters are:

Hence the equation is:
P(x) = (x - 1)²x²(x + 4)
P(x) = (x² - 2x + 1)(x + 4)x²
P(x) = (x³ + 2x² - 7x + 1)x²

Item b:
The roots are:

Hence:
P(x) = a(x - 4)²x(x + 4)
P(x) = a(x² - 16)x(x - 4)
P(x) = a(x³ - 16x)(x - 4)

It passes through the point x = 5, P(x) = 36, hence:
45a = 36.
a = 4/5
a = 0.8
Hence:

Item 3:
The roots are:

Hence:
P(x) = a(x - 3)²(x + 2)
P(x) = a(x² - 6x + 9)(x + 2)
P(x) = a(x³ - 4x² - 3x + 18)
For the y-intercept, x = 0, y = -1.8, hence:
18a = -1.8 -> a = -0.1
Thus the function is:
P(x) = -0.1(x³ - 4x² - 3x + 18)
More can be learned about the Factor Theorem at brainly.com/question/24380382
#SPJ1
9514 1404 393
Answer:
486√3 ft² ≈ 841.8 ft²
Step-by-step explanation:
The area of a regular hexagon with side length s is ...
A = (3√3)/2s²
For the side length of 18 ft, the area is ...
A = (3√3)/2(18 ft)² = 486√3 ft² ≈ 841.8 ft²