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3 years ago

Find the zeros of the polynomial function: f(x) = 9x^3 - 27x^2 - 4x + 12.

Mathematics

1 answer:

hichkok12 [17]3 years ago

3 0

Answer:

{-2/3, 2/3, 3}

Step-by-step explanation:

The equation can be factored by grouping.

f(x) = (9x^3 -27x^2) +(-4x +12)

f(x) = 9x^2(x -3) -4(x -3)

f(x) = (9x^2 -4)(x -3)

We recognize the first factor as the difference of squares, so know it can be further factored to give ...

f(x) = (3x -2)(3x +2)(x -3)

The zeros are the values of x that make these factors be zero:

3x -2 = 0 ⇒ x = 2/3

3x +2 = 0 ⇒ x = -2/3

x -3 = 0 ⇒ x = 3

The zeros of the polynomial are x = -2/3, 2/3, 3.

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Find the area of a regular octagon with a perimeter of 80 ft and an apothem of 12.07 feet

Finger [1]

Answer:

The area of a regular octagon with a perimeter of 80 ft and an apothem of 12.07 feet is 482.8 ft².

Step-by-step explanation:

An octagon is a polygon with eight sides. An octagon is regular (also called a regular octagon) is a polygon with all eight sides equal.

The apothem of a regular octagon is the shortest distance between the center and any of its sides, in other words, it is the distance that separates the center of the polygon from the central point of each side of the octagon.

The area is calculated using the following formula:

$Area=\frac{n*L*Ap}{2}$

Where:

n is the number of sides.
L is the length of one of the sides.
Ap is the value of the apothem.

Being n = 8 being an octagon and the perimeter P the sum of the sides of the octagon (P = 8 * L), the area of the regular octagon can be calculated by:

$Area=\frac{P*Ap}{2}$

In this case:

P=80 ft
Ap=12.07 ft

Replacing:

$Area=\frac{80ft*12.07ft}{2}$

Solving:

Area=482.8 ft²

The area of a regular octagon with a perimeter of 80 ft and an apothem of 12.07 feet is 482.8 ft².

3 0

3 years ago

A new battery is expected to have a storage capacity of 60 ampere-hour (A h). A sample is tested, resulting in a 2-side confiden

antoniya [11.8K]

Answer:

Option B) The battery storage capacity is significantly different than 60 Ah, at a confidence level of 95 %

Step-by-step explanation:

We are given the following in the question:

Mean storage capacity = 60 ampere-hour

95% confidence interval =

$63\leq \mu \leq 72$

Thus, the correct answer based on the confidence interval is

Option B) The battery storage capacity is significantly different than 60 Ah, at a confidence level of 95 %

Since it is a two sided test we test whether the mean storage capacity is 60 Ah or different than 60 Ah

Thus, the battery storage is different from 60 Ah because the mean storage capacity does not lie in the 95% confidence interval.

4 0

3 years ago

Need help!!! solve for p) n = (p-k) ------ j Sorry for the terrible fraction

almond37 [142]

Answer:

nj +k = p

Step-by-step explanation:

n = (p-k)/j

Multiply each side by j

nj = (p-k)/j *j

nj = p-k

Add k to each side

nj +k p-k+k

nj +k = p

8 0

2 years ago

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Someone help me please :)

igor_vitrenko [27]

Answer:

<h2>mark me as brilliant ~_~</h2>

Step-by-step explanation:

3 0

3 years ago

798/6 plsssssss help

siniylev [52]

Answer:

133

Step-by-step explanation:

If you divide 798 by 6 you would get 133

Plz mark brainliest

3 0

3 years ago

Read 2 more answers