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2 years ago

One root of f(x)=x^3-4x^2-20x+48 is x = 6. What are all the factors of the function? Use the Remainder Theorem.

Mathematics

1 answer:

luda_lava [24]2 years ago

7 0

Answer:

(x - 6)(x + 4)(x - 2)

Step-by-step explanation:

since x = 6 is a root then (x - 6) is a factor

x³ - 4x² - 20x + 48 ÷ (x - 6)

= (x - 6)(x² + 2x - 8)

= (x - 6)(x + 4)(x - 2) ← factors of f(x)

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2/x2-9 - 3x/ x2-5x+6 please show work

Luda [366]

Answer: -3x^3 - 7x^2 - x + 39

Step-by-step explanation:

2/(x^2 -9) - 3x/(x^2-5x+6)

get those denominators factored out

2/(x-3)(x+3) - 3x/(x-3)(x-2)

Multiply both by both denominators

2(x-3)(x-2) - 3x(x-3)(x+3)

Multiply it out

(2x^2 - 10x + 12) - (3x^3 + 9x^2 -9x - 27)

Simplify and it becomes

-3x^3 -7x^2 -x + 39

5 0

2 years ago

Stephen makes wooden shelves for his room he starts with a board that is 20 feet long.Stephen wants to make the shelves 3/4 foot

jek_recluse [69]

The number of shelves stephen can make is approximately 27

<h3><u>Solution:</u></h3>

Given that Stephen makes wooden shelves for his room

Stephen wants to make the shelves 3/4 foot long

He starts with a board that is 20 feet long

To find: number of shelves he can make

So the number of shelves stephen can make can make is found out by dividing 20 feet long board by 3/4 foot long

$\text {number of shelves }=\frac{\text { total length of board stephen has }}{\text { length of each board }}$

$\text {number of shelves }=\frac{20}{3 / 4}=\frac{20}{0.75}=26.6$

So the number of shelves stephen can make is approximately 27

3 0

2 years ago

Jenny owns a salon. She had 150 customers at the end of the third quarter, 151 customers at the beginning of the third quarter,

Ira Lisetskai [31]

There is a 96% customer retention rate for the third quarter.

Given

Jenny owns a salon.

She had 150 customers at the end of the third quarter, 151 customers at the beginning of the third quarter, and five new customers in the third quarter.

<h3>Customer retention rate</h3>

It determines the percentage of customers that the company has retained over a given period.

The customer retention rate is determined by;

$\rm Customer \ retention \ rate=\dfrac{Given \ period -New \ customers}{Initial \ number}\times 100$

Substitute all the values in the formula;

$\rm Customer \ retention \ rate=\dfrac{Given \ period -New \ customers}{Initial \ number}\times 100\\\\\rm Customer \ retention \ rate=\dfrac{150-5}{151}\times 100\\\\ Customer \ retention \ rate=\dfrac{145}{151}\times 100\\\\ Customer \ retention \ rate=0.96 \times 100\\\\ Customer \ retention \ rate=96$

Hence, there is a 96% customer retention rate for the third quarter.

To know more about customer retention rate click the link given below.

brainly.com/question/25668470

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1 year ago

Look at the image of the two hangers. Based on the image, what is one thing that must be true? What is one thing that could be t

Musya8 [376]

Answer:

One thing that must be true is that the objects will cause some leaning because their masses are unequal, judging from the volume that the objects can hold. One thing that could be true is that the triangle could be heavier than the square, leading to a leaning toward the left. The second pic cannot be true, for there are too much mass concentrated on one side to maintain equilibrium.

7 0

2 years ago

Please help down below

Alex

Answer:

1 7/10 is the answer

Step-by-step explanation:

let me know if not

3 0

2 years ago

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