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patriot [66]
3 years ago
13

Find a polynomial function with leading coefficient 1 that has the given zeros, multiplicities, and degree. Zero: 2, multiplicit

y: 3 Zero: 0, multiplicity: 2 Degree: 5
Mathematics
1 answer:
valkas [14]3 years ago
7 0

Given:

Zero: 2, multiplicity: 3

Zero: 0, multiplicity: 2

Degree: 5

Leading coefficient = 1

To find:

The polynomial function.

Solution:

The general form of a polynomial is

P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}

where, a is a constant, c_1,c_2,...,c_n are zeroes with multiplicity m_1,m_2,...,m_n.

Using the given information and the general form of a polynomial, we get

P(x)=a(x-2)^{3}(x-0)^{2}

P(x)=ax^2(x^3-6x^2+12x-8)

P(x)=a(x^5-6x^4+12x^3-8x^2)

Leading coefficient is 1, so the value of a is also 1.

P(x)=1(x^5-6x^4+12x^3-8x^2)

P(x)=x^5-6x^4+12x^3-8x^2

Therefore, the required polynomial is P(x)=x^5-6x^4+12x^3-8x^2.

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Ludmilka [50]
The question wants us to find 3 times the volume of the pool.
This is because we are told that the pool must be filled 3 times during the summer and asked how many cubic feet of water is required to fill the pool all summer.

Step 1: Find the volume of the pool.
Volume is calculated by multiplying length by width by height.
Pool length = 5 ft.
Pool width = 4 ft.
Pool height = 2 ft.
Pool volume = 5 • 4 • 2
5 • 4 • 2 = 40
The volume of the pool is 40 cubic feet.

Step 2: Find 3 times the volume of the pool.
Volume = 40 ft.^3
3 times volume = 3 • 40 ft.^3
3 • 40 ft.^3 = 120 ft.^3
3 times the volume of the pool is 120 cubic feet.

Answer:
The pool requires 120 cubic feet of water in order to be filled enough over the course of the summer.

Hope this helps!
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3 years ago
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Which of the following data could be graphed using a dot plot? Select all that apply.​
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Step-by-step explanation:

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A student has gotten the following grades on his tests. What is the minimum grade he must get on the last test in order to have
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3 years ago
The length of a rectangle is 5 inches less than twice its width. The perimeter of the rectangle is 26 inches. What is the width
Yakvenalex [24]

Answer:

w= 6

Step-by-step explanation:

I just started by making an educated guess using the values already given. Then I inserted that into the problem to see if it worked.

L= 2w - 5

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L = 2(6) - 5

L = 12-5

L = 7

Then, multiply L by 2 to account for both side lengths of the rectangle.

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Subtract that value from the total perimeter to find what the width must equal.

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I know this was kind of long, but I hope it helps! :)

3 0
3 years ago
Please help will give brainliest
Vladimir [108]

\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}

\frac{4}{5}  +  \frac{3}{15} -  \frac{2}{3}   \\

<u>Taking </u><u>LCM</u>

\frac{12 + 3 - 10}{15}  \\  \\ \longrightarrow \:  \cancel\frac{5}{15}  \\  \\ \longrightarrow \:  \frac{1}{3}

hope helpful ~

8 0
2 years ago
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