Which of the following describes the roots of the polynomial function f (x) = (x + 2) squared (x minus 4) (x + 1) cubed?–2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3
–2 with multiplicity 3, 4 with multiplicity 2, and –1 with multiplicity 4
2 with multiplicity 2, –4 with multiplicity 1, and 1 with multiplicity 3
2 with multiplicity 3, –4 with multiplicity 2, and 1 with multiplicity 4

Answers

Answer 1

Answer:

The roots and their respective multiplicity are –2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3 thus option (A) is correct.

What are the roots of an equation?

The roots of an equation are the solution of that equation, since an equation consists of hidden values of the variable so to determine them by different processes and then the resultant is called roots.

For example root of x -4 = 0 is x = 4 so 4 will be the only root of this linear equation.

As per the given function,

f(x) = (x + 2)²(x - 4)(x + 1)³

The roots are the points at which the value of the function is zero.

f(x) = 0

(x + 2)²(x - 4)(x + 1)³ = 0

(x + 2)² = 0

x = -2 (with a multiplicity of 2)

(x - 4) = 0

x = 4 (with a multiplicity of 1)

(x + 1)³ = 0

x = -1 (with a multiplicity of 3)

Hence "The roots and their respective multiplicity are –2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3 thus option (A) is correct".

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Answer 2

Answer:

Answer:

Step-by-step explanation:

$f(x) = (x + 2)^2(x-4)(x + 1)^3$

x+2=0

x+2-2=0-2

x=-2.....(x+2) was squared...exponent of 2...multiplicity of 2

x-4=0

x-4+4=0+4

x=4....(x-4) has no visible exponent which means it is essentially to the power of 1...multiplicity of 1

x+1=0

x+1-1=0-1

x=-1....(x+1) was cubed...exponent was 3...multiplicity of 3

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Which of the following is the graph of f(x) = 3|x – 4| + 1?

Answers

The graph of the given linear function f(x) = 3|x – 4| + 1 is shown below.

How to find the function which was used to make graph?

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having an increasing output for inputs greater than that value of x.

If we know that the function crosses the x-axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

The graph of the given linear function f(x) = 3|x – 4| + 1 is shown below.

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Answer:

the graph to this equation is

Step-by-step explanation:

hope this helps :)

Two numbers, if the first one increases by 1, and the second one decreases by 1, then their product increases by 2020. If the first number decreases by 1, and the second one increases by 1, what value does the product decrease?

Answers

Answer:

The product decreases 2022.

Step-by-step explanation:

(x + 1)(y - 1) = xy + 2020

xy - x + y - 1 = xy + 2020

-x + y = 2021

(x - 1)(y + 1) = xy + x - y - 1

+ 2021 = -x + y

----------------------------------

(x - 1)(y + 1) + 2021 = xy - 1

(x - 1)(y + 1) = xy - 2022

The product decreases 2022.

Please help me with this

Answers

Answer:

9x^2 + 12x

Step-by-step explanation:

The area of the blue

3* 3x^2 = 9x^2

The area of the pink is

3* 4x = 12x

Add them together

9x^2 + 12x

The volume V of a growing spherical cell is V = 4 3 πr3, where the radius is measured in micrometers (1 µm = 10−6m). Find the average rate of change of V with respect to r when r changes from 6 to each of the following. (Round your answers to one decimal place.) (i) 6 to 9 µm
(ii) 5 to 6 µm
(iii) 5 to 5.1 µm

Answers

Final answer:

The average rate of volume change of a growing spherical cell for different changes in radius can be calculated using the formula for the volume of a sphere and the formula for average rate of change (ΔV/Δr).

Explanation:

To find the average rate of change of the volume V with respect to the radius r, you will need to subtract the initial volume from the final volume and then divide by the change in radius. This is represented by the formula ΔV/Δr, where Δ represents change in.

For r changing from 6 to 9 µm, ΔV = V(9) - V(6) = 4/3π(9^3) - 4/3π(6^3). Therefore, ΔV/Δr = (4/3π(9^3) - 4/3π(6^3)) / (9 - 6).
For r changing from 5 to 6 µm, ΔV = V(6) - V(5) = 4/3π(6^3) - 4/3π(5^3). Therefore, ΔV/Δr = (4/3π(6^3) - 4/3π(5^3)) / (6 - 5).
For r changing from 5 to 5.1 µm, ΔV = V(5.1) - V(5) = 4/3π(5.1^3) - 4/3π(5^3). Therefore, ΔV/Δr = (4/3π(5.1^3) - 4/3π(5^3)) / (5.1 - 5).

These calculations will give you the average rate of volume change for each of the radius changes indicated.

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Find the area of the shape