Question

***********BRAINLIEST IF 2 PPL ANSWER*******Thank u!!!

Answer 1

Answer:

Step-by-step explanation:

Problem one

P(x) = x^3 - 4x^2 + 5x - 20 Factor the common factors from the 1st and 2nd term and the common factor from the 3rd and 4th term.

P(x) = x^2(x - 4) + 5(x - 4) Notice that x - 4 appears on either side of the plus sign. That means that x - 4 is a common factor.

P(x) = (x - 4)(x^2 + 5). The only real factor there is x - 4. It's the factor that is going to determine how many years it will take to break even. x^2 + 5 gives 2 complex answers

x - 4 = 0

x = 4

Problem 2

The graph has to cut the x axis when two consecutive domain values go from + to - or from - to plus.

This event happens twice.

x                y

2.5            1.1

3                -0.08

and again at

4                -0.3

4.5              0.7

I think the answer is B.

Answer 2

Problem 1

Answer: year 4

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The break-even point is when the profit is $0. You neither earn money nor lose it.

Plug in p(x) = 0 and solve for x

p(x) = x^3 - 4x^2 + 5x - 20

x^3 - 4x^2 + 5x - 20 = p(x)

x^3 - 4x^2 + 5x - 20 = 0 ... replace p(x) with 0

(x^3 - 4x^2) + (5x - 20) = 0

x^2(x - 4) + 5(x - 4) = 0

(x^2+5)(x - 4) = 0

x^2+5 = 0 or x-4 = 0

The equation x^2+5 = 0 has no real solutions; however x-4 = 0 solves to x = 4.

So plugging x = 4 into p(x) will lead to p(x) = 0. Meaning that the company breaks even at year 4.

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Problem 2

Answer: choice B) between 2.5 and 3.0; between 4.0 and 4.5

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Look at the f(x) column. Specifically we are looking for the times when the numbers change from positive to negative, or vice versa. Somewhere in between this change, y will have to equal 0 at some point (at least once). Note how in row 2 and row 3, we have f(x) = 1.1 change to f(x) = -0.8; so the change is from positive to negative.

This means f(x) = 0 for some x value between x = 2.5 and x = 3.5. Also, the same kind of logic applies for the last two rows of the table as well pointing to another root between x = 4.0 and x = 4.5 (check out the attached images)