Descarte's rule of signs say that this either 0 or 2 positive roots and one negative root. The "rational root theorem" tells you that the only possible rational roots are and . Have you tried those?

Descarte's rule of signs tells you that this has2. f(x) = X^4 - 3x^3 + 6x^2 - 12x + 8nonegative roots. The "rational root theorem" tells you that any roots must be 1, 2, 4, or 8. Try them.

f(x)= -.25(x^2- 80x)+ 100. 80/2= 40 and 40^2= 1600 so, completing the square, f(x)= -.25(x^2- 80x+ 1600- 1600)+ 100= -.25(x^2- 80x+ 1600)+ 400+ 100= -.25(x- 40)^2+ 500.Question 3: a company manufactures scooters and estimates profit depending on advertising expenses using the function: f(x) = -.25x^2 + 20x + 100

what expense in advertising will yield the maximum profit? what would the profit be?

Since a square is never negative but multiplying by -.25 means -.25(x- 40)^2 is never positive, that is always "500 minus something". It will never be larger than 500 but will be equal to 500 when x= 40.

Those look like years. I am going to assume that "200" was supposed to be "2000". A linear function is of the form y= ax+ b. Since it passes through (2000, 2), x= 2000, y= 2 satisfies that equation. Since it passes through (2050, 4), x= 2050, y= 4 satisfies that equation.Question 4: i could not past the graph on this problem i hope that does not cause any problems.

the graph above indicates the recent anticipated rise in global precipitation as greenhouse gases increase over time. selecting the coordinates (200,2) and (2050,4), write a linear function that would enable us to predict the % increase by 2150.

That means we have 2= 2000a+ b and 4= 2050a+ b. Solve those equations for a and b (subtracting one equation from the other immediately eliminates b). Once you have found a and b, evaluate ax+ b for x= 2150.

again it is greatly appreciated to all you are willing to help me with these four questions.