Can someone help me with these problems for an assignment

1.Solve ((x+4)(3-x))/ ((x-2)²) > 0 and writeinterval notationfor the solution set.

Show careful algebraic work/explanation.

2,Forf (x)= x³-4x-8 use the Intermediate Value Theorem to determine which interval must contain a zero of f(x).(no explanation required). _______

A.Between 0 and 1

B.Between 1 and 2

C.Between 2 and 3

D.Between 3 and 4

3.f(x)= (3x² - 3x)/ (x²+x-12)

(a) State the domain.

(b) State they-intercept.

(c)State thex-intercept(s).

(d) State the vertical asymptote(s).

(e) State the horizontal asymptote

4.Forz= 6 + 2iandw= 7-3i, findz/w. Simplify as much as possible, writing the result in the forma+bi, whereaandbare real numbers.Show work.

5.Find the solutions of the equation 5x²- 2x+3=0 Show algebraic work.

6.The marketing department has found that, when the new model calculators are sold at a price ofpdollars per unit, the revenue R (in dollars) as a function of the price is:

R(p)= -150p²+21,000p

(a) The revenue function is a quadratic function and so its graph is a parabola.

Does the parabola open up or down? __________

(a)What unit price should be established in order to maximize revenue?

(c) If this price is charged, what is the maximum revenue?

7.Solve the equation

(47/y²- 25)+ (2/y-5) = (1/y+5)