Determine an equation for the straight line that is parallel to 2x 3y = 4 and has x-intercept at x = 1/3 .

2. Clearly state what each of your variables denotes.

(a) It costs a lamp-maker $5 to manufacture each of her lamps, which she currently sells at $35 each and, at this sales price, sells 40 lamps each month. Market research shows that for each $3 decrease in sales price she will sell 10 more lamps each month. Assuming a linear relationship between the decrease in sales price and the number of lamps sold each month, express the lamp-makers monthly profit as a function of her decrease in sales price.

(b) A storage shed is in the shape of a rectangular box on a square base, with a flat roof. The material used for the base and the roof costs $3 per square foot, and the material for the four sides cost $2 per square foot; and the total cost of the material for the shed was $7,500. Express the volume of the shed as a function of the (length of each) side of the square base.

3. Factor the polynomial 3x^ 5/2 2x^4 6x^3 + 8x^2

4. Combine (x + 19)/(x^2 1) (12x 4)/(x^2 x) + 3 into a single rational function, factor, and cancel. Leave your function fully factored; clearly display all the steps of your working.

5. For y = (2x^4 + 4x^3)/(3x^4 + 15x^3 + 24x^2 + 12x) determine the holes, horizontal and vertical asymptotes, x and y intercepts, and the sign-chart. Before deriving any geometric information, leave your function in fully factored, cancelled form; clearly display all the steps of your working.