16. Mrs. Hunneycutt makes dog sweaters. Her profit each month is a function of the price she charges for each sweater. Her total profits, y (in hundreds of dollars), based
on the sales price, x, can be modeled by the function y=-3x2 + 39x - 108.
Identify any zeros of the function, and interpret what the zeros mean in terms of the
situation

The total profits will be zero at sales prices of $4 and $9

Step-by-step explanation:

∵ The function is y = -3x² + 39x - 108, where

The zeroes of the function are the values of x at y = 0

→ To find the zeroes of the function above equate y by 0

∵ 0 = -3x² + 39x - 108

→ Switch the two sides

∴ -3x² + 39x - 108 = 0

→ Divide all terms by -3 to simplify the equation

∴ x² - 13x + 36 = 0

→ Let us factor the trinominal into two brackets

∵ The last term is +ve and the middle term is -ve

∴ The two brackets have (-) sign in the middle ⇒ (... - ...)(... - ...)

∵ x² = (x)(x)

∵ 36 = (4)(9)

∵ (4)(x) + (9)(x) = 4x + 9x = 13x ⇒ the value of the middel term

→ That means the factors of the trinomial are (x - 4) and (x - 9)

∴ x² - 13x + 36 = (x - 4)(x - 9)

→ Replace the trinomial by its factors

∴ (x - 4)(x - 9) = 0

→ Equate each bracket by 0 to find x

∵ x - 4 = 0

→ Add 4 to both sides

∴ x = 4

∵ x - 9 = 0

→ Add 4 to both sides

∴ x = 9

∴ The zeroes of the functions are 4 and 9

∵ x represents the sales price in dollars

∴ The sales prices which make zero profit are $4 and $9

∴ The total profits will be zero at sales prices of $4 and $9

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

step-by-step explanation: