The financial planner for a beauty products manufacturer develops the system of equations below to determine how many combs must be sold to generate a profit. the linear equation models the income, in dollars, from selling x plastic combs; the quadratic equation models the cost, in dollars, to produce x plastic combs. according to the model, for what price must the combs be sold? { y=x/2 y=-0.03(x-95)^2+550 a. $0.03 each b. $0.50 each c. $0.95 each d. $2.00 each

Solution:

The two equations, which are

1. The linear equation models the income, in dollars, from selling x plastic combs is given as

2. The quadratic equation models the cost, in dollars, to produce x plastic combs is given as

Selling price of x, plastic comb

Selling price of one plastic comb

               = $0.50

So, selling price of each plastic comb= $ 0.50 each→→Option (B)

The correct answer is B, or $0.50.

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answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.