The profit, in dollars, of a small business can be modeled by the function P(x)=0.3x^2+7x-40, where c is the number of units sold. How many units need to be sold for the business to make a profit of 60$?

The correct answer is 10 units.

Step-by-step explanation:

Profit function of a small business is given by P(x) = 0.3 + 7x - 40, where x is the number of units sold.

The small business intend to make a profit of $60.

To find out the number of units the business has to sell in order to have a profit of $60 is given by,

P(x) = 0.3 + 7x - 40 = 60

⇒ 0.3 + 7x - 100 = 0

⇒ 3 + 70x - 1000 = 0

⇒ x = -70 ± ×

⇒ x = -70 ± 130 ×

⇒ x = 10 or -

Quantity sold cannot be negative giving us the value of x as 10 units.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions