The profit, in dollars, of a small business can be modeled by the function P(x) = 0.3x2 + 7x – 40, where x is the number of units sold. How many units need to be sold for the business to make a profit of $60?

10 units need to be sold for the business to make a profit of $60

Step-by-step explanation:

The profit, in dollars, of a small business can be modeled by the function

P(x) = 0.3 x² + 7x - 40, where x is the number of units sold

∵ The profit is $60

- That means substitute P(x) by 60

∴ P(x) = 60

- Equate 0.3 x² + 7x - 40 by 60

∵ 0.3 x² + 7x - 40 = 60

- Subtract 60 from both sides

∴ 0.3 x² + 7x - 100 = 0

- Multiply both sides by 10

∴ 3x² + 70x - 1000 = 0

Now let us factorize the left hand side into two factors and equate each factor by 0 to find x

∵ 3x² = (3x)(x)

∵ -1000 = (100)(-10)

∵ (3x)(-10) + (x)(100) = -30x + 100x = 70x

- That means the factors are (3x + 100) and (x - 10)

∴ The factors of 3x² + 70x - 1000 are (3x + 100) and (x - 10)

∴ (3x + 100)(x - 10) = 0

Equate each factor by 0

∵ 3x + 100 = 0

- Subtract 100 from both sides

∴ 3x = - 100

- Divide both sides by 3

∴ x =

We will refused this answer because number of units sold must be positive integer

∵ x - 10 = 0

- Add 10 to both sides

∴ x = 10

10 units need to be sold for the business to make a profit of $60

the answer is (4,3)

since the rule for r0, 90º is (-y,x) and it was already applied to form the image, all you have to do is reverse the answer using this formula.

step-by-step explanation: