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

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation:

1. 180°. the sum of the interior angles of a triangle is 180°, for the equilateral triangle that it has three equals side is 60°+60°+60°=180°.

2. 60°. each interior angle of a equilateral triangle is 60°

3. 120°. the measure of ∠m is 120°, the sum of the angles ∠m and ∠n is equal to 180°. so, in order to find the measure of ∠m, we have ∠m+∠n=180° > ∠m=180°-∠n > ∠m=180°-60°=120°.

4. 360°. the sum of the exterior angles of an equilateral triangle is ∠m+∠r+∠x=120°+120°+120°=360°. the exterior angles of any triangle always add 360°.