George has opened a new store and he is monitoring its success closely.

He has found that this store’s revenue each month can be modeled by r(x)=x2+6x+10 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars.

He has also found that his expenses each month can be modeled by c(x)=x2−4x+5 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars.

What does (r−c)(4) mean about George's new store?

The new store will have a profit of $2300 after its fourth month in business.

The new store will sell 2300 items in its fourth month in business.

The new store will have a profit of $4500 after its fourth month in business.

The new store will sell 4500 items in its fourth month in business.

(r - c)(4) means "The new store will have a profit of $4500 after its fourth month in business" ⇒ 3rd answer

Step-by-step explanation:

George has opened a new store and he is monitoring its success closely

He has found that:

∵ r(x) = x² + 6x + 10

∵ r(x) is the revenue

∵ c(x) = x² - 4x + 5

∵ c(x) is the expenses

- The profit is the difference between the revenue and the

   expenses

∴ The profit = r(x) - c(x)

∵ r(x) - c(x) can me written as (r - c)(x)

∴ The profit = (r - c)(x)

∴ The profit = (x² + 6x + 10) - (x² - 4x + 5)

- Remember (-)(-) = (+) and (-)(+) = (-)

∴ The profit = x² + 6x + 10 - x² + 4x - 5

- Add the like terms

∴ The profit = (x² - x²) + (6x + 4x) + (10 - 5)

∴ The profit = 10x + 5

∴ (r - c)(x) = 10x + 5

- Substitute x by 4

∵ x = 4 ⇒ 4 months

∴ (r - c)(4) = 10(4) + 5

∴ (r - c)(4) = 45

∵ r and c are in hundred dollars

∴ The profit = $4500

(r - c)(4) means "The new store will have a profit of $4500 after its fourth month in business"

step-by-step explanation:

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