Answer:
General Formulas and Concepts:
- Order of Operations: BPEMDAS
- Distance Formula:
- Midpoint Formula:
Step-by-step explanation:
<u>Step 1: Define</u>
(5, -1)
(-9, -1)
<u>Step 2: Find distance </u><em><u>d</u></em>
- Substitute:
- Simplify:
- Subtract/Add:
- Evaluate:
- Evaluate:
<u>Step 3: Find Midpoint</u>
- Substitute:
- Subtract:
- Divide:
By cross-multiplying, we get
15x + 30 = 24
15x = -6
x = -3 / 5
Answer:
A 1 1/2 miles per hour
Step-by-step explanation:
Take the amount of miles he can row in 1/4 of an hour (3/8) and multiply it by 4, since it will tell you how many miles he can row in one hour. You get 12/8 miles per hour, which simplifies to 1 1/2 miles per hour
Hopefully this helps - let me know if you have any questions!
Answer:
(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:
- 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
- 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
∵ 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"
