Answer:
The width of the scale model is 33 inches.
Step-by-step explanation:
This question is solved making a relation with the scale model.
In the scale, 3 inches are worth 11 real feet.
The actual width of the building is 121 feet, so we find it's scale by a rule of three.
3 inches - 11 feet
x inches - 121 feet
Simplifying by 3, both sides
The width of the scale model is 33 inches.
For this case, the first thing you should know is that by definition, the vertical angles are congruent.
We have then:
∠1 and ∠2 are vertical angles.
Therefore, by definition:
∠1 = ∠2
On the other hand we have:
∠2 has a measure of 31 °.
Thus:
∠1 = ∠2 = 31 °
Answer:
the measure of ∠1 is:
∠1 = 31 °
Answer:
y=4x-2
Step-by-step explanation:
y=mx+b
plug in known variables
6=(4)(2)+b
simplify
b=-2
plug in m and b
y=4x-2
The original volume equation looks like this: V = 1/3 * h * (x^2)
After the side is reduced by 0.002, the new volume would look like V1 = 1/3 * h
* (x-0.002) ^ 2
Then we have:
V-V1 = 1/3*h*(x^2) - 1/3*h*(x – 0.002) ^2
= 1/3 * h *(x^2 - (x – 0.002) ^2)
= 1/3 * h * (0.004x - 0.00004)
The rate of decreasing is computed by:
(V-V1)/V * 100% = [1/3 * h *(0.004x - 0.00004)] / [1/3 * h * (x ^ 2)] *
100% this would be equal to (0.004x - 0.00004) / (x^2) * 100%
So replace x by 200, you’ll get:
(0.004(200) - 0.00004) / (200^2) * 100%
= 0.001999% is the rate of decreasing.
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"
