Answer:
- B. Yes, because ED is perpendicular to DT which makes a right angle.
Step-by-step explanation:
Plot the given points and connect in pairs to get a triangle.
Visually we can say it is a right triangle as legs TD and ED seem perpendicular.
Let's confirm this by finding the slopes.
<u>Slope of TD:</u>
- m = (-1 - 4)/(1 -(-2)) = -5/3
<u>Slope of ED:</u>
- (-1 - 2)/ (1 - 6) = -3/-5 = 3/5
<u>Product of the slopes is:</u>
This confirms DT⊥ED
Correct choice is B
Answer:
h = 10 m
Step-by-step explanation:
The formula for area of a trapezoid is
A = (1/2)(B + b)h where B is the bottom base, b is the top base, and h is the height.
We are given B = 16, b = 14, and A = 15, plug those values in and simplify
150 = (1/2)(16 + 14)(h)
150 = (1/2)(30)(h)
150 = (15)h (half of 30 is 15)
10 m = h (divide both sides by 15 to isolate h)
Step-by-step explanation:
<u>Part a</u>
P(x) = 0
150x - x^2 = 0
x(150-x)
x=0,150
Laura should sell 150 pies in order to "break-even" on her sales.
<u>Part b</u>
Because the maximum profit occurs at the vertex of the function,
x = -b/2a = -150/-2 = 75
P(75) = 150 * 75 - 75^2 = 5625
Laura maximizes her profit to $5625 when she sells exactly 75 pies.
Answer: The approximate difference in the ages of the two cars is 2 years
Step-by-step explanation:
Now, since the first car (Car A) depreciates annually at a rate of 10% and is currently worth 60% or 40% less than its original value, we can calculate the number of years it took the car to depreciate to just 60% of its original worth:
= Current value/rate of depreciation
= 60%/10%
= 6 years
So, if the car depreciates by 10% every year from the year it was worth 100% of it's original value, it will take 6 years for the car to now worth just 60%
In the same manner, if the second car (Car B) is depreciating at an annual rate of 15% and is likewise currently worth just 60% or 40% less than its original value, we can calculate the number of years it will take the car to depreciate to 60% of its original worth.
= Current worth/ rate of depreciation
= 60%/15%
= 4 years
So, if the car (Car B) is depreciating at a rate of 15% per annum, the car will depreciate to just 60% in a period of 4 years.
Therefore, if the 2 cars are currently worth just 60% of their original values (recall that it took the first car 6 years and the second car 4 years to depreciate to their current values), the approximate difference in the ages of the two cars assuming they both started depreciating immediately after the years of their respective manufacture is:
= 6 years - 4 years
= 2 years