Step-by-step explanation:
step 1. x + 51 + 39 + 127 = 360 (1 revolution is 360°)
step 2. x + 90 + 127 = 360
step 3. x + 127 = 270. (subtract 90 on both sides)
step 4. x = 143° (subtract 127 on both sides)
After discount: $418; total (including tax): $388.74
Answer:
12a^2 - 9a + 5
Step-by-step explanation:
(5a^2 - 6a - 4) - (-7a^2 + 3a - 9)
5a^2 + 7a^2 = 12a^2
-6a - 3a = -9a
-4 + 9 = 5
12a^2 - 9a + 5
Answer:
An explicit representation for the nth term of the sequence:

It means, option (B) should be true.
Step-by-step explanation:
Given the geometric sequence

A geometric sequence has a constant ratio, denoted by 'r', and is defined by

Determining the common ratios of all the adjacent terms

As the ratio is the same, so
r = 4
Given that f₁ = -1/2
substituting r = 4, and f₁ = -1/2 in the nth term


Thus, an explicit representation for the nth term of the sequence:

It means, option (B) should be true.
Answer:
80 movies must be streamed.
Step-by-step explanation:
To find the average cost, you must divide the total cost by the number of movies watched.
When you watch 1 movie, you pay the initial fee of $80 plus a $4 purchase of the film.
The equation is shown as such:
average cost = (total cost)/(number of movies)
Your total cost can be represented as
, while the number of movies is represented as
.
You want the average to equal 5, so your equation is shown as follows:

simplifying this, we get

which can then be simplified to

X = 80 movies.