F(x) is continuous for all x.
Pick a point and show that f(x) is either negative or positive. Pick another point and show that f(x) is negative, if positive, or positive, if negative.
At x = 30, f(30) - 1000 = 900 + 10sin(30) - 1000 ≤ 0
Now, show at another point f(x) - 1000 is positive, and hence, there would be root between 30 and such point.
Let's pick 40.
At x = 40, f(40) - 1000 = 1600 + 10sin(40) - 1000 ≥ 0
Since f(x) - 1000 is continuous, there lies a root between 30 and 40, and hence, 30 ≤ c ≤ 40
Answer: 
Step-by-step explanation:
The triangle CDE is shown in the image attached.
The formula for calculate the distance between two points is:
Then, we can calculate the lenght of each side of the triangle:
Therefore, the perimeter is:
To answer this we would need the expressions given.
Answer:
The correct answer is option A.
Step-by-step explanation:
Let's start by analyzing the information we have.
We know that Carmen pays 5% tax on everything she buys, and has made a purchase of $ 70.
But they also tell us that there is $ 25 of that purchase that will not be charged with taxes.
Therefore, what will be charged with taxes will be:
70-25 = 45
Now we must know how much is 5% of 45 and that we can find out by multiplying 45 by 0,05:
45.0,05 = 2,25
Now that we know that the tax was 2.25, we just have to add it to the total purchase to find out how much Carmen paid:
2.25 + 70 = 72.25
Therefore, the total value of the purchase is 72.25.
