Answer:
x = 6
Step-by-step explanation:
As the function f(x) is an exponencial function, it will grow faster than g(x), that is a linear function.
For small values of x, we have that f(x) < g(x). For example:
f(1) = 1/2 * 2 = 1
g(1) = 5*1 + 2 = 7
f(2) = 1/2 * 4 = 2
g(2) = 5*2 + 4 = 14
So we just need to check some integer values and see when f(x) will be bigger than g(x). It will not be a big value, as the exponencial function grows very fast.
For x = 5, we have:
f(5) = 1/2 * 32 = 16
g(5) = 5*5 + 4 = 29
For x = 6, we have:
f(6) = 1/2 * 64 = 32
g(6) = 5*6 + 4 = 34
For x = 7, we have:
f(7) = 1/2 * 128 = 64
g(7) = 5*7 + 4 = 39
So the largest integer value of x for f(x) ≤ g(x) is x = 6.
Another way to solve this is by plotting both equations, and then checking where they cross, that is, where f(x) = g(x).
The answer to the question is b
Answer:
Step-by-step explanation:
Please refer to the attached figure for labeling of given diagram:
We are given the following angles:
Angles opposite to each other when they are formed by crossing of two lines are known as vertically opposite angles. And vertically opposite angles are always equal to each other.
Using property of vertically opposite angles:
Line CD is a straight line, so 
Also,
Hence, <em>answer</em> is 
.
Answer:
-3072
Step-by-step explanation:
ar^(n-1)
a is the first term.
r is the common ratio.
3(-4)^(6-1)
3(-4)^5
3(-1024)
= -3072
The 6th term of the geometric sequence is -3072.
Answer: There are 45 miles that she have to travel to get to the next down.
Step-by-step explanation:
Since we have given that
1 inch = 15 miles
If there are given 3 inches.
We need to find the number of miles she have to travel to get to travel to get to the next town.
So, it becomes,
Hence, there are 45 miles that she have to travel to get to the next down.
