I believe that angle DEF is 29 and angle FEG is 61.
We apply the Pythagorean theorem twice and obtain:
12 ^ 2 = x ^ 2 + (15-d) ^ 2
9 ^ 2 = x ^ 2 + d ^ 2
We observe that it is a system of two equations with two unknowns whose solutions are:
(x, d) = (-36/5, 27/5)
(x, d) = (36/5, 27/5)
We ignore the negative solution, therefore, the solution is:
(x, d) = (36/5, 27/5)
Answer:
The length of the new fence is:
x = 36/5 meters
Answer:
Option D, Yes, Devon should have evaluated f(3)
Step-by-step explanation:
f(x) = x^3 + x^2 − 10x + 8
<u>Step 1: Evaluate using F(3) NOT f(-3)</u>
f(3) = 3^3 + 3^2 - 10(3) + 8
f(3) = 27 + 9 - 30 + 8
f(3) = 14
Since the factor is (x - 3) the x value is x - 3 + 3 = 0 + 3 -> x = 3 not x = -3
Answer: Option D, Yes, Devon should have evaluated f(3)
The answer is 138 million.
Step 1. Calculate the growth rate.
Step 2. Calculate the population number in 2014.
We will use the formula for exponential growth:
A = P * eⁿˣ
where:
A - the final amount (value)
P - the initial amount (value)
e - the mathematical constant (e ≈ 2.72)
n - the growth rate
x - the time
Step 1:
A = 120 million = 120 000 000
P = 114 million = 114 000 000
n = ?
x = 1997 - 1991 = 6
Therefore:

Logarithm both sides of the equation:

Step 2:
Now when we know the growth rate, it is easy to estimate the population in 2014
A = ?
P = 120 000 000
n = 0.0083
t = 2014 - 1997 = 17

Thus, the population will be 138 million in 2014