Answer:
the equation in letter D is a linear function.
Answer:

Step-by-step explanation:
![\ln \dfrac{4y^5}{x^2}\\\\=\ln(4y^5) - \ln(x^2)~~~~~~~~~~~;\left[ \log_b\left( \dfrac mn \right) = \log_b m - \llog_b n \right]\\\\=\ln 4 + \ln y^5 - 2\ln x~~~~~~~~~~~~;[\log_b m^n = n \log_b m ~\text{and}~\log_b(mn) = \log_b m + \log_b n ]\\\\=\ln 4 + 5 \ln y -2 \ln x\\\\=\ln 4 -2 \ln x +5 \ln y](https://tex.z-dn.net/?f=%5Cln%20%5Cdfrac%7B4y%5E5%7D%7Bx%5E2%7D%5C%5C%5C%5C%3D%5Cln%284y%5E5%29%20-%20%5Cln%28x%5E2%29~~~~~~~~~~~%3B%5Cleft%5B%20%5Clog_b%5Cleft%28%20%5Cdfrac%20mn%20%5Cright%29%20%20%3D%20%5Clog_b%20m%20-%20%5Cllog_b%20n%20%5Cright%5D%5C%5C%5C%5C%3D%5Cln%204%20%2B%20%5Cln%20y%5E5%20-%202%5Cln%20x~~~~~~~~~~~~%3B%5B%5Clog_b%20m%5En%20%3D%20n%20%5Clog_b%20m%20~%5Ctext%7Band%7D~%5Clog_b%28mn%29%20%3D%20%5Clog_b%20m%20%2B%20%5Clog_b%20n%20%5D%5C%5C%5C%5C%3D%5Cln%204%20%2B%205%20%5Cln%20y%20-2%20%5Cln%20x%5C%5C%5C%5C%3D%5Cln%204%20-2%20%5Cln%20x%20%2B5%20%5Cln%20y)
Answer:
= 3n + 3
Step-by-step explanation:
The sequence is arithmetic with explicit formula
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
From the recursive formula
a₁ = 6 and d = 3 [ the constant being added to A(n - 1) ] , then
= 6 + 3(n - 1) = 6 + 3n - 3 = 3n + 3
Answer and explanation:
Statement - If the difference of two numbers is even then so is their sum.
Let the two even numbers be '2m' and '2n' with m and n are integers.
The difference of two number is

Now, The sum of the numbers is

Let
where k is an integer
Then,
which is also an even number as 2 is multiplied with it.
So, If the difference of two numbers is even then so is their sum.
For example -
Let two even number 2 and 4.
The difference is
, 2 is even.
The sum is
, 6 is even.
You can just put the 10 over 1 and multiply across. Then simplify! Hope this helps (: