Answer:

Step-by-step explanation:
Using the pythagorean theorem, you can find that the distance between the two points is
. Hope this helps!
3n = 1/81; divide both sides by 3 to isolate n:
3n/3 = 1/81 divided by 3. Remember that when you divide, you use the reciprocal and multiply instead!!
n = 1/81(1/3) = 1/243. Now plug 1/243 back in for n, and 3/243 is equivalent to 1/81
Answer:
i don't know a counterexample for the first one
A counterexample for the second one is a leaf bug
A counterexample for the third one is a trapezoid, rectangle, rhombus
We can figure this out using the explicit formula.

n represents the term we are looking for.
f(1) represents the first term in the sequence, which in this case, is 7.
d represents the common difference, which in this case, is +3.
f(n) = 7 + 3(n - 1)
f(n) = 7 + 3n - 3
f(n) = 4 + 3n
Now, we can input 214 for n and solve.
f(214) = 4 + 3(214)
f(214) = 4 + 642
f(214) = 646
The 214th term in this sequence is 646.