Answer:
D
Step-by-step explanation:
A and D are the only ones that make sense but, A is incorrect because ice is an example of a solid, a solid isn't an example of ice.
Answer:
There is no answer
My Logic:
The picture does not specify the degree of angle for each corner, nor can i understand what the random "a" is. also the side all the way to the left has an un-readable number.
Answer:

Step-by-step explanation:
We will prove by mathematical induction that, for every natural n,

We will prove our base case (when n=1) to be true:
Base case:
As stated in the qustion, 
Inductive hypothesis:
Given a natural n,

Now, we will assume the inductive hypothesis and then use this assumption, involving n, to prove the statement for n + 1.
Inductive step:
Let´s analyze the problem with n+1 stones. In order to move the n+1 stones from A to C we have to:
- Move the first n stones from A to C (
moves). - Move the biggest stone from A to B (1 move).
- Move the first n stones from C to A (
moves). - Move the biggest stone from B to C (1 move).
- Move the first n stones from A to C (
moves).
Then,
.
Therefore, using the inductive hypothesis,

With this we have proved our statement to be true for n+1.
In conlusion, for every natural n,

Answer: -2a^3 + 9a^2 + 45a + 18b^2 + 6ab^2
Step-by-step explanation:
(a + 3) * (-2a^2 + 15a + 6b^2)
We open the brackets with (a + 3)
a ( -2a^2 + 15a + 6b^2) + 3(-2a^2 + 15a + 6b^2)
Opening the brackets
= a * -2a^2 = -2a^3
a * 15a = 15a^2
a * 6b^2 = 6ab^2
3 * -2a^2 = -6a^2
3 * 15a = 45a
3 * 6b^2 = 18b^2
Let's arrange those values weve gotten together ,don't forget the signs each carry
= -2a^3 + 15a^2 + 6ab^2 - 6a^2 + 45a + 18b^2
Collect the like terms
= -2a^3 + 15a^2 - 6a^2 + 6ab^2 + 45a + 18b^2
= -2a^3 + 9a^2 + 6ab^2 + 45a + 18b^2