Short answer: 36.
This is a combination/permutation problem.
To put it simple, a die has 6 sides, there are 7 days but 1 is already determined (12 laps).
So if we multiple the options (sides on a die) × the number of days (6) we get:
6 × 6 = 36 possible outcomes.
To show this we can get
12, 13, 14, 15, 16, 17, 18
12, 13, 14, 15, 16, 17, 19
12, 13, 14, 15, 16, 17, 20
... all the way to
12, 18, 24, 30, 36, 42, 48
The highest power is 2.
Explanation:
Because x has a maximum power of 2, there will be 2 answers. if it were 3, there could be up to 3 answers, etc.
While solving this problem, you gather all terms on one side so the equation looks like
x
2
−
81
+
17
=
0
x
2
−
64
=
0
then factor
(
x
−
8
)
(
x
+
8
)
=
0
then, because any number times 0 equals 0, we know that one of the two parts in the parenthesis must be equal to 0, so
x
−
8
=
0
or
x
+
8
=
0
and so the two answers
x
=
8
,
−
8
come to be.
Let's assume the gemstones are A, B, C, D, E
1. A, B
2. A, C
3. A, D
4. A, E
5. B, C
6. B, D
7. B, E
8. C, D
9. C, E
10. D, E
A: 10 different rings are possible.
Hope this helps. - M