LFT says that for any prime modulus

and any integer

, we have

From this we immediately know that

Now we apply the Euclidean algorithm. Outlining one step at a time, we have in the first case

, so

Next,

, so

Next,

, so

Finally,

, so

We do the same thing for the remaining two cases:


Now recall the Chinese remainder theorem, which says if

and

, with

relatively prime, then

, where

denotes

.
For this problem, the CRT is saying that, since

and

, it follows that



And since

, we also have


Answer: A
Step-by-step explanation: Add the amount of candles for both sets together (6 in each set, so 12) and then divide 36 by 12 for 3.
Answer:
reflection over the x-axis
shifted 3 right
shifted 2 up
Step-by-step explanation:
This function is quadratic. Quadratic graphs are written as y=a(x-h)^2+k. Where a is a non-zero number that affects the vertical appearance of the graph, h is the horizontal placement, and k is the vertical placement.
When a is negative then, the graph has been reflected over the x-axis. This makes it look like it has been turned upside down. The variable h affects how the x-values are shifted. In this equation, h looks negative but it is actually positive because if you look at the formula, h is being subtracted. Positive h values move the graph right. So, the graph is shifted 3 units to the right. Finally, k does the same thing as h but on the vertical (y) axis. So, +2 makes the graph shift 2 units up.
S(x) = 22x + 124
s(5) = 22(5) + 124
s(5) = $234
300 = 22x + 124
-124 -124
176 = 22x
divide by 22
8 = x
The rule for regular polygons are very easy. The number of reflectional symmetries is same as the number of sides. Regular polygons have all sides the same length and all angles same. Reflection symmetry means that you can fold the shape along that line and it will match up.
For this question, we want the number of reflectional symmetries of a regular decagon. Decagon is a 10 sided figure. Hence, the number of reflectional symmetries is 10.
There are 5 symmetry lines from one vertex to opposite vertex and 5 more symmetry lines form midpoint of one side to midpoint of opposite side.
ANSWER: 10