a.
By Fermat's little theorem, we have
5 and 7 are both prime, so 
and 
. By Euler's theorem, we get
Now we can use the Chinese remainder theorem to solve for 
. Start with
- Taken mod 5, the second term vanishes and
. Multiply by the inverse of 4 mod 5 (4), then by 2.
- Taken mod 7, the first term vanishes and
. Multiply by the inverse of 2 mod 7 (4), then by 6.
b.
We have 
, so by Euler's theorem,
Now, raising both sides of the original congruence to the power of 6 gives
Then multiplying both sides by 
gives
so that is the inverse of 25 mod 64. To find this inverse, solve for 
in 
. Using the Euclidean algorithm, we have
64 = 2*25 + 14
25 = 1*14 + 11
14 = 1*11 + 3
11 = 3*3 + 2
3 = 1*2 + 1
=> 1 = 9*64 - 23*25
so that 
.
So we know
Squaring both sides of this gives
and multiplying both sides by tells us
Use the Euclidean algorithm to solve for .
64 = 3*17 + 13
17 = 1*13 + 4
13 = 3*4 + 1
=> 1 = 4*64 - 15*17
so that 
, and so 
No it is not proportional. Since she brought the last apple for 1/2 the price, the equation won’t be linear (straight line) anymore so it won’t be proportional. Proportional means the same unit rate.
250cm^2
To find the area of shape B we need to find the factor by which you multiply to get from 12 to 15. To find this we divide 15 by 12 to get 1.25. We now multiply the area of shape A (200) by the factor 1.25 to get the answer. The answer is 250cm^2.
Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.
Answer:
5xy
Step-by-step explanation:
x and y can only go into both into once
3+p=8
-p -p
3=8-p
-8 -8
-5=-p
swap signs
5=p
