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 
The expression equivalent to the total distance Rhonda drove is 51x = 275
Given:
Distance 1:
Number of miles = 51 miles
Number of hours = 5 hours
Distance 2:
Number of miles = 55 miles
Number of hours = x hours
<em>Ratio of miles to number of hours</em> = 51 miles : 5 hours
<em>Ratio of miles to number of hours</em> = 55 miles : x hours
Equate the ratios
51 : 5 = 55 : x
51/5 = 55/x
cross product
51 × x = 5 × 55
51x = 275
x = 275 / 51
x = 5.392156862745098
Approximately,
x = 5.4 hours
Therefore, the number of hours taken to travel 55 miles is 5.4 hours
Read more:
brainly.com/question/3796978
Answer: 200 meters per minute
Explanation: we know that she can run 100 meters per 30 seconds. the question is asking in terms of minutes, however. we have to convert the seconds into minutes. How many minutes is 30 seconds? well, 60 seconds are in a minute so 30 seconds are in half a minute. 30 seconds = .5 minutes.
Now, we have to find how many meters she runs per minute. this means how many meters she runs in one minute. we create a proportion:
100 meters/ .5 minutes = x meters / 1 minute
we cross multiply to get 100 = .5x
then, we simplify by dividing each side by .5 which equals
200=x
60 / 5 = 12 miles per gallon
36 miles = 12 miles / gal * x gallons
divide by 12
36/12 =x gallons
3 =x
He needs 3 gallons
Answer:
Mommy
Step-by-step explanation:
mommy mommy mommy mommy mommy