Answer:
omg stop taking the poimts away from me it eas right nesus
Answer:
The prove is as given below
Step-by-step explanation:
Suppose there are only finitely many primes of the form 4k + 3, say {p1, . . . , pk}. Let P denote their product.
Suppose k is even. Then P ≅ 3^k (mod 4) = 9^k/2 (mod 4) = 1 (mod 4).
ThenP + 2 ≅3 (mod 4), has to have a prime factor of the form 4k + 3. But pₓ≠P + 2 for all 1 ≤ i ≤ k as pₓ| P and pₓ≠2. This is a contradiction.
Suppose k is odd. Then P ≅ 3^k (mod 4) = 9^k/2 (mod 4) = 1 (mod 4).
Then P + 4 ≅3 (mod 4), has to have a prime factor of the form 4k + 3. But pₓ≠P + 4 for all 1 ≤ i ≤ k as pₓ| P and pₓ≠4. This is a contradiction.
So this indicates that there are infinite prime numbers of the form 4k+3.
Answer:
; 
Step-by-step explanation:
Score of the first two quizzes: 75 and 97
Let n represent the third score
Average score would be: 
.
Given that the average score fall between 85 and 90, this can be represented by the compound inequality as shown below:
Solve for n in each statement that makes up the compound inequality:
Multiply both sides by 3
Subtract 172 from each side of the inequality
Also,
Multiply both sides by 3
Subtract 172 from both sides of the inequality
Combining both together, the possible values of her third quiz score would be:
The triangle inequality tells you the third side will be between the difference and sum of the other two sides.
5 < third side < 21
