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.
How can expressions be written and evaluated to solve for unknowns in the real world?
Writing expressions requires figuring out which quantity in a situation is unknown, and define a variable to represent that quantitiy.
We look for words in the problem that will help us out what kind of operation to use in a given situation.
Example:
Donna bought 5 chocolate bars, and then ate some. Write an expression to represent how many chocolate bars Donna has left.
If we let the variable c represent the number of chocolates Donna has eaten, then we can write the expression on how many bars Donna has left as: 5 - c
Answer: All real numbers
Step-by-step explanation:
All real numbers
Interval Notation:
(
−
∞
,
∞
)
(-∞,∞)
Answer:
p = -3
Step-by-step explanation:
−0.63p − 5.04 + 3.57 = 7.05 + 2.21p
−0.63p − 1.47 = 7.05 + 2.21p (add 0.63p to both sides)
− 1.47 = 7.05 + 2.21p + 0.63p
− 1.47 = 7.05 + 2.84p (subtract 7.05 from both sides)
− 1.47 - 7.05 = 2.84p
-8.52 = 2.84p (rearrange)
2.84p = -8.52 (divide both sides by 2.84)
p = -8.52 / 2.84
p = -3
Answer: can't add an answer, but for the first all 3 angles add up to 180 in a triangle for the second, plug 5 in and also check if all three add up to 180
Step-by-step explanation:
