Answer:
Lets say that P(n) is true if n is a prime or a product of prime numbers. We want to show that P(n) is true for all n > 1.
The base case is n=2. P(2) is true because 2 is prime.
Now lets use the inductive hypothesis. Lets take a number n > 2, and we will assume that P(k) is true for any integer k such that 1 < k < n. We want to show that P(n) is true. We may assume that n is not prime, otherwise, P(n) would be trivially true. Since n is not prime, there exist positive integers a,b greater than 1 such that a*b = n. Note that 1 < a < n and 1 < b < n, thus P(a) and P(b) are true. Therefore there exists primes p1, ...., pj and pj+1, ..., pl such that
p1*p2*...*pj = a
pj+1*pj+2*...*pl = b
As a result
n = a*b = (p1*......*pj)*(pj+1*....*pl) = p1*....*pj*....pl
Since we could write n as a product of primes, then P(n) is also true. For strong induction, we conclude than P(n) is true for all integers greater than 1.
Answer:
-3
Step-by-step explanation:
Point A is half way between -17 and 5. This is span has a total distance of 17 + 5 = 22. Half way is 11 units from -17 or 5. So -17 + 11 = -6.
Point B is halfway between A at -6 and 0. This is a distance of 6. So halfway is 3 units away at -3.
Answer:
C
Step-by-step explanation:
3^2 + 5^2 = x^2
9 + 25 = x^2
x^2 = 34
x = sqrt(34)
so the answer is C
Answer: C
Step-by-step explanation:
The x times 4 equals the y in each column.
4 is probably the answer. Hope this helps. :)
