Answer:
See explanation below
Step-by-step explanation:
To prove by contradiction, we are going to assume that a and b are odd.
If a and b are odd, then there exists integers j, k > 0 such that
a = 2j + 1 and b= 2k + 1
We're going to rewrite the original expression substituting a and b by their odd expression.
![a^{2} +b^{2} = (2j+1)^{2} +(2k+1)^{2} =4j^{2} +4j+1+4k^{2} +4k+1=4j^{2} +4k^{2} +4j+4k+2\\=4(j^{2} +k^{2}+j+k) +2](https://tex.z-dn.net/?f=a%5E%7B2%7D%20%2Bb%5E%7B2%7D%20%20%3D%20%282j%2B1%29%5E%7B2%7D%20%2B%282k%2B1%29%5E%7B2%7D%20%3D4j%5E%7B2%7D%20%2B4j%2B1%2B4k%5E%7B2%7D%20%2B4k%2B1%3D4j%5E%7B2%7D%20%2B4k%5E%7B2%7D%20%2B4j%2B4k%2B2%5C%5C%3D%3Cstrong%3E4%28j%5E%7B2%7D%20%2Bk%5E%7B2%7D%2Bj%2Bk%29%20%2B2%3C%2Fstrong%3E)
Now we have to cases, c is even or c is odd.
Case 1: If c is odd.
If c is odd, then c² is also odd, but we have that the expression above is even. Therefore, this is a contradiction.
Case 2: If c is even.
If c is even then it's multiple of 2, and c² is multiple of 4, but the expression above is not multiple of 4 (because it has the form 4g + 2). Therefore we have a contradiction.
Thus, a or b must be even.
4y = - 2x + 12
y = - 2/4x + 3
The y intercept is 3
Hi , we are going to begin with the numbers that are divisible with 2025 .
Basically I'm aware that 2 is not divisible , so we are going to use 3 .
2025 divided by 3 = 675 divided by 3 = 225 divided by 3 = 75 divided by 3 = 25 divided by 5 = 5
I used 5 because I cant use 3 , in other words you can divide 25 and 3 , but you will not get a whole number .I stopped when I divided 25 and 5 because I got 5 which is a [prime number] , when you are doing this type of exercises , when you see a prime number you have to stop.
So the prime factorization is 3 times 3 times 3 times 3 times 5 times 5.
Answer:
1 quart and 6 ounces
Step-by-step explanation:
32 ounces are in a quart