Answer:
No, mn is not even if m and n are odd.
If m and n are odd, then mn is odd as well.
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Proof:
If m is odd, then it is in the form m = 2p+1, where p is some integer.
So if p = 0, then m = 1. If p = 1, then m = 3, and so on.
Similarly, if n is odd then n = 2q+1 for some integer q.
Multiply out m and n using the distribution rule
m*n = (2p+1)*(2q+1)
m*n = 2p(2q+1) + 1(2q+1)
m*n = 4pq+2p+2q+1
m*n = 2( 2pq+p+q) + 1
m*n = 2r + 1
note how I replaced the "2pq+p+q" portion with r. So I let r = 2pq+p+q, which is an integer.
The result 2r+1 is some other odd number as it fits the form 2*(integer)+1
Therefore, multiplying any two odd numbers will result in some other odd number.
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Examples:
- 3*5 = 15
- 7*9 = 63
- 11*15 = 165
- 9*3 = 27
So there is no way to have m*n be even if both m and n are odd.
The general rules are as follows
- odd * odd = odd
- even * odd = even
- even * even = even
The proof of the other two cases would follow a similar line of reasoning as shown above.
Answer:
C
Step-by-step explanation:
The perimeter would be 2*(4(2x+1) + 3(x+4)) because the right side length and the top side length are known. The left side length must equal the right side length and the bottom side length must equal the top side length. So the answer must be:
2*(4(2x+1) + 3(x+4)) = 2*(8x+4+3x+12) = 2*(11x+16) = 22x+32
C. 22x+32
The correct answer to this question is 6 in
Answer:
2016in^3 more water is needed.
Step-by-step explanation:
Take the three sides and multiply them together
14in*24in*12in=4032in^3
Since only have the tank is full divide your answer by 2
4032/2=2016in^3
To get your final answer of 2016in^3.