Answer and Step-by-step explanation:
(a) Given that x and y is even, we want to prove that xy is also even.
For x and y to be even, x and y have to be a multiple of 2. Let x = 2k and y = 2p where k and p are real numbers. xy = 2k x 2p = 4kp = 2(2kp). The product is a multiple of 2, this means the number is also even. Hence xy is even when x and y are even.
(b) in reality, if an odd number multiplies and odd number, the result is also an odd number. Therefore, the question is wrong. I assume they wanted to ask for the proof that the product is also odd. If that's the case, then this is the proof:
Given that x and y are odd, we want to prove that xy is odd. For x and y to be odd, they have to be multiples of 2 with 1 added to it. Therefore, suppose x = 2k + 1 and y = 2p + 1 then xy = (2k + 1)(2p + 1) = 4kp + 2k + 2p + 1 = 2(kp + k + p) + 1. Let kp + k + p = q, then we have 2q + 1 which is also odd.
(c) Given that x is odd we want to prove that 3x is also odd. Firstly, we've proven above that xy is odd if x and y are odd. 3 is an odd number and we are told that x is odd. Therefore it follows from the second proof that 3x is also odd.
Here there are 20 members in all.
Each member paid $2.60.
Total amount paid by members = 20 × 2.60 = $52
The club paid $47.50 to hire the hall. ......Answer
Hence the amount received by the hall = 52 - 4.50 = $ 47.50
The Hall charged $47.50 as the fee.
Step-by-step explanation:
So what you can do is first get ride of the parentheses around 5-m so:
Then, you can simplify the numbers inside the parentheses, so:
Then, you can get rid of the parentheses by distributing the - sign:
Next, just combine like terms:
or 
