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.
7.5-3.25=4.25 tons.
The truck weights 4.25 tons.
Check with other answers, although I'm pretty sure its correct.
Heart if helpful :D
Step-by-step explanation:
We will use the Thales theorem since ED and CB are parallel and A,D and B are in the same lign wich is the same for C,E and A
since we have two similar sides and one similar angle between them it will be SAS similarity
Answer: 6.125 or 6¹/₈ units of water
Step-by-step explanation:
There are 7 people in the family and each of them are mean to drink 7/8ths of water.
The amount of water all 7 should take is therefore:
= 7 * 7/8
= 49/8
= 6.125 or 6¹/₈ units of water
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