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.
Answer: No. You reversed the domain and range
#2) B) x ≥ 0
#3) B) [0, ∞)
<u>Step-by-step explanation:</u>
#2 is asking about the domain, which is all of the x-values.
The graph appears to be touching the y-axis so it equals 0 and all other x-values are greater than zero. (0, 1), (1, 0), (2, -0.8), (3, -1.5), etc. All of the x-values are moving toward the right, which is positive infinity. --> x ≥ 0
#3 is asking for the range, which is all of the y-values.
The vertex is at (0, 0) and all other y-values are above zero (positive numbers), moving toward positive infinity. --> [0, ∞)
Since y is 5.2 you can substitute it in your equations 5.2 = -5x - 40 then you do things like normal add 40 in both sides and divide -5 in both sides you get 9.04
Answer:
Second option: -3x^2
Step-by-step explanation:
A is the product of -x and 3x, then:
A=(-x)(3x)→A=-3x^2
