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.
Multiply both sides by y...
(3/y)y-(6/y)y-2y
Simplify it...
(3/y)y=3
(6/y)y=6
3=6-2y
Subtract 6 from both sides...
-2y=-3
Divide both sides by -2...
y=3/2
The solution is y=3/2
The first and last represent functions, no function has an input with two separate outputs
Answer:
C, B, A
Step-by-step explanation:
The sides in order from shortest to longest are ...
AB = m-2
AC = m
BC = m+4
The angles opposite these sides will be in order, smallest to largest. The angle opposite is the one whose letter is <em>not</em> in the line segment name.
C, B, A
Answer:
37+x+53 = 180
x=90
Step-by-step explanation:
To find x, we need to use the fact that a straight line equals 180 degrees.
37+x+53 = 180
Combining like terms
90+x = 180
Subtract 90 from each side
90-90+x = 180-90
x = 90
