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.
If in 2 hours he read 200 pgs then in 1 hour will be 50 pgs
Answer:
The phone could be either 24 feet away from them or 70 feet away from them because the person that lost the phone could be on the other side of the cell phone tower
Step-by-step explanation:
Answer:
The correct option is C. 126 in²
Step-by-step explanation:
Diameter of the container = 5 inches
⇒ radius of the container = 2.5 inches
Height of the container = 8 inches
To find how much paper is needed to create the label : We need to find the lateral surface area of the cylindrical shaped container
Lateral Surface Area of Cylinder = 2·π × radius × height
= 2 × 3.14 × 2.5 × 8
= 125.66 square inches
≈ 126 square inches
Hence, 126 square inches of paper is needed to create the label.
So, The correct option is C. 126 in²
Answer:
Based on your line, what is the likely test score of a student who does not study for the test? 45
