Answer:
Any integer x can be represent in form of 3k, 3k+1, or 3k + 2 (k is integer).
Case 1: x = 3k => x^2 - 2 = 9k^2 - 2, which will not be divisible by 3
(notice that 2 is not divisibble by 3, but 9k^2)
Case 2: x = 3k + 1 => x^2 - 2 = 9k^2 + 6k + 1 - 2 = 9k^2 + 6k - 1, which will not be divisible by 3
(notice that 1 is not divisibble by 3, but 9k^2 + 6k)
Case 3: x = 3k + 2 => x^2 - 2 = 9k^2 + 12k + 4 - 2 = 9k^2 + 12k - 2, which will not be divisible by 3
(notice that 2 is not divisibble by 3, but 9k^2 + 12k)
=> x^2 - 2 will never be divisible by 3
Hope this helps!
:)
Answer:
8 and 8; 64
Step-by-step explanation:
1. x + y = 16
2. y = 16 - x
3. Product = xy = x (16 - x) = -
+ 16x = f(x)
4. x-coordinate of the vertex = ![\frac{-16}{2(-1)} =8](https://tex.z-dn.net/?f=%5Cfrac%7B-16%7D%7B2%28-1%29%7D%20%3D8)
5. y = 16 - 8 = 8
6. xy = 8(8)= 64
Let the sides be a, b and c
Given:
b= 6cm
c= 10cm
To find: Side a
Solution:
By Pythagoras’ theorem:
a^2+b^2=c^2
a^2+6^2=10^2
a^2+36=100
a^2=100-36
a^2=64
a= root of 64
a=8cm
<h3>
Answer: 140 degrees</h3>
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Explanation:
See the diagram below.
We start with triangle PQR with the given angles mentioned. Then you extend out segment QR to form line QR. It goes off infinitely in both directions.
The exterior angle x adds to the interior angle Q = 40 to get 180
x+40 = 180
x+40-40 = 180-40 ... subtract 40 from both sides
x = 140
The exterior angle is 140 degrees