Answer:
See explanation below
Step-by-step explanation:
To prove by contradiction, we are going to assume that a and b are odd.
If a and b are odd, then there exists integers j, k > 0 such that
a = 2j + 1 and b= 2k + 1
We're going to rewrite the original expression substituting a and b by their odd expression.
Now we have to cases, c is even or c is odd.
Case 1: If c is odd.
If c is odd, then c² is also odd, but we have that the expression above is even. Therefore, this is a contradiction.
Case 2: If c is even.
If c is even then it's multiple of 2, and c² is multiple of 4, but the expression above is not multiple of 4 (because it has the form 4g + 2). Therefore we have a contradiction.
Thus, a or b must be even.
Answer:
Number of elements in set = n(B) = 3 . Therefore, Number of elements in power set = 2^n(B) = 2^3 = 8 . Hope helped!
Step-by-step explanation:
First, use triangle angle sum theorem on the triangle on the right.
180-(43+57)=80
Use vertical angles theorem,
the missing angle of the triangle on left is 80 as well.
Use triangle angle sum theory again.
2x+80=180,
x=50
Answer:
80°
Step-by-step explanation:
The sum of the angles of any triangle must add up to 180°. If you form a triangle with an angle of 40° and another angle of 60°, the sum of those two angles is 40 + 60 = 100, so the measure of the third angle: 180 - 100 = 80°.
Answer:
2.5
Step-by-step explanation:
Given
See attachment for number line
Required
Determine the opposite of the point
Represent the point with x; we have to first, determine point x
From the number line:
The opposite of number x is -x
Hence, the opposite of the point is 2.5