Base case: if <em>n</em> = 1, then
1² - 1 = 0
which is even.
Induction hypothesis: assume the statement is true for <em>n</em> = <em>k</em>, namely that <em>k</em> ² - <em>k</em> is even. This means that <em>k</em> ² - <em>k</em> = 2<em>m</em> for some integer <em>m</em>.
Induction step: show that the assumption implies (<em>k</em> + 1)² - (<em>k</em> + 1) is also even. We have
(<em>k</em> + 1)² - (<em>k</em> + 1) = <em>k</em> ² + 2<em>k</em> + 1 - <em>k</em> - 1
… = (<em>k</em> ² - <em>k</em>) + 2<em>k</em>
… = 2<em>m</em> + 2<em>k</em>
… = 2 (<em>m</em> + <em>k</em>)
which is clearly even. QED
Answer:

Step-by-step explanation:

The descryption gives you the above <em>Slope-Intercept Equation</em>. Parallel equations have SIMILAR <em>RATE</em><em> </em><em>OF</em><em> </em><em>CHANGES</em><em> </em>[<em>SLOPES</em>], therefore
remains as is, and perfourming
will give you that answer.
I am joyous to assist you at any time.
Answer:c)21
Step-by-step explanation:
i just took the quiz
They are all larger than 90 degrees, and in a triangle they would all be obtuse angles.
Given :
A holiday meal cost 12.50 a person plus a delivery fee of $30 at we cater.
The same meal cost $15 a person with no fee at Good Eats.
To Find :
When does we cater become the better deal.
Solution :
Let , x is number of order .
Cost at cater , C = 12.5x + 30 .
Cost at Good Eats , G = 15x .
We need to find :
G > C

Therefore, after 12th order cater will be more value for money.
Hence, this is the required solution.