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
The answer is 1x10^2 or just simply 10^2.
Answer:
markup 3 dollars a shirt. Total markup 900$
Step-by-step explanation:
Answer:
Option C is correct
76 feet
Step-by-step explanation:
Area of square(A) is given by:

where, s is the side of the square.
As per the statement:
A square ceiling has an area of 360 square feet.
⇒A = 360 square feet.
then;

⇒
Perimeter(P) of square is given by:

then;

Therefore, 76 feet molding does he need.
Answer:
the area of the trapezoid would be a = 708; if following that 8 m is the area, 110 m is the base, and 12 m is the height (apologizes if this is the answer you are not looking for)
Step-by-step explanation:
as much as I would like to, I'm really not the best at explaining things