Answer:
the answer is in last picture
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:
x = 8
Step-by-step explanation:
These angles are alternate interior angles and m is parallel to n, so they're congruent, meaning that they're equal!
So we can make our equation:
6x - 2 = 46
6x = 48
x = 8
Hope this helps!
Answer:
I got 5.65
Step-by-step explanation:
36/8= 4.5, 4.5 +1.25= 5.65
A rectangle’s area is width x height. So plug in what you know and solve. 212.5 = w x 17. To solve 212.5/17= 12.5. So the width must be 12.5.
