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
X=0, y=6
x=1, y=4
x=2, y=2
x=3, y=0
x=4, y=-2
Hope this helps :)
Answer:
OK what is equation ??????
25,000 + 600 considering they would meet at 0, so they are 25,600 feet apart
Carmel would need 7 gas tanks. (2,240 ÷ 320 = 7)
Carmel would need $273 because since she needs $39 dollars for one gas tank, you would have to multiply that by 7. (39 x 7 = $273)
