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:
<em><u>x=9, y=12</u></em>
Step-by-step explanation:
-5x+4y=3
--------A
x=2y-15----------B
Putting the value of x from B in A
-5(2y-15) +4y=3
-10y+75+4y=3
-6y=3-72
-6y=-72
y=72/6= 12
Putting the value of y =12 in B
x= 2(12)-15
x= 24-15
x=9
Answer:
no
Step-by-step explanation:
half is bigger then 1/3 think of it like this split a pizza into 2 pieces and the other into 3 take one out of both which is bigger if that helps
Answer:
Step-by-step explanation:
The result can be shown in multiple forms.
Exact Form:
24
−
16
√
2
Decimal Form:
1.37258300
…
