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
M is dependent and h is independent
m=money and h=hours, p =money per hour
m=ph
Answer:
72/149
Step-by-step explanation:
Just to clarify, the curly braces mean the same thing as normal parenthesis.
(12 + 5^2) = (12 + 25) = 37
(-7-15)^2 = (-22)^2 = 484
6^3 = 216
(12 + 5^2) - (-7-15)^2 = 37 - 484 = 447
6^3 / ((12 + 5^2) - (-7 - 15)^2) = 216 / 447 = 72/149
Answer:
Slope = Rise over Run
Rise = 2
Run = 3
Slope = 2/3
Let me know if this helps!
A = length x width
15,000 = (w + 30) x w
15,000 =
+ 30w
0 =
+ 30w - 15,000
Use quadratic formula to find that w= -15 + or - 5
. Because distance cannot be negative, the width is -15 + 5
meters or approximately 108.39 meters. This means that the length is approximately 138.39 meters.
