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:
F) 15/8
Step-by-step explanation:
<em>A. 17/15</em>
<em>B. 8/17</em>
<em>C. 15/17</em>
<em>D. 8/15</em>
<em>E. 17/8</em>
<em>F. 15/8</em>
Answer:
v=2
Step-by-step explanation:
9v=16+v
9v-v=16
8v=16
v=16/8
v=2
Answer:
x = 12
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
10x-10 = 60 +4x+2
Combine like terms
10x-10 = 62+4x
Subtract 4x from each side
10x-4x -10 = 62 +4x-4x
6x -10 = 62
Add 10 to each side
6x-10+10 = 62+10
6x= 72
Divide by 6
6x/6 = 72/6
x = 12
Answer:
1.89
Solution:
We have -44x - 86 = -3
First, we move the non x terms to the RHS of the equation. To do this, we add 86 to both sides.
Note: if a = b, then a + c = b + c
Therefore, -44x - 86 + 86 = -3 + 86
or, -44x = 83
Next, divide both sides by -44, which is the coefficent of x
Note: if a = b, then a ÷ c = b ÷ c
-44x
-44
=
83
-44
or, x = -1.89
Explaination:
This is right I guess
