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: the answer is d pls give brainlEst
Step-by-step explanation:im sorry i guess my math was wronge
Answer: - 19/4
Step-by-step explanation:
To find the slope , all we need to do is to write the equation in the form y = mx + c , where m is the slope and c is the y - intercept.
That means we need to make y the subject of the formula in the equation.
4y = 152 - 19x
Divide through by 4
y = 152/4 - 19x/4
y = 38 - 19x/4
Therefore the slope is -19/4
Answer:
y = -3/4x - 2
Step-by-step explanation:
y = -3/4x + b
1 = (-3/4) × -4 + b
1 = 3 + b
-2 = b
b = -2
y = -3/4x -2