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
I’m guessing it is 1 million because you can only round up since it’s value is not above 1 million.
Given function : 3x−6y=12.
We are given x : −2 0 4.
We need to find the values of y's for x=-2, x=0 and x=4.
Plugging x=-2 in the given equation, we get
3(-2)−6y=12
-6 - 6y = 12.
Adding 6 on both sides, we get
-6+6 - 6y = 12+6
-6y = 18.
Dividing by -6 on both sides, we get
y= -3.
On the same way, plugging x=0.
3(0)−6y=12
-6y =12.
y=-2.
Plugging x=4,
3(4)−6y=12
12 -6y = 12.
Subtracting 12 on both sides.
12-12 -6y = 12-12
-6y=0
y=0.
Therefore,
<h3>x −2 0 4</h3><h3>y -3 -2 0</h3>
Assuming you are multiplying 5 times 2/11 then you just put 5/1 because anything divided by 1 is still one, and then multiply 5/1 by 2/11. Meaning, 5 times 2 is 10. And 1 times 11 is 11. So it would be 2/11. You multiply the numerators(top number) and denominators(bottom number). 2/11 is already simplified
Answer:
Step-by-step explanation:
Answer:
The relationship between the number of cups of water and sugar in the recipe is w = ¹/₃(s)
Step-by-step explanation:
Given;
number of cups of sugar = s
number of cups of water = w
The relationship between the number of cups of water and sugar in this recipe is given as;
½ cup of sugar is proportional to 1 ½ cups of water
Therefore, the relationship between the number of cups of water and sugar in the recipe is w = ¹/₃(s)
