Answer:
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Step-by-step explanation:
Answer:
The answer is True
Step-by-step explanation:
A <em>mathematical induction</em> consists in only 2 steps:
<u>First step</u>: Show the proposition is true for the first one valid integer number.
<u>Second step</u>: Show that if any one is true then the next one is true
Finally, if first step and second step are true, then the complete proposition is true.
So, given 
First step: using and replacing n=2 (the first valid integer number >1)


As the result is an integer number, so the first step is true.
Second step: using any next number,
, let it replace

As the First step is true, we know that

,
So let it replace in the previous expression
![6*k+6*(n^2+2*n+1)\\6*[k+(n^2+2*n+1)]](https://tex.z-dn.net/?f=6%2Ak%2B6%2A%28n%5E2%2B2%2An%2B1%29%5C%5C6%2A%5Bk%2B%28n%5E2%2B2%2An%2B1%29%5D)
Finally
![\frac{6*[k+(n^2+2*n+1)]}{6} =k+(n^2+2*n+1)](https://tex.z-dn.net/?f=%5Cfrac%7B6%2A%5Bk%2B%28n%5E2%2B2%2An%2B1%29%5D%7D%7B6%7D%20%3Dk%2B%28n%5E2%2B2%2An%2B1%29)
where the last expression is an integer number
So the second step is true, and the complete proposition is True
Answer:
Where are the functions and the graph?
Step-by-step explanation:
Answer:
4.12 kg
Step-by-step explanation:
Regular cakes:
1 dozen normal sponge cakes: 264 g plain flour
Vegetarian cakes:
1 dozen cakes: 264 g plain flour
4 eggs are replaced by 4 * 30 g of flour = 120 g flour
total flour for 1 dozen vegetarian cakes = 264 g + 120 g = 384 g
Proportion for regular cakes:
12 cakes to 264 g flour = 100 cakes to x grams flour
12/264 = 100/x
12x = 26400
x = 2200
2200 g flour for 100 regular cakes
Proportion for vegetarian cakes:
12 cakes to 384 g flour = 60 cakes to y grams flour
12/384 = 60/y
12y = 384 * 60
12y = 23040
y = 1920
1920 g flour for 60 vegetarian cakes
Total flour needed:
2200 g + 1920 g = 4120 g
4120 g * 1 kg/(1000 g) = 4.12 kg
Answer: 4.12 kg
Answer:
A: HL
Step-by-step explanation:
The hypotenuses of these right triangles are marked congruent.
One leg of these right triangles is marked congruent.
The HL theorem applies.