Answer:
200 cm²
Step-by-step explanation:
Find the areas of all of the faces
17 × 2 = 34 (Top Face)
8 × 15 = 120 (Both Triangles)
15 × 3 = 30 (Bottom Face)
8 × 2 = 16 (Back Face)
Add them all together
120 + 34 + 30 + 16 = 200 cm²
When building a Venn Diagram, I always start from the area with the most overlap to the areas of least overlap. Once you have placed the 3 in the middle, you have counted those people, and therefore you must subtract them from the other surveys. Example: since there are 3 people that like all three subjects, now only have 5 students that like just math and English instead of 8.
Therefore:
A) 36 Students were in the survey
*Add all the numbers within the Venn diagram up. Overlapping doesn't matter because no one is double counted.
B) 6 People liked only Math
*Can't touch any other circle but Math
C) 20 Students liked English and math, but not history
*You add 9+5+6, since these bubbles are not overlapping with history.
I Hope this helps and let me know if you have any further questions!
Is it multiple choice or do you have to write a answer?
Answer:
None of these.
Step-by-step explanation:
Let's assume we are trying to figure out if (x-6) is a factor. We got the quotient (x^2+6) and the remainder 13 according to the problem. So we know (x-6) is not a factor because the remainder wasn't zero.
Let's assume we are trying to figure out if (x^2+6) is a factor. The quotient is (x-6) and the remainder is 13 according to the problem. So we know (x^2+6) is not a factor because the remainder wasn't zero.
In order for 13 to be a factor of P, all the terms of P must be divisible by 13. That just means you can reduce it to a form that is not a fraction.
If we look at the first term x^3 and we divide it by 13 we get
we cannot reduce it so it is not a fraction so 13 is not a factor of P
None of these is the right option.
<h2>
Answer with explanation:</h2>
We are asked to prove by the method of mathematical induction that:

where n is a positive integer.
then we have:

Hence, the result is true for n=1.
- Let us assume that the result is true for n=k
i.e.

- Now, we have to prove the result for n=k+1
i.e.
<u>To prove:</u> 
Let us take n=k+1
Hence, we have:

( Since, the result was true for n=k )
Hence, we have:

Also, we know that:

(
Since, for n=k+1 being a positive integer we have:
)
Hence, we have finally,

Hence, the result holds true for n=k+1
Hence, we may infer that the result is true for all n belonging to positive integer.
i.e.
where n is a positive integer.