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Eduardwww [97]
3 years ago
7

True or false: the Pythagorean theorem can be applied to every triangle

Mathematics
2 answers:
Mnenie [13.5K]3 years ago
4 0

Answer:

False

Step-by-step explanation:

The Pythagorean theorem can only be applied to right triangles.

Scilla [17]3 years ago
3 0
False because it must have a right angle.
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What are the coordinates of the point is 1/4 of the way from A (-6, -3) to B (6, 1)?
Amiraneli [1.4K]

Answer:

(-3, -2)

Step-by-step explanation:

To find the coordinates of the point is 1/4 of the way from A (-6, -3) to B (6, 1), we are going to be using the midpoint formula, which states that:

The midpoint is at (\frac{x_{1} +x_{2} }{2}, \frac{y_{1} +y_{2} }{2}). Where:

(x_{1}, x_{2}) = (-6, 6)

(y_{1}, y_{2}) = (-3, 1)

Then, the midpoint is at:

(\frac{-6 +6 }{2}, \frac{-3+1}{2}) = (0, -1)

Now, to find the coordinates of the point that is 1/4 of the way, we are going to calculate the midpoint between the point 'A' and the midpoint previously caculated, as follows:

(x_{1}, x_{2}) = (-6, 0)

(y_{1}, y_{2}) = (-3, -1)

⇒ (\frac{-6 +0}{2}, \frac{-3-1}{2}) = (-3, -2)

Therefore, the point is 1/4 of the way from A to B is:  (-3, -2)

8 0
3 years ago
PLEASE ANSWER THIS ITS URGENT
Oksi-84 [34.3K]

Answer:

  • Option C

Explanation:

First, I plotted both the lines on the graph, then I graphed the inequality.<u> </u><em>Please check out image.</em> Looking at the image, we can tell that the graph matches with Graph-C. Hence, Option C is correct.

Hoped this helped!

3 0
2 years ago
Read 2 more answers
Prove for any positive integer n, n^3 +11n is a multiple of 6
suter [353]

There are probably other ways to approach this, but I'll focus on a proof by induction.

The base case is that n = 1. Plugging this into the expression gets us

n^3+11n = 1^3+11(1) = 1+11 = 12

which is a multiple of 6. So that takes care of the base case.

----------------------------------

Now for the inductive step, which is often a tricky thing to grasp if you're not used to it. I recommend keeping at practice to get better familiar with these types of proofs.

The idea is this: assume that k^3+11k is a multiple of 6 for some integer k > 1

Based on that assumption, we need to prove that (k+1)^3+11(k+1) is also a multiple of 6. Note how I've replaced every k with k+1. This is the next value up after k.

If we can show that the (k+1)th case works, based on the assumption, then we've effectively wrapped up the inductive proof. Think of it like a chain of dominoes. One knocks over the other to take care of every case (aka every positive integer n)

-----------------------------------

Let's do a bit of algebra to say

(k+1)^3+11(k+1)

(k^3+3k^2+3k+1) + 11(k+1)

k^3+3k^2+3k+1+11k+11

(k^3+11k) + (3k^2+3k+12)

(k^3+11k) + 3(k^2+k+4)

At this point, we have the k^3+11k as the first group while we have 3(k^2+k+4) as the second group. We already know that k^3+11k is a multiple of 6, so we don't need to worry about it. We just need to show that 3(k^2+k+4) is also a multiple of 6. This means we need to show k^2+k+4 is a multiple of 2, i.e. it's even.

------------------------------------

If k is even, then k = 2m for some integer m

That means k^2+k+4 = (2m)^2+(2m)+4 = 4m^2+2m+4 = 2(m^2+m+2)

We can see that if k is even, then k^2+k+4 is also even.

If k is odd, then k = 2m+1 and

k^2+k+4 = (2m+1)^2+(2m+1)+4 = 4m^2+4m+1+2m+1+4 = 2(2m^2+3m+3)

That shows k^2+k+4 is even when k is odd.

-------------------------------------

In short, the last section shows that k^2+k+4 is always even for any integer

That then points to 3(k^2+k+4) being a multiple of 6

Which then further points to (k^3+11k) + 3(k^2+k+4) being a multiple of 6

It's a lot of work, but we've shown that (k+1)^3+11(k+1) is a multiple of 6 based on the assumption that k^3+11k is a multiple of 6.

This concludes the inductive step and overall the proof is done by this point.

6 0
3 years ago
Read 2 more answers
A growing farming conglomerate increases its water usage at a rate of 10% every year. If it
Elena-2011 [213]

The quantity of water the farming conglomerate would use 17 years from now is 65,708.11.

<h3>What is the amount of water that would be used 17 years from now?</h3>

The formula for calculating the amount of water that would be needed 1 years from now:

FV = P (1 + r)^N

  • FV = Future value
  • P = Present value
  • R = interest rate
  • N = number of years

13000 x 1.1^17 = 65,708.11

To learn more about future value, please check: brainly.com/question/18760477

8 0
2 years ago
6 times the sum of 12 and 8
White raven [17]
12 * 8 = 96 * 6 = 576
6 0
3 years ago
Read 2 more answers
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