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3 years ago

These are to be written but silly old me needs some help.

Mathematics

1 answer:

Maslowich3 years ago

5 0

In Pattern 1, they all contain the blue points. In Pattern 2, they all seem to share a center point. I'm not sure about Challenge 1 though.

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Complete the statement with a situation and a unit of your choice. Then answer the question

gayaneshka [121]

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3 years ago

Read 2 more answers

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:

kondaur [170]

$\text{Proof by induction:}$
$\text{Test that the statement holds or n = 1}$

$LHS = (3 - 2)^{2} = 1$
$RHS = \frac{6 - 4}{2} = \frac{2}{2} = 1 = LHS$
$\text{Thus, the statement holds for the base case.}$

$\text{Assume the statement holds for some arbitrary term, n= k}$
$1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2} = \frac{k(6k^{2} - 3k - 1)}{2}$

$\text{Prove it is true for n = k + 1}$
$RTP: 1^{2} + 4^{2} + 7^{2} + ... + [3(k + 1) - 2]^{2} = \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2} = \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$

$LHS = \underbrace{1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2}}_{\frac{k(6k^{2} - 3k - 1)}{2}} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1)}{2} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2[3(k + 1) - 2]^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2(3k + 1)^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}$
$= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}$
$= \frac{k(6k^{2} + 15k + 11) + 2}{}$
$= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$
$= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}$
$= RHS$

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.

3 0

4 years ago

Please Help!!

vekshin1

The function p(x) = x^3 is a polynomial. Here the “variable”, x, is being raised to some constant power. The function f(x)=3^x is an exponential function (the variable is the exponent).

Exponential functions tend to get very big very quickly, and though they start out smaller than polynomial functions, they will always eventually become bigger. Notice that the two functions meet at x = 2 and x = 4.

5 0

3 years ago

THIS IS DUE TOMORROW! PLEASE ANSWER THIS!!!

Flura [38]

3: multiply the change per minute by how many minutes: 3.1x15=46.5. 5: Is your opinion, I can't tell you how to feel. But a negative times a negative is a positive, so if there is an even number of negatives no matter how many positives there are it will be positive, if there is an odd number of negatives it will be negative. :) Hope this helps!

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3 years ago

Every _____ tessellates.<br> A. Decagon<br> B. Polygon<br> C. Triangle<br> D. Hexagon

olga2289 [7]

The answer is letter B. Every polygon tesselates. Since the word 'tesselate' here means a pattern of shapes put together without any gaps, then I think every polygon tesselates if they are put side by side together in varying amounts and leave absolutely no gaps or spaces between each other.

8 0

4 years ago