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3 years ago

12

A line crosses the coordinates (-3,5) and (4,-2). What is the slope of the line?

1 answer:

ICE Princess25 [194]3 years ago

8 0

Answer:

Slope = -1

Step-by-step explanation:

$\frac{-2-5}{4-(-3)}=\frac{-7}{7} =-1$

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Use an induction proof to prove this statement:<br> For n≥1, 4^n+5 is divisible by 3.

Tpy6a [65]

Answer:

See below

Step-by-step explanation:

We shall prove that for all $n\in\mathbb{N},3|(4^n+5)$ . This tells us that 3 divides 4^n+5 with a remainder of zero.

If we let $n=1$ , then we have $4^{1}+5=9$ , and evidently, $9|3$ .

Assume that $4^n+5$ is divisible by $3$ for $n=k, k\in\mathbb{N}$ . Then, by this assumption, $3|(4^n+5)\Rightarrow4^k+5=3m,\: m\in\mathbb{Z}$ .

Now, let $n=k+1$ . Then:

$4^{k+1}+5=4^k\cdot4+5\\=4^k(3+1)+5\\=3\cdot4^k+4^k+5\\=3\cdot4^k+3m\\=3(4^k+m)$

Since $3|(4^k+m)$ , we may conclude, by the axiom of induction, that the property holds for all $n\in\mathbb{N}$ .

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