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3 years ago

7

Some conveyor belts have two pulleys. If one pulley has a diameter of 45 cm and another has a diameter of 20 cm, what is the rat

io of the smaller diameter to the largest diameter?

1 answer:

siniylev [52]3 years ago

5 0

20:45 or 4:9 if simplified

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Jim’s football team started a play on the 50 yard line. On the first play, the team had a 7-yard gain. On the second play, they

lawyer [7]

This is a basic addition/subtraction question. It's saying that they started at the 50 yard line. On the play, they gained 7 yards. So, we'll add 50+7 = 57.

They're at the 57 yard line at this point. On the second play they lost 10 yards (how unfortunate). Thereby, we will subtract 57-10=47.

50 yards +7 yards. -10 yards.

The answer will be that they'll be on the 47 yard line on the next play.

5 0

3 years ago

Read 2 more answers

Prove the following by induction. In each case, n is apositive integer.<br> 2^n ≤ 2^n+1 - 2^n-1 -1.

frutty [35]

<h2>Answer with explanation:</h2>

We are asked to prove by the method of mathematical induction that:

$2^n\leq 2^{n+1}-2^{n-1}-1$

where n is a positive integer.

Let us take n=1

then we have:

$2^1\leq 2^{1+1}-2^{1-1}-1\\\\i.e.\\\\2\leq 2^2-2^{0}-1\\\\i.e.\\2\leq 4-1-1\\\\i.e.\\\\2\leq 4-2\\\\i.e.\\\\2\leq 2$

Hence, the result is true for n=1.

Let us assume that the result is true for n=k

i.e.

$2^k\leq 2^{k+1}-2^{k-1}-1$

Now, we have to prove the result for n=k+1

i.e.

<u>To prove:</u> $2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1$

Let us take n=k+1

Hence, we have:

$2^{k+1}=2^k\cdot 2\\\\i.e.\\\\2^{k+1}\leq 2\cdot (2^{k+1}-2^{k-1}-1)$

( Since, the result was true for n=k )

Hence, we have:

$2^{k+1}\leq 2^{k+1}\cdot 2-2^{k-1}\cdot 2-2\cdot 1\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{k-1+1}-2\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-2$

Also, we know that:

$-2$

(

Since, for n=k+1 being a positive integer we have:

$2^{(k+1)+1}-2^{(k+1)-1}>0$ )

Hence, we have finally,

$2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1$

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.

$2^n\leq 2^{n+1}-2^{n-1}-1$ where n is a positive integer.

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3 years ago

7 Write an equation for the table of values. Explain how you got your answer.

e-lub [12.9K]

Answer:

y= 3x+1

Step-by-step explanation:

(You can describe the steps for your explanation. See below for the attachment)

5 0

3 years ago

Each angle of an equiangular triangle is what degree angle

Alexandra [31]

An equiangular triangle adds up to 180 so divide that by 3, which is the number of sides, and you get, 60, therefore, each side is 60<span>° angle.</span>

5 0

3 years ago

Citrus2011 [14]

First I'd expand the brackets so that you can re-simplify the values, so:
(2x + 3)(3x + 4)
6x^2 + 9x + 8x + 12
6x^2 + 17x + 12
The answer A. 2x(3x + 4) + 3(3x + 4) can be simplified the same way, with 6x^2 + 8x + 9x + 12, and so the answer is A. I hope this helps!

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3 years ago

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