CoolStuffYT

Well, that's for the SUM of the interior angles. The question is asking for the "interior angle," which is just one angle.

So you got the interior angles as 540 for a pentagon and 720 for a hexagon, right? That is correct.

Now just divide 540 by 5 because a pentagon has 5 angles to find the measure of one angle. 540 divided by 5 is 108.

Same thing - divide 720 by 6 b/c a hexagon has 6 angles. 720 divided by 6 is 120.

Now - \(108:120=9:10=\frac{9}{10}\)

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2) We see that tenth is 10, second is 2, and thirty-fourth is 34, and \(10-2=8\) as well as \(34-10=24\).

Now, we see that \(\frac{24}{8}=3\), so the common ratio is 3.

Therefore, the fourth term in the geometric sequence is in the \(24\times 3=72\)nd term in the arithmetic sequence.

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What is the perimeter of a rectangle?

It is \(2l+2w\), where \(l\) is the length and \(w\) is the width.

However, we can write \(l\) in terms of \(w\), because it says so up in the question.

\(l=2w+8\) because twice the width is \(2w\), and we add 8.

\(w=w\)

Substituting, we get \(2(2w+8)+2(w)=2(2w+8)+2w\).

According to you, we should not simplify.

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Elaborating on CPhill's answer...

See that 2:43PM to 3PM is just 2:43PM to 2:59PM, with one extra minute. We can do this to avoid confusion. This is simple. \(59-43=16\), and \(16+1=17\). Therefore, the time from 2:43PM to 3PM is 17 minutes long.

3PM to 5PM is simple - we see there are \(5-3=2\) hours between the times. This accounts for \(2\times 60=120\) minutes between 3PM to 5PM, because 60 minutes make up an hour.

Finally, we can see that 5PM to 5:18PM is simply 18 minutes. 

Adding all the minutes up, we get \(17+120+18\) total minutes walking and that equals \(155\) minutes. This is also equal to 2 hours 35 minutes.

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Thank you!

We know a square has all 90 degree angles and equivalent side lengths, and the diagonal is \(10\sqrt2\).

So, you could make a right triangle, with two of the sides and the diagonal!

\(x^2+x^2=(10\sqrt2)^2\) so \(2x^2=200, x^2=100, x=10\)because x cannot be negative.

This is the side length of the square, so now just multiply it by four to get 40 cm.

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\(343_{10}=1000_7\)

So the 4 or 5 must be in the 49's, 7's or 1's place.

There are \(49\times 2=98\) , \(7\times 2=14\) , and \(1\times 2=2\), so \(98+2+14=114\).

There are 114 of those integers.

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35%<40% and the rewards are greater, so the company should invest.

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We could count it out, but that would take a long time.

We could make a pairing tree, but there is an even easier way!

If we just multiply the numbers, we get the total number of outifts! \(4\times 7\times 3=84\).

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:P