Yes. / = divide & * = multiply.
As for the equation, 10 divided by 1 2/3 is 15
<span>Let's say in general you want "n" adjacent squares. Each one needs a top, so that's n toothpicks. Each one needs a bottom, so that's another n toothpicks, and we're up to 2n total. You need one on the far left, and one on the far right, which brings us up to 2n + 2 toothpicks. Now we need to worry about the middle ones. But notice that you don't need n toothpicks for the interior because adjacent squares share. It turns out that you only need n-1. That brings us up to a grand total of 3n + 1 toothpicks, which would be 301 for n = 100.
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Answers:
- Problem 1) 40 degrees
- Problem 2) 84 degrees
- Problem 3) 110 degrees
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Explanation:
For these questions, we'll use the inscribed angle theorem. This says that the inscribed angle is half the measure of the arc it cuts off. An inscribed angle is one where the vertex of the angle lies on the circle, as problem 1 indicates.
For problem 1, the arc measure is 80 degrees, so half that is 40. This is the measure of the unknown inscribed angle.
Problem 2 will have us work in reverse to double the inscribed angle 42 to get 84.
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For problem 3, we need to determine angle DEP. But first, we'll need Thales Theorem which is a special case of the inscribed angle theorem. This theorem states that if you have a semicircle, then any inscribed angle will always be 90 degrees. This is a handy way to form 90 degree angles if all you have is a compass and straightedge.
This all means that angle DEF is a right angle and 90 degrees.
So,
(angle DEP) + (angle PEF) = angle DEF
(angle DEP) + (35) = 90
angle DEP = 90 - 35
angle DEP = 55
The inscribed angle DEP cuts off the arc we want to find. Using the inscribed angle theorem, we double 55 to get 110 which is the measure of minor arc FD.
Let, speed of 1st bicyclist is x.
So, speed of 2nd bicyclist is x-3 .
We know, relative speed when two objects moves towards each other :

Now, distance travelled in 3 hours is (98-2) miles .
So,

Therefore, speed of bikes are 17.5 mph and 14.5 mph.
Hence, this is the required solution.
7,3...
since we don't know how many stops after there are we will assume it just continues on and put three dots. (...)
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