Problem 1
<h3>Answers:</h3><h3>arc AB = 122 degrees</h3><h3>angle ADB = 61 degrees</h3>
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Explanation:
Arc BC is 58 degrees. The arc AB combines with it to form semicircle ABC, which is basically arc ABC with measure 180
This must mean arc AB is 180-58 = 122 degrees
When in doubt, chances are the number 180 might be involved (in some way) when it comes to geometry problems. Of course, this isn't always a guarantee. The number does show up a lot though.
Once we determine what arc AB is equal to, we cut it in half to get the inscribed angle ADB. Refer to the inscribed angle theorem. Notice how angle ADB subtends the arc AB.
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Problem 2
<h3>Answer: 9</h3>
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Explanation:
x = length of AE
Since AC = 13, this makes EC = 13-x
We'll use the intersecting chords theorem to find x.
(AE)*(EC) = (BE)*(DE)
x*(13-x) = 6*6
13x-x^2 = 36
-x^2 + 13x - 36 = 0
x^2 - 13x + 36 = 0
(x-9)(x-4) = 0
x-9 = 0 or x-4 = 0
x = 9 or x = 4
This means AE could be 9 units long or 4 units long.
Usually the diagram isn't drawn to scale so we don't really use it all too much (other than initial set up). However, if the diagram was drawn to scale, then notice that AE is over the halfway point of AC. This means we would be able to rule out x = 4 since 4 is not over the halfway point of 13. I have a feeling this is what your teacher might be going for.
In short, only AE = 9 is possible.
Answer:
32
Step-by-step explanation:
80 x 0.4
0.40 = 40% in decimal form, 1 = 100% if that helps.
It’s the first one.
less than or equal to, makes it a closed circle
To solve this problem, we are going to use a method called dimensional analysis. This involves canceling out units by multiplying by fractions equivalent to 1. We begin with our given information, that the jet flies 500 miles in one hour, and we multiply that by the fraction 1 hour/60 minutes, which is equivalent to 1. We also have to multiply by 1 minute/60 seconds, because we are looking for the amount of miles the jet flies in seconds.
500 miles/1 hour * 1 hour/60 minutes * 1 minute/60 seconds = 500 miles/3,600 seconds
Now that we have our equivalent in seconds, we must multiply by 10 seconds in order to find our answer.
500 miles/3,600 seconds * 10 seconds = approximately 1.3888 miles
Therefore, the jet flies about 1.39 miles in 10 seconds.
Hope this helps!
Answer: b is the answer
Step-by-step explanation:
