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.
you need to make the denominators that same and then you simply simplify the problem
9 4/12 = 9 1/3
You could either divide the 6 on each side and have 4=-3+x, so x=7, or you could distribute the 6 into the expression, so 24=-18+6x. Then 42=6x, and x=7.
Answer:
It would take them 6.667 minutes to paint 50 square feet together.
Step-by-step explanation:
This is a classic work problem. If Sam can do the job in 10 minutes, she can get done 1/10 of the job in one minute. If you can do the job in 5 minutes, you can 1/5 of the job done in one minute. To find out how many minutes it will take them together to paint 25 square feet, set the addition of their times equal to 1/x:
x is how long it takes them to get the job done together. Find the common denominator and multiply it through be everything to get rid of the denominators altogether. That denominator is 10x:
Simplify to get the simple equation x + 2x = 10 and 3x = 10. That means that x=3 1/3. That's how long it takes to do 25 square feet. Double that time for 50 square feet.
Answer:
Step-by-step explanation:
- -2.8f + 0.9f - 12 - 4 =
- (-2.8 + 0.9)f - (12 + 4) =
- -1.9f - 16
