Pay attention here because I'm adding an extra letter to our circle to help keep track of the values in our formula. OUTSIDE of the intercepted arc I'm adding the point E. So the major arc is arc BEG and the minor arc is arc BG. The formula then for us is ∠
. We just don't have values for the arcs yet. If the measure of the central angle is 4x+238, then the measure of arcBG is also 4x+238. Around the outside of the circle is 360°. So we will use it in an expression. ArcBEG=360-(4x+238). Fitting that into our formula we have ![2x+146= \frac{1}{2}[(360-4x-238)-(4x+238)]](https://tex.z-dn.net/?f=2x%2B146%3D%20%5Cfrac%7B1%7D%7B2%7D%5B%28360-4x-238%29-%284x%2B238%29%5D%20)
. Doing all the simplifying inside there we have 
and 
. Multiply both sides by 2 to get rid of the fraction: 4x+292=-8x-116. Combine like terms to get 12x = -408 and divide to solve for x. x = -34. Fourth choice down from the top.
a number is multiplied by 8 and that product is added to 2. The sum is equal to the product of 2 and 25 . Find the number
1 answer:
Answer:
6
Step-by-step explanation:
So we have a number (let's call it x) and it was multiplied by 8 and added by 2. Therefore:
And we are told that the sum is equal to the product of 2 and 25 (or 50). Thus:
To find the number, we just need to find x. Thus, subtract 2 from both sides:
Divide both sides by 8:
And we're done!
So, our original number was 6.
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