so, what we do is, we multiply the value by a power of 10, that moves the recurring numbers to the left of the dot, in this case we want moved the "15", so we'll need two zeros, so we'll be using 100.
![\bf 0.151515\overline{15}~\hspace{7em}x=0.151515\overline{15} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{array}{|lll|ll} \cline{1-3} &&\\ 100\cdot x&=&15.1515\overline{15}\\ &&15+0.1515\overline{15}\\ &&15+x \\&&\\ \cline{1-3} \end{array}\implies 100x=15+x \\\\\\ 99x=15\implies x=\cfrac{15}{99}\implies \stackrel{simplified}{x=\cfrac{5}{33}}](https://tex.z-dn.net/?f=%5Cbf%200.151515%5Coverline%7B15%7D~%5Chspace%7B7em%7Dx%3D0.151515%5Coverline%7B15%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7B%7Clll%7Cll%7D%20%5Ccline%7B1-3%7D%20%26%26%5C%5C%20100%5Ccdot%20x%26%3D%2615.1515%5Coverline%7B15%7D%5C%5C%20%26%2615%2B0.1515%5Coverline%7B15%7D%5C%5C%20%26%2615%2Bx%20%5C%5C%26%26%5C%5C%20%5Ccline%7B1-3%7D%20%5Cend%7Barray%7D%5Cimplies%20100x%3D15%2Bx%20%5C%5C%5C%5C%5C%5C%2099x%3D15%5Cimplies%20x%3D%5Ccfrac%7B15%7D%7B99%7D%5Cimplies%20%5Cstackrel%7Bsimplified%7D%7Bx%3D%5Ccfrac%7B5%7D%7B33%7D%7D)
Answer:
0.666
Step-by-step explanation:
<h3>
Answer: 60 degrees</h3>
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Explanation:
The given angle is ∅ = 300. This x value is between 270 and 360, so we're in quadrant IV (the southeast quadrant)
The rule to get the reference angle y for this quadrant is
Ф = 360-∅
This tells us the angle made with the positive x axis
Ф = 360-∅
Ф = 360-300
Ф = 60
A 60 degree angle forms with the positive x axis as shown in the diagram below.