<p>9) In a plane, lines are drawn through a given point O so that the measure of each non-overlapping angle formed about point O is 60 degrees. How many different lines are there?</p>
<p>The answer is 3. Please explain.</p>
<p>10) For how many different positive intefer values of K does (Kx-6)^2=0 have integer solutions?</p>
<p>Answer is 4. Pleases explain.</p>
<p>For the first one, imagine a plane with point P. If you were to put three lines through that point, which each had angles of 60 degrees, you would form a semicircular arc. Therefore, half the semi-circle (180 degrees) plus 60 X 3, equals 360 degrees.</p>
<p>for 10
first
(kx-6)^2=0 (squareroot both sides)
kx-6=0
kx=6
in order fro both k and x to be integers, you are basically trying to find factor pairs of 6
in that case, 1,6, 2,3
so thats 4 answers for either</p>
<p>For 9, I think you should draw some lines to see whether how many lines divide the plane into 6. In this case, angle of 60 degrees isn't unnecessary to get the solution.
For 10, according to Rainynightstarz', k * x=6. Because both k and x are integers: </p>
<p>1 * 6 = 6
6 * 1 = 6
2 * 3 = 6<br>
3 * 2 = 6; (total of 4)</p>