<h1>7 Positive integers x, y, and z satisy the equations x^(-1/2)=1/3 and y^z=16. If z>y, what is the value of x+y ?</h1>
<p>a.5
b.7
c.11
d.13
e.15</p>
<p>Here should be a graph for #8 but I don't know how to upload it.</p>
<h1>8 In the semicircle above, the center is at (4,0). Which of the following are x-coordinates of two points on this semicircle whose y-coordinates are equal?</h1>
<p>a.1 and 6
b.1 and 8
c.2 and 6
d.2 and 8
e.3 and 6</p>
<p>You know that 1/sqrt(x) = 1/3, so sqrt(x) = 3. Square both sides, and x = 3^2 = 9. For y^z, it’s either 2^4 or 4^2… Since z>y, it must be 2^4, so y = 2. So x+y = 11.</p>
<p>Not sure about the second one as I don’t have a book nearby. Maybe take a picture and upload it via imgur.com? </p>
<p>For some reason I don’t really like #7 in terms of quality (it is two disjoint problems). Just my opinion though.</p>
<p>For #8, the answer is C. A little tricky to explain without a picture, but the main idea is that (assuming the semicircle is oriented correctly) the circle/semicircle is symmetric about x = 4, and since 4 is halfway between 2 and 6, the y-coordinates at x=2 and x=6 should be equal.</p>