<ol>
<li><p>If x is not equal to 0 and x is inversely proportional to y, which of the following is directly proportional to 1/(x^2)?
e.y^2</p></li>
<li><p>Point A is a vertex of an 8-sided polygon the polygon has 8 sides of equal length and 8 angles of equal measure. When all possible diagonals are drawn from point A in the polygon, how many triangles are formed?</p></li>
<li><p>(x-8)(x-k)=x^2-5kx+m
In the equation above, k and m are constants. If the equation is true for all values of x, what is the value of m?
a.8
b.16
c.24
d.32
e.40</p></li>
<li><p>1,2,2,3,3,3,4,4,4,4...
All positive integers appear in the sequence above, and each positive integer k appears in the sequence k times. In the sequence, each term after the first is greater than or equal to each of the terms before it. If the integer 12 first appears in the sequence as the nth term, what is the value of n?</p></li>
</ol>
<p>
</p>
<p>Just flip 1/(x)^(2) = (x)^(2) = (y)^(2). You can also plug numbers in let x = 2. 1/4 or y^2 = 4/1.</p>
<p>
</p>
<p>I HIGHLY doubt this problem will ever appear on the SAT because frankly it will take way too long and it is a sequence (not tested on the SAT). Answer = 632 triangles
Source: [The</a> Number of Triangles Formed by](<a href=“http://www.cs.uwaterloo.ca/journals/JIS/sommars/newtriangle.html]The”>http://www.cs.uwaterloo.ca/journals/JIS/sommars/newtriangle.html)</p>
<p>
</p>
<p>We know 1 appears once, 2 appears twice, 3 appears three times, etc. Summation of 1+2…+11.</p>
<p>1+2+3+4+5+6+7+8+9+10+11 = 66 + 1 (the one is for the first 12) = 67</p>
<p>Sorry didn’t see #8. Here you go:</p>
<p>
</p>
<p>x^2-8x-kx+8k=x^2-5kx+m (FOIL out the left side)
-8x-kx+8k = -5kx+m (subtract x^2)
-8x-kx = -5kx … and … 8k = m (break up the equation)
-x(8+k) = -x(5k) (Factor out a -x)
8+k = 5k
8 = 4k
k = 2</p>
<p>Plug into k = 2 … 8k = m.
8(2) = m
m = 16</p>
<p>some kids need help</p>
<p>@AvidStudent</p>
<p>All of these questions are from BB (2nd edition) practice test #3. I know this because I just took this test yesterday and I recognize the problems. Nevertheless, you misinterpreted #8 because it says the diagonals drawn from ONLY point A. </p>
<p>The solution of #8 itself: The number of triangles that can be formed when you draw all the diagonals from a single point in a regular polygon can be represented by (n-2), where n is the number of vertices. So an 8-sided polygon would yield (8-2) = 6 triangles.
Alternatively, you could just draw an octagon and the diagonals from a single point, and count the triangles formed.</p>
<p>The triangle question is #7…and yes, to contribute and confirm: ‘AvidStudent’ misinterpreted the question. The answer is 6.</p>