<p>Will greatly appreciate help or tips from anyone. Need the last few explanations the most. Thanks.</p>
<p>Here's something I typed up for my tutor so it might sound a little odd. </p>
<ol>
<li>Picked K, was about to assume that two of the shaded triangles were equal to the area of EGFH but I couldn't justify that with geometric rules so I thought it was indeterminable, I am probably just missing a rule. But if I had assumed what I thought was right then it would 2:6 which is the answer 1:3.</li>
<li>Don't understand this one at all. Tried to isolate Y on both sides of the equation and input both equations into the calculator and I got two parallel lines. The first equation would be y= c-bx/a and the second one would be y = c+bx/a. Their slopes would have to be negative reciprocals to be perpendicular like the answer says it is wouldn't they? </li>
<li>I think I kind of see my mistake now. I picked K and didn't notice the spike(triangles on top of each side of the inner hexagon. Only 4 lines from the tips of the triangles to the other tips and then 4 lines splitting 4 spikes on one side and 4 spikes on the other so 8 together. Is this reasoning correct? </li>
<li>I have no idea what this question is asking for or how the right answer or any yield in an infinite number of solutions.</li>
<li>Stupid mistake,only took in the account for one small window when there were two. See my mistake. Don't need to go over.</li>
<li>I got this right but only be a lengthy plug and chug. Okay so you have A= P(1 + 0.01i)^n so then my next step would be divide P by both sides. A/P= (1+0.01i)^n. Then I would multiply both sides 1/A to get P isolated. P= (1+0.01i)^n/A. But there are no choices here that match up with this at all. So i had to resort to a plug and chug method. Strangely the correct answer is what I found but flipped... O_o. Did I have some algebraic mistake when I was doing the problem? I have went over it a couple of times and don't see anything wrong with my algebra.</li>
<li>Don't understand at all. How can you find the answer when n can be anything???!!!</li>
<li>Don't understand what the question is asking for at all.</li>
</ol>
<ol>
<li><p>All of the triangles have the same area, which can be proven using the formula for area of a triangle, (1/2)bh. For triangle AGB, you can multiply half the length of BA (half of the base) by half the distance of BF (triangle height). Do this with the other triangle type, say triangle AGE. You can multiply half the length of AE (half of the base) by half the length of BA (height). Using this reasoning, one can see that the two triangle types have the same area. So, ff you draw in line EF, it becomes clear that the ratio of unshaded to shaded triangles is 2:6, or 1:3. Hope that wasn’t super confusing…</p></li>
<li><p>If a, b, and c are all positive integers, there is no way that those two equations could represent the same line unless b = 0 (which it can’t, b/c it needs to be positive). So III is incorrect. Also, if you solve each equation for y (put it in slope-intercept form), then you can see that the two slopes differ from each other. Therefore, there is no way that the two lines can be parallel, b/c parallel lines have the same slope. So, only II is true: the lines must be intersecting.</p></li>
<li><p>You are correct.</p></li>
<li><p>A system of equations has an infinite number of solutions if they both simplify to be the same equation. So this question is asking the value of a that would make the second equation equivalent to the first. So you can multiply the first equation by 3 to get 6x - 3y = 24. The left side of the second equation is 6x - 3y, the same as the first, so you can use direct substitution to get 24 = 4a. Solve to get a = 6.</p></li>
<li><p>To solve for P, you can divide both sides of the equation by (1+0.01i)^n. You’re left with only P on the right and your answer on the left (K).</p></li>
<li><p>I’ll think about it. I have no idea either :P</p></li>
<li><p>The two numbers that are 5 units away from -3 are -8 and 2. From this point, you can plug these numbers into each of the equations for x to see which works (F).</p></li>
</ol>
<p>I hope this helped and was not optimally confusing. :)</p>
<p>■■■■■ oh my bad! And btw if you needed help with 59 i got the explanation. So -3=x is the only solution right? So that means that the factors of the that equation would be (x+3) and (x+3). Because set x+3=0 and you get x=-3. And then you mulitply (x+3)(x+3) and get x^2+6x+9=0 and then you set 6x= mx. See how 6x matches up in line with mx for the original equation? Then you simply isolate m by didviding x on both sides and you get 6=m!</p>
<ol>
<li>Note that the area of ABC (denoted [ABC]) is [ABC] = (1/2) xy sin 70°. Also, [PQR] = (1/2) xy sin 110°. </li>
</ol>
<p>Since sin 70° = sin 110°, we can say that [ABC] = [PQR] = 30, so the answer is J.</p>
<ol>
<li>Suppose the arithmetic sequence is given by a<em>n = a + (n-1)d so that a</em>6 = a + 5d = 8 and a_10 = a + 9d = 13. Hence we have the system</li>
</ol>
<p>a + 5d = 8
a + 9d = 13</p>
<p>Subtract the first equation from the second to obtain 4d = 5 → d = 1.25. Substituting into either equation we get a = 1.75.</p>
<p>Finally, the sum of the first four terms is a + (a+d) + (a+2d) + (a+3d) = 4a + 6d = 4(1.75) + 6(1.25) = 14.5, G. There’s probably a faster way but this method works.</p>