<p>For 2, draw a perpendicular from R to the base PT. Assume it intersects the line PT at point X. For the purpose of calculating the areas think of PT as the base of the large enclosing triangle RQT and RX as its height. So the area of the large enclosing triangle RQT is (1/2) PT*RX.</p>
<p>You need to recall a bit of geometry to take the next step. The triangles RPT and RQS are “similar”. They have the same angles, and therefore their sides (including their height) have the same relative proportions – i.e. the small triangle’s sides are 1/2 of those of the large triangle, and the same for the heights.</p>
<p>If this isn’t obvious, you need to recall a simple theorem regarding the angles cut by the lines through the midpoints. Look this up.</p>
<p>Then the area of the small triangle (above the trapezoid) is (1/2) (PT/2)*(RX/2) or 1/4 of the area of the large triangle. That means that the trapezoid’s area is 3/4 that of the large enclosing triangle.</p>
<p>If you forgot all about similar triangles then you can still get this problem. Note that no where are the lengths of the sides of the triangle specified. That suggests that the ratio is most likely independent of the lengths! So pick a simple 3-4-5 right triangle for RPT (and hence area 6), and use the Pythagoras’s theorem to figure out the sides of the small triangle above. You’ll quickly see that The sides of the small triangle are 1.5, 2, and 2.5 (and hence area 1.5). The trapezoid’s area is the difference, 4.5.</p>
<p>For 4, I got C as the answer. Recall v=d/t. We know the time is 3 minutes, and we need to find the distance she travels. if she travels from the first marker, to n+1 marker, you will find by drawing a line with markers, that the distance is 66<em>n. Or you can think of it as (n+66)-66, since 1 marker is 66 meters from the last. Since t=3, d/t=66</em>n/3=22n. which is C. Someone feel free to correct if im wrong</p>
<p>I’m pretty sure #1 is A) 40. The area of the floor needed to be covered is 360 in.^2 and the are of the piece of tile is 9. Then 360/9=40. I don’t understand how you got 200…</p>
<h1>3 I think it’s D) 45 i would put the 2in cube next to the 3 in cube and the 1in cube on top of the 2 in cube. so l=5 w=3 and h=3 5x3x3=45</h1>
<h1>5 (270/3)<em>4=360 (360/3)</em>4=480 I don’t know if that’s completely right though, is there a change in # of deers from say the beginning of 1999 and end of 1998 or is that counted as one thing? Working backwards, at the start of 1998 if it was 480, by the end of 1998/beginning of 1999 3/4 of 480 would be 360 then by the end of 1999 3/4 of 360 would be 270.</h1>
<h1>6 2000-(2<em>9)=1982. If he worked 9 consecutive terms and each term is 2 years, then 9</em>2=18 which is his total length worked and if he retired in 2000, 2000-18=1982</h1>
<h1>7 I said B) One, can’t really explain it but there would only be one other point 5 units from A and 3 units from B. If you draw it out it’s easy to see. If you connect the dots it makes a quadrilateral.</h1>
<h1>8 96 in.^3. Original vol=6<em>6</em>6= 216 in.^3. Once you cut off the 1 in. segments you’re left with l=4 in. w=4 in. h=6 in. 4<em>4</em>6=96in.^3</h1>
<h1>9 19. I got C) 1,400 but I am not sure if that is right. I just did 70*20 but I think I was supposed to factor in something about how it’s measuring the length from the time the front enters to the time the back leaves. That one’s tricky and would have stumped me if I was actually taking the test. 20. I started to work out but it took way too long and there were like 10 more steps that I had to do and if I was on taking the test I probably would have said screw it. Sorry I couldn’t help with that one!</h1>
<h1>10 D) 3(X+Y)=10(X)+Y. Three times the sum of the two digits 3(X+Y) is equal to the the number XY, X being the 10s place digit and Y being the 1s place. So you must multiply X by 10 to get it in the 10s place and adding Y since it’s already in the 1s place 10(X)+Y.</h1>
<h1>11 C) be built. I’m pretty sure it should say “have been built”. Cause it’s saying the pyramid is thought to have been built some 4,300 years ago. It wouldn’t make sense to say “The pyramid is thought to be built some 4,300 years ago.”</h1>
<h1>12 A) 3. If the k is 3 and b=15 than a must be 5. 5<em>3=15, 15</em>3=45, 45*3=135, and so on.</h1>
