2 Math Questions

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1

<p>Here it goes:</p>

<h1>1 Here's the figure:</h1>

<p><a href="http://oi40.tinypic.com/24291ee.jpg%5B/url%5D"&gt;http://oi40.tinypic.com/24291ee.jpg&lt;/a&gt;&lt;/p>

<p>In the figure above, sides AB and CD of a trapezoid ABCD are congruent. Trapezoids congruent to ABCD are placed adjacent to one another, sharing one of their nonparallel sides as shown. This is continued until the trapezoids form a closed ring. How many trapezoids, including the 3 shown, are needed to form the closed ring?</p>

<p>The answer is 18. I somehow managed to imagine how the figure would be completed and got to 18, but I'm sure that's not the way it's supposed to go down...</p>

<h1>2</h1>

<p>If (x+a)(7x+b)=7x^2+cx+6 for all variables of x and if a and b are positive integers, what is one possible value of c?
Answers: 13, 17, 23, 43</p>

<p>Thx!</p>

2

<p>For the first one, each trapezoid has a 20 degree increase every time. 18 * 20 = 360 degrees, so the answer would be 18. </p>

<p>For the second one, the key part is the six. a * b = 6, so if you plug in random numbers for a and b (ex: 3, 2), you will get one of the answers.</p>

3

<p>just in case you don’t get my solution for the first one, here’s a diagram to better understand the problem: <a href=“http://i44.■■■■■■■.com/63yd6x.jpg[/url]”>http://i44.■■■■■■■.com/63yd6x.jpg&lt;/a&gt;&lt;/p&gt;

4

<p>Omipotent24 </p>

<p>Not trying to hijack this question, but how did you figure out that the change in each trapezoid is 20 degrees?</p>

5

<p>@ Solate: I think the diagram is a good explanation for the problem. It can be found here: [Image</a> - ■■■■■■■ - Free Image Hosting, Photo Sharing & Video Hosting](<a href=“http://■■■■■■■.com/view.php?pic=63yd6x&s=5]Image”>http://■■■■■■■.com/view.php?pic=63yd6x&s=5). The angle would be 20 degrees because the two angles of the trapezoid equal 160, and there’s 180 degrees in a line. The difference would equal 20 degrees and it would continue all the way until you reach 360 to form a complete circle.</p>

6

<p>Thanks xD I even tried to do that initially when I was looking at the picture, I guess I failed somehow xD</p>