# collegeboard 1st edition questions...

pg 776 #8
pg 807 #15
pg 805 #7
pg 805 #8</p>

<p>thank you.</p>

<p>776 - #8 - perpendicular lines have slopes that are negative reciprocals. Since all four sides of a rectangle are perpendicular, they'll all have a product of -1. So the product of AB and BC is -1, and the product of CD and DA is -1. Multiply those two together and you get 1. </p>

<p>805 - #7 - the faster Josephine goes, the steeper the line (the greater distance in the least amount of time), so you need the least steep line first, followed by the steepest line, followed by the middle line. Only (E) has that. </p>

<p>805 - #8 - When two lines intersect at a point, it means that point is on both lines. So (root6, k) is on y = x^2 - 7 and y = -x^2 + j. First plug (root6, k) into the first equation to get k = -1. Then plug (root6, -1) into the second equation to get j = 5. </p>

<p>807 - #15 - Angles are affected by side lengths, and the side length affects the angle opposite it. Try drawing out some triangles and you'll see the effect that elongating certain sides has on different angles. For example, draw two triangles, each with one side of 6. On the first, make the other two sides 6 and 6. This gives you an equilateral triangle and each angle will be 60. </p>

<p>On the second, make the other two sides 12. This will make the angle opposite the side of 6 smaller than 60. </p>

<p>Each triangle has side XY, and its the angle opposite this side that we're looking for. So to get this angle as small as possible, you need the triangle where the other two sides are the longest, which is triangle XDY. You know XDY has the longest sides because each triangle has XY, and XD is longer than XA, XB, XC and XE. Since they're all right triangles, XD will be the longest hypotenuse. </p>

<p>Hope this helps!</p>