Mr. Aškinson spends a total of $47 to buy some packages of art pencils and some erasers for his class. The pencils cost $8 per package, and he spends $7 on erasers.
Complete the equation that could be solved to find the number of packages of pencils, n, Mr. Atkinson buys.

Polygon mnopq is dilated by a scale factor of 0.8 with the origin as the center of dilation, resulting in the image m′n′o′p′q′. the coordinates of point m are (2, 4), and the coordinates of point n are (3, 5). the slope of is .

In the figure below, ∠dec ≅ ∠dce, ∠b ≅ ∠f, and segment df is congruent to segment bd. point c is the point of intersection between segment ag and segment bd, while point e is the point of intersection between segment ag and segment df. the figure shows a polygon comprised of three triangles, abc, dec, and gfe. prove δabc ≅ δgfe.

How many ordered pairs of positive integers satisfy xy=32?