Rectangle MNPQ is rotated using the origin as the center of rotation, resulting in rectangle M’N’P’Q’, as shown below.

Which rotation may have occurred?

a 45° rotation clockwise

a 45° rotation counterclockwise

a 90° rotation clockwise

a 90° rotation counterclockwise

Bring the fraction a/a-4 to a denominator of 16-a^2

The figure shows triangle def and line segment bc, which is parallel to ef: triangle def has a point b on side de and point c on side df. the line bc is parallel to the line ef. part a: is triangle def similar to triangle dbc? explain using what you know about triangle similarity. part b: which line segment on triangle dbc corresponds to line segment ef? explain your answer. part c: which angle on triangle dbc corresponds to angle f? explain your answer. asap

Use the ratio test to determine whether ∑n=14∞n+2n! converges or diverges. (a) find the ratio of successive terms. write your answer as a fully simplified fraction. for n≥14, limn→∞∣∣∣an+1an∣∣∣=limn→∞.