Every triangle in the figure at right is equilateral. what is the measure of ∠age?

step:

1. use the corollaries of the isosceles triangle theorem. each angle in an equilateral triangle measures 60° 2. use those two angles to find m∠age.

problem:
m angle agf =
m angle fge =
m angle age = m angle agf + m angle fge
= __ + __
=

You and a friend race across a field to a fence and back. your friend has a 50-meter head start. the equations shown represent you and your friend's distances dd (in meters) from the fence tt seconds after the race begins. find the time at which you catch up to your friend. you: d=∣−5t+100∣d=∣−5t+100∣ your friend: d=∣−313t+50∣∣

At the olympic games, many events have several rounds of competition. one of these events is the men's 100-meter backstroke. the upper dot plot shows the times (in seconds) of the top 8 finishers in the final round of the 2012 olympics. the lower dot plot shows the times of the same 8 swimmers, but in the semifinal round. which pieces of information can be gathered from these dot plots? (remember that lower swim times are faster.) choose all answers that apply: a: the swimmers had faster times on average in the final round. b: the times in the final round vary noticeably more than the times in the semifinal round. c: none of the above.

Consider that lines b and c are parallel. what is the value of x? what is the measure of the smaller angle?