Let $H$ be the orthocenter of the equilateral triangle $\triangle ABC$. We know the distance between the orthocenters of $\triangle AHC$ and $\triangle BHC$ is $12$. What is the distance between the circumcenters of $\triangle AHC$ and $\triangle BHC$?

Louise measured the perimeter of her rectangular scrapbook to be 154 cm. if the scrapbook is 45 cm wide, how long is the scrapbook?

2people are trying different phones to see which one has the better talk time. chatlong has an average of 18 hours with a standard deviation of 2 hours and talk-a-lot has an average of 20 hours with a standard deviation of 3. the two people who tested their phones both got 20 hours of use on their phones. for the z-scores i got 1 for the chatlong company and 0 for talk-a-lot. what is the percentile for each z-score?

What are the solutions of the system? solve by graphing. y = x^2 + 3x + 2 y = 2x + 2