In acute triangle $abc$ we have $\cos a \cos b = \frac{1}{3}$ and $\sin a \sin b = \frac{1}{2}.$ if the area of triangle $abc$ is 1, what is the area of the orthic triangle? (the orthic triangle has vertices at the feet of the altitudes of the triangle.)

Abuyer pays a deposit to the seller in advance before completing the transaction. which term best defines this? a. down payment b. earnest money c. mortgage application fee

20+ ! come and answer quick! triangle mno is reflected over the x-axis and then translated up 4 and right 3. how can the transformation be amended such that the translation can occur before the reflection and have the image remain in the same position? a translate the pre-image down 4 and right 3 and then reflect the figure over the x-axis. b translate the pre-image up 3 and right 4 and then reflect the figure over the x-axis. c translate the pre-image up 4 and left 3 and then reflect the figure over the y-axis. d translate the pre-image down 3 and right 4 and then reflect the figure over the x-axis.

Abag contains 3 red marbles 4 white marbles and 5 blue marbles if one marble is drawn from the bag what is the probability that the marble will be blue