Determine the difference quotient for f(x)=−6x2−x+4

Aclassroom is made up of 11 boys and 14 girls. the teacher has four main classroom responsibilities that she wants to hand out to four different students (one for each of the four students). if the teacher chooses 4 of the students at random, then what is the probability that the four students chosen to complete the responsibilities will be all boys?

Parabolas y=−2x^2 and y=2x^2+k intersect at points a and b that are in the third and the fourth quadrants respectively. find k if length of the segment ab is 5.

Javier bought a painting for $150. each year, the painting's value increases by a factor of 1.15. which expression gives the painting's value after 77 years?