Find the value of the number LaTeX: aa such that the families of curves LaTeX: y=\left(x+c\right)^{-1}y = ( x + c ) − 1and LaTeX: y\:=\:a\left(x\:+\:k\right)^{\frac{ 1}{3}}y = a ( x + k ) 1 3 are orthogonal trajectories.

Cassie is traveling 675 miles today to visit her brother and his family. so far, she has stopped for gas three times. at the first stop, she put in 7.1 gallons of gas and paid $23.79. at her second stop, she put in 5.8 gallons of gas and paid $19.08. and, at the third stop, 6.6 gallons and paid $20.39. at which stop did casey pay the most for gas?

Select the correct answer. what is the exact value of sin (157.5°)? a. 'sqrt(2 - sqrt(2))/2 b. *"-"'sqrt(2 + sqrt(2))/29 c.'sqrt(2 + sqrt(2))/4" d. "-"sqrt(2 + sqrt(2))/4)

If two parallel lines are cut by a transversal, interior angles on the same side of the transversal are supplementary. a. always b. sometimes c. never