What are the coordinates of X′ for the transformation LaTeX: \left(T_{<-3,1>}\circ D_4\right)\left(\bigtriangleup TUX\right)( T < − 3 , 1 > ∘ D 4 ) ( △ T U X ) of T(−7, −6), U(−8, 3), and X(2, 1)?

(geometry help please)

Michael is training for a marathon. in his first week he plans to run 8miles. what path should he take

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?

What is the area of the shaded sector?