Let f(x) = x + 4 and g(x) = x-3. If g is a vertical translation off, how many units and in what direction is f translated to form g?

Atorch and a battery cost 2.50 altogether.the torch costs 1.50 more than the battery.what fraction of the total price is the torch? give your answer in its simplest form.

Drag each number to the correct location on the statements. not all numbers will be used. consider the sequence below. -34, -21, -8, 5, complete the recursively defined function to describe this sequence

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?