if you apply the changes below to the quadratic parent function f(x) = x^2 what is the equation of the new function

shift 6 units right
shift 4 units down

a. g(x) = (x+6)^2 - 4
b. g(x) = (x-4)^2 + 6
c. g(x) = (x-4)^2 - 6
d. g(x) = (x-6)^2 - 4

In trapezoid abcd, ac is a diagonal and ∠abc≅∠acd. find ac if the lengths of the bases bc and ad are 12m and 27m respectively.

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?

The area of each triangle is 7 square units. the surface area of the triangular prism is