Derive the equation of the parabola with a focus at (0, –4) and a directrix of y = 4. (2 points) a f(x) = –16x2 b f(x) = – x2 c f(x) = x2 d f(x) = 16x2

In a recent basketball game between the storm and the chargers, the number of points scored by the storm in the first half was equal to the number of points scored by the chargers in the second half of the game. in the first half, the storm scored 64 points, which is one - third of the total points that were scored during the game. during the second half, the chargers scored 16 points more than one - fourth the points scored in the game. you want to know how many total points that were scored during the game. 1. write an equation that models this situation. then, solve the equation. 2. how many total points were scored during the game? explain your reasoning. 3. does your answer make sense? justify your reasoning.

Figure abcde is a regular pentagon. segment ae is located at a (2, 1) and e (4, 1). what is the perimeter of abcde? 4 units 6 units 8 units 10 units

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?