Given: D is the midpoint of AB; E is the midpoint of AC. Prove: DE ∥ BC

On a coordinate plane, triangle A B C is shown. Line segment D E goes from side A B to side A C. Point A is at (2 b, 2c), point E is at (a + b, c), point C is at (2 a, 0), point B is at (0, 0), and point D is at (b, c).

Complete the missing parts of the paragraph proof.

Proof:

To prove that DE and BC are parallel, we need to show that they have the same slope.

slope of DE = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFraction = StartFraction c minus c Over a + b minus b EndFraction = =

slope of BC =

Therefore, because
, DE ∥ BC.

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?