Determinants are used to write an equation of a line passing through two points. An equation of the line passing through the distinct points $$\left( x _ { 1 } , y _ { 1 } \right) \text { and } \left( x _ { 2 } , y _ { 2 } \right)$$ is given by $$\left| \begin{array} { l l l } { x } & { y } & { 1 } \ { x _ { 1 } } & { y _ { 1 } } & { 1 } \ { x _ { 2 } } & { y _ { 2 } } & { 1 } \end{array} \right| = 0.$$ Use this information to work the exercise. Use the determinant to write an equation of the line passing through (3, -5) and (-2, 6). Then expand the determinant, expressing the line s equation in slope-intercept form.

10 ! a train starts from grand city and travels toward belleville 388 miles away. at the same time, a train starts from belleville and runs at the rate of 47 miles per hour toward grand city. they pass each other 4 hours later. find the rate of the train from grand city.

What is negative 3/9 times negative 2/8 ?

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?