Write an equation to represent the number puzzle. Use x as the
variable. Then find the solution using guess-check-and-improve.
7 added to the square of a number is equal to 7 times the number,
minus 5. What is the number? (There are two solutions.)
a. 7 + x = 7x − 5, 2 c. 7 + x2 = 7x − 5, 2 or 3
b. 7 + x2 = 7x − 5, 3 or 4 d. 7 + x2 = 7x − 5, 4 or 5

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?