Juan is buying flowers for his mother. He has $18 to spend and sees that roses are $3 each and carnations are $1.50 each. He wants to buy 3 times as many carnations as roses and spend all of his money on flowers. Write a system of equations that models this situation. Is there a viable solution that meets Juan’s conditions? Explain.

In djkl, side jk measures 10.6 inches, side kl measures 7 inches, and side jl measures 5 inches. based on the information that is provided, which could be a correct set of angle measures for these sides? angle j = 23.2°, angle k = 33.5°, angle l = 23.2° angle j = 23.2°, angle k = 33.5°, angle l = 123.2° angle j = 123.2°, angle k = 23.2°, angle l = 33.5° angle j = 33.5°, angle k = 23.2°, angle l = 123.2°

The graph below shows the height of a projectile t seconds after it is launched. if acceleration due to gravity is -16 ft/s2, which equation models the height of the projectile correctly?

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?