What is an essential government role in market economies? to control prices and costs to prevent monopolies and collusion to provide luxury items to market goods and services

In a market economy depending on the level of government control their could potentially be no role for the government. However, government involvement could range from preventing monopolies all the way to impacting prices. It depends on the type of market economy. 

Remember soh-cah-toasoh: cah: toa: now, looking at the picture we can see that we have an angle, the hypotenuse and want to find the value of the adjacent side to the angle. so we use cah to find the adjacent angle. plug in what we have: we need to solve for x now so we get it by itself on one side: plug this into your calculator and you'll find that: