# ALgebra problems

8. The difference of two numbers is 36. The larger is 6 less than 4 times the smaller. What are the two numbers?

9. The base of a ladder is 6 feet away from the wall. The top of the ladder is 7 feet from the floor. Find the length of the ladder to the nearest thousandth.

10. A company produces doll houses and sets of doll furniture. The doll houses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week. Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week. Write a system of inequalities representing this situation, where *x* is the number of doll houses and *y* is the number of furniture sets.

11. Evaluate , if possible.

12. Evaluate , if possible.

13. State whether is rational or irrational.

14. State whether is rational or irrational.

15. The area of a square is 83 cm^{2}. Find the length of a side to the nearest hundredth.

16. The time in seconds that it takes for an object to fall from rest is given by , in which *s* is the distance fallen (in feet). Find the time required for an object to fall from the ground from a building that is 800 feet high. Round your answer to the nearest hundredth of a second.

17. Simplify.

18. Simplify. Assume *x* represents a positive real number.