# solving quadratic equations and inequality

Solve

13) Approximately 1% of US students were studying abroad in 1994. Based on data from the Institute of International Education, the number of US students in study-abroad programs from 1994-1997 can be modeled using the equation

y = 7248x + 76207, where x =0 corresponds to year 1994. Using this model, what would you expect to be the number of US students studying aboard in 1995?

14) A storage tank has two inlet pipes, A and B. With only inlet pipe A open, the tank fills twice as fast as with only inlet pipe B open. With both pipes open, the tank fills in 6 hours. How long does it take for each inlet pipe alone to fill the tank?

15) A chemist needs a 12% nitric acid solution. How much 8% acid should be mixed with 40 ml of 20% acid to get the 12% solution?

Perform the indicated operations. Write the answers in standard form.

16) (6 + 7i)(6 - 7i)

17) (3 - 4i) + (2 - 6i) - (1 - i)

18) solve by factoring: x^2 - 5x = 6

19) solve the completing the squares: r^2 + 8r + 10 = 0

20) clear the equations of fractions and solve using quadratic formula: 2/3x^2 + 9/4x = 1/3

21) Lisa plans to replaces the floor covering in her 12' x 14' kitchen. She wants to have a border of even width made of a special material, but has decided she can only afford about 30 square feet of the special material. How wide a border can she have?

22) solve sqrt(x - 2) + 2 = sqrt(x +5)

23) solve the quadratic inequality. Write the answer in interval form, and graph the answer on a number line. x^2 + x >=20

24) solve the rational inequality 3/(5 -2x) <3

25) solve the absolute value inequality: |4b + 3|> 7

#### Solution Summary

It shows step-by-step solutions on how to solve quadratic equations and inequality. It also includes several examples of word problems, such as time needed when working together.