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Math 152B Midterm III

Please do all of the following problems.  All work and all answers must be done on your own paper.  Credit earned will be based on the steps that you show that lead to the final solution.  Good Luck!

 

 

Problem 1: 

Write down the quadratic formula

  Solution

 

Problem 2:

Aislynn paid $26 for two adult tickets and three children’s tickets to the movies.  Kevin paid $48 for 4 adult tickets and 5 children’s tickets.  What is the price of an adult ticket?

  Solution

 

Problem 3:

Sketch the solution set for the following inequalities

A     3x + y  <  6

  Solution

B.     x  >  2

  Solution

C.    2x + y  >  0

  Solution

 

Problem 4:

Use the discriminant to determine the nature of the roots of the following quadratics.

A.     2x2 + 3x + 4  =  0

  Solution

B.    3x2 + x - 4  =  0 

  Solution

C.      4354324532453x2 + 2x + 6798797698766  =  0

  Solution

 

Problem 5:   Solve the following system.

  2x - 3y  = 13

    x + 2y   =  -4

Solution

 

Problem 6:  

Solve the equation by using the factoring or root method.

A) 10x2  =  13x + 3 

            Solution

B)   2x2 + 15 = 11

  Solution

 

Problem 7:  

Solve the following by completing the square

   5x2 - 20x + 21  =  0

Solution

 

Problem 8: 

Solve the following by any method

A)   6x2 + 5x - 4  =  0 

    Solution

B)    2x3 - 18x  =  0 

    Solution

 

Problem 9 

The pressure p in pounds per square foot of a wind is directly proportional to the square of the velocity v of he wind.  If a 10-mi/hr wind produces a pressure of 0.3 lb/ft2, what pressure will a 100-mi/hr wind produce?

    Solution

Problem 10

Please answer the following true or false.  If false, explain why or provide a counter example.  If true, explain why.

A)  Suppose that (1,2) and (3,5) are both solutions to the system of equations

        ax + by  =  c

        dx + ey  =  f

Then the two equations represent the same line

    Solution

B)  If -  1 is a root of the quadratic equation

        ax2 + bx + c = 0

then

    +  1 is also a root.

    Solution

 

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