🚀 go-pugleaf

See if you get these right!  No prize, just my praise!  Here are the rules for your work:

Since some don't have the square root symbol, this symbol will be used ~, fractions will have the / (ex. 2/5 is two-fifths)

Answers should be in simplest form (example: if you get x=4+~20/2, then you should write x=2+~5)

For word problems:
Clearly state in words the meaning of any variable.  Include the units being used.  (ex.:  "Let r=Sally's rate in miles per hour")

For graphs:
Label the x-axis and y-axis
Use solid lines, dashed lines, and shading when appropriate
For graphs, I suggest using a drawing program such as notepad, Corel Draw, or Paint Shop Pro.


OK  HERE ARE THE PROBLEMS!

1.  Derive the quadratic formula for -bx�+cx-a=0.  Assume b=0

2.  Give an example of a quadratic equation that has
   a. Exactly two real solutions
   b. Exactly one real solution
   c. NO real solutions

3.  Solve for x.  2/x-2 + 3/x+5 = 5x+4/x�+3x-10

4.  A contractor has a 60 pound mixture that is one-fourth cement and three-fourths sand.  How much of a mixture that is half cement and half sand needs to be added to produce a mixture that is one-third cement?

5.  A new labor contract provides for a wage increase of $1.50 per hour and a reduction of 6 hours in the workweek.  A worker who received $441 per week under the old contract will receive $432 per week under the new contract.  Complete the following:
   a. Old work week (hours)
   b. Old wage ($ per hour)
   c. New work week (hours)
   d. New wage ($ per hour)

6.  Solve the following inequalities:
   a. (x-2)(x-2)(x+3)(x+3)<0
                          -
   
   b. (x-2)(x-2)(x+3)(x+3)>0

   c. |n�-5n+4|>0

   d. |t+3/t-2|<1

7.  The professor for a certain history class has decided to calculate grades based on the following:
    Four regular exams  60%
    Attendance & Participation 20%
    Final exam 20%
    Blake has a perfect attendance & participation score and received grades of 78,83,81, and 70 on the four regular exams.  What does Blake need to get on the final to end up with a course grade of at least 80?  Note: your answer should be a range

8.  Graph 2x+3y is not equal to 4.  Note this is an inequality

9.  Consider the points A(-2,5) B(5,3) C(3,-4) in the xy-plane.  These points form a triangle.  Which of the following are true?  Justify your answers!
   a.  ABC is an isosceles triangle  TRUE or FALSE
   b.  ABC is an equilateral triangle  TRUE or FALSE
   c.  ABC is a right triangle TRUE or FALSE

10.  Give an example of a line which contains the origin (0,0), but CANNOT be written in the form Ax+By=C where A,B, and C are integers.  Justify your answers!