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Review 5.1 to 5 Practice for Quiz.pptx

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					Review 5.1 to 5.3
        Practice for Quiz
            Lesson Quiz: Part I Variation

1. The volume V of a pyramid varies jointly as the
   area of the base B and the height h, and
   V = 24 ft3 when B = 12 ft2 and h = 6 ft. Find B
   when V = 54 ft3 and h = 9 ft.
   18 ft2


2. The cost per person c of chartering a tour bus
   varies inversely as the number of passengers
   n. If it costs $22.50 per person to charter a
   bus for 20 passengers, how much will it cost
   per person to charter a bus for 36 passengers?
  $12.50
                               Example 3


Given: y varies inversely as x, and y = 4 when x = 10. Write and
graph the inverse variation function.




            k
      y=                 y varies inversely as x.
            x
             k           Substitute 4 for y and 10 for
      4=
            10           x.
       k = 40            Solve for k.
            40
       y=
             x            Write the variation formula.
                        Example 3 Continued
To graph, make a table of values for both positive and negative values of x.
Plot the points, and connect them with two smooth curves. Because
division by 0 is undefined, the function is undefined when x = 0.



   x         y           x        y
  –2       –20           2       20
  –4       –10           4       10
  –6      –20/3          6      20/3

  –8        –5           8        5
          5.2 Simplifying Rational Expressions Example 1

Simplify. Identify any x-values for which the expression is undefined.

       6x2 + 7 x + 2
        6x2 – 5 x – 5



     (2x + 1)(3x + 2)          (2x + 1)
                         =                     Factor; then divide out common
     (3x + 2)(2x – 3)          (2x – 3)        factors.



The expression is undefined at ????
               Example 2: Multiplying Rational Expressions


Multiply. Assume that all expressions are defined.



       3 x 5y 3                10 x3y4           x–3           x+5
A.                                        B.              
       2 x 3y 7                9 x 2y 5         4x + 20        x2 – 9
            3
        3x y
           5 3         5
                               10x3y4            x–3                x+5
                                                          
        2 x 3y 7           3
                                9 x 2y 5        4(x + 5)       (x – 3)(x + 3)


       5 x3                                         1
       3 y5                                     4(x + 3)
                              Dividing: Example


Divide. Assume that all expressions are defined.


       2x2 – 7 x – 4                      4 x 2– 1
                          ÷
          x –9
            2                         8x2 – 28 x +12

       2x2 – 7 x – 4                  8x2 – 28x +12
                          
          x –9
            2                            4 x 2– 1

       (2x + 1)(x – 4)                 4(2x2 – 7x + 3)
                              
       (x + 3)(x – 3)                  (2x + 1)(2x – 1)

        (2x + 1)(x – 4)                 4(2x – 1)(x – 3)
                                  
         (x + 3)(x – 3)                 (2x + 1)(2x – 1)
           4(x – 4)
            (x +3)
             Example 5: Solving Simple Rational Equations


Solve. Check your solution.

      x2 – 3 x – 10
                          =7
          x–2

         (x + 5)(x – 2)
                               =7       Note that x ≠ 2.
            (x – 2)
                      x+5=7

                           x=2
   Because the left side of the original equation is undefined when x = 2,
   there is no solution.

				
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