# 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

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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