Download varies inversely

Percents
Direct and
Inverse
Variation
Simplifying
Rational
Expressions
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Ratio and
Proportions
Review
Solve the proportion.
16 12

4
x
16 12

4
x
16 x  12  4
16 x 48

16 16
x3
Solve the proportion.
w  4 5

2w
6
w  4 5

2w
6
6( w  4)  5(2 w)
6 w  24  10 w
6 w
 6w
24 16 w

16
16
3
 w
2
Solve the proportion.
8
3

x  2 x 1
8
3

x  2 x 1
8( x  1)  3( x  2)
8 x  8  3x  6
 3x  3x
5x  8  6
8 8
5 x 14

5
5
14
x
5
Solve the proportion.
2
a

a7 5
2
a

a7 5
 2  5  a(a  7)
 10  a  7 a
2
0  a  7 a  10
0  (a  2)(a  5)
a 2  0 a5  0
a2
a5
Check your answers:
2
2

27 5
2 2

5 5
2
2
5

57 5
2 5

2 5
Solve the proportion.
2 t 1

3t
t
2 t 1

3t
t
Check your answers:
2  t  3t (t  1)
2t  3t 2  3t
2t
 2t
0  3t 2  5t
0  t (3t  5)
0  t 3t  5  0
5
t
3
2
0 1

3 0
0
undefined
5 3  1

2

3   5 3
 5 3
2 23

5 53
2 2

5 5
52 is 12.5% of what number?
52 is 12.5% of what number?
is
%

of 100
52 12.5

x 100
52 100  12.5 x
5200 12.5 x

12.5 12.5
x  416
How much money is 35% of $750?
How much money is 35% of $750?
is
%

of 100
x
35

750 100
100 x  35  750
100 x 26250

100
100
x  $262.50
How much is 4.3% of 500 tons?
How much is 4.3% of 500 tons?
is
%

of 100
x
4.3

500 100
100 x  4.3  500
100 x 2150

100
10 0
x  21.5
30 inches is what percent of 40 feet?
30 inches is what percent of 40 feet?
is
%

of 100
40 feet = 480 inches
30
x

480 100
30 100  480 x
3000 480 x

480
480
6.25%  x
In the survey, 572 people said they think
the ozone layer is getting worse. What
was the total number of people surveyed?
is
%

of 100
572 55

x
100
100  572  55 x
57200 55 x

55
55
x  1040 people
The variables x and y vary directly.
When x = 18 and y =6, write an
equation that relates x and y.
The variables x and y vary directly.
When x = 18 and y =6, write an
equation that relates x and y.
y  kx
6 k (18)

18
18
1
k
3
1
y x
3
The variables x and y vary inversely.
When x = 16 and y = 1, write an
equation that relates x and y.
The variables x and y vary inversely.
When x = 16 and y = 1, write an
equation that relates x and y.
k
y
x
1 k

1 16
16 1  k 1
16  k
16
y
x
The volume V of a gas at constant
temperature varies inversely with the
pressure P. When the volume is 100
cubic inches, the pressure is 25
pounds per cubic inches. Write an
equation that relates V and P.
The volume V of a gas at constant temperature varies
inversely with the pressure P. When the volume is
100 cubic inches, the pressure is 25 pounds per cubic
inches. Write an equation that relates V and P.
k
V
P
100 k

1
25
100  25  k 1
2500  k
2500
V
P
The graph models the relationship between
the time needed to paint a house and the
number of painters. For the values shown,
the time needed T and the number of
painters n vary
inversely. Find an
inverse variation
model relating T
and n.
The graph models the relationship between the time needed to paint
a house and the number of painters. For the values shown, the time
needed T and the number of painters n vary inversely. Find an
inverse variation model relating T and n.
k
T
n
4.5 k

1
6
4.5  6  k 1
27  k
27
T
n
Decide if the data in the table show
represents direct or inverse variation.
Inverse variation
Simplify the expression.
18 x
12 x
2
18x
1 2  3  3  x  x 3x


12 x
2 2 3  x
2
2
Simplify the expression.
42 x  6 x
36 x
3
42 x  6 x
6 x (7  x ) 7  x


36 x
6 6 x
6
3
2
2
Simplify the expression.
2 x  11x  6
x6
2
2 x  11x  6 (2 x  1)( x  6)

 2x 1
x6
( x  6)
2
Simplify the expression.
x5
2
x  8 x  15
x 5
x 5
1


2
x  8 x  15 ( x  3)( x  5) x  3
Simplify the expression.
x  9 x  14 x
2
x 4
3
2
x  9 x  14 x x( x  9 x  14) x( x  2)( x  7) x( x  7)



2
x 4
( x  2)( x  2)
( x  2)( x  2)
x2
3
2
2
Use the substitution method to
solve the linear system.
s t4
2t  s  19
s t4
2t  s  19
2t  (t  4)  19
3t  4  19
4 4
3t 15

3 3
t 5
s t4
s  5 4
s9
(9,5)
Simplify the expression.
 2x y 


 3 xy 
3
4
3
 2x y 


 3 xy 
3
3
4
9
12
3
2 x y
33 x 3 y 3
8 x 9 3 y12 3
27
6 9
8x y
27
Use the quadratic formula to
solve the equation.
y  3x  6 x  24
3
y  3x  6 x  24
3
b  b2  4ac
x
2a
6  (6)2  4(3)(24)
x
2(3)
6  324
x
6
6  18
x
6
x  4, 2
Solve the following equation
by factoring.
3 y  y  21y  7
3
2
3 y  y  21y  7
3
2
(3 y  y )  (21 y  7)
3
2
y (3 y  1)  7(3 y  1)
2
( y  7)(3 y  1)
2
Sketch the graph of the
inequality.
y  4x  0
y  4x  0
4x 4x
y  4x  0
x-intercept:
0  4x  0
4x  0
x0
y-intercept:
y  4(0)  0
y0
Test (2,2)
2  4(2)  0
2 8  0
6  0