Algebra Rules Review Sheet Page 13

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REVIEW OF ALGEBRA
13
77–82
127–142
Simplify the radicals.
Solve the inequality in terms of intervals and illustrate
the solution set on the real number line.
3
2
4
32x
4
s
s
77.
78.
79.
s32 s2
127.
128.
2x
7
3
4
3x
6
3
4
s
54
s
2
129.
130.
1
x
2
1
5x
5
3x
5
6
s
96a
80.
81.
82.
sxy sx
3
y
s16a
4
b
3
5
3a
s
131.
132.
0
1
x
1
1
3x
4
16
2
133.
134.
x
1 x
2
0
x
2x
8
83–100
Use the Laws of Exponents to rewrite and simplify the
2
2
135.
136.
x
3
x
5
expression.
10
8
16
10
6
3
2
83.
84.
137.
x
x
0
3
9
2
4
16
9
4
n
2n 1
x
2x
a
a
138
x
1 x
2 x
3
0
85.
86.
3
n 2
x
a
139.
3
140.
3
2
x
x
x
3x
4x
3
4
1
1
a
b
x
y
87.
88.
1
1
5
5
1
a
b
x
y
141.
142.
4
3
1
x
x
89.
1 2
90.
1 5
3
96
2 3
4 3
91.
92.
125
64
143.
The relationship between the Celsius and Fahrenheit tempera-
5
2
4 3 2
5
3
10
3 5
ture scales is given by
C
F
32
, where
C
is the temper-
93.
94.
2x
y
x
y
z
9
ature in degrees Celsius and
F
is the temperature in degrees
(
)
3
95.
5
96.
4
s
y
6
s
a
Fahrenheit. What interval on the Celsius scale corresponds to
1
5
sx
8
the temperature range
50
F
95
?
97.
98.
(
)
5
4
st
s
x
3
144.
Use the relationship between
C
and
F
given in Exercise 143 to
1 2
t
sst
find the interval on the Fahrenheit scale corresponding to the
4
99.
100.
4
4
s
r
2n 1
s
r
1
2 3
s
temperature range
20
C
30
.
145.
As dry air moves upward, it expands and in so doing cools at a
101–108
Rationalize the expression.
rate of about
1
C for each 100-m rise, up to about 12 km.
(
)
sx
3
1 sx
1
(a) If the ground temperature is
20
C, write a formula for the
101.
102.
temperature at height .
h
x
9
x
1
(b) What range of temperature can be expected if a plane takes
x sx
8
h
h
s2
s2
103.
104.
off and reaches a maximum height of 5 km?
x
4
h
146.
If a ball is thrown upward from the top of a building 128 ft
2
1
105.
106.
high with an initial velocity of
16 ft s
, then the height above
h
3
s5
sx
sy
the ground seconds later will be
t
107.
108.
2
3x
4
x
2
x
2
x
sx
sx
sx
2
h
128
16t
16t
During what time interval will the ball be at least 32 ft above
109–116
State whether or not the equation is true for all values
the ground?
of the variable.
109.
2
110.
2
sx
x
sx
4
x
2
147– 148
Solve the equation for .
x
16
a
a
1
147.
148.
x
3
2x
1
3x
5
1
111.
112.
1
x
y
1
1
16
16
x
y
x
1
2
1
2
149–156
113.
114.
Solve the inequality.
x
y
1
y
4
x
2
x
149.
150.
x
3
x
3
3 4
7
115.
x
x
151.
x
4
1
152.
x
6
0.1
116.
6
4 x
a
6
4x
4a
153.
154.
x
5
2
x
1
3
117–126
Rewrite the expression without using the absolute value
155.
156.
2x
3
0.4
5x
2
6
symbol.
117.
118.
5
23
2
157.
Solve the inequality
a bx
c
bc
for , assuming that , ,
x
a
b
and are positive constants.
c
119.
120.
s5
5
2
3
158.
Solve the inequality
ax
b
c
for , assuming that , , and
x
a
b
121.
122.
x
2
if
x
2
x
2
if
x
2
c
are negative constants.
123.
124.
x
1
2x
1
159
Prove that
ab
a
b
. [Hint: Use Equation 3.]
2
2
125.
126.
x
1
1
2x
2
2
160.
Show that if
0
a
b
, then
a
b
.

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