60
CHAPTER P
Prerequisites
CHAPTER P
Review Exercises
Exercise numbers with a gray background indicate problems that
the authors have designed to be solved
without a calculator
.
The collection of exercises marked in
red
could be used as a chapter test.
In Exercises 1 and 2, find the endpoints and state whether the interval
is bounded or unbounded.
1.
3
0, 5
4
2.
1
2
3.
Distributive Property
Use the distributive property
to write the expanded form of
.
4.
Distributive Property
Use the distributive property
to write the factored form of
.
In Exercises 5 and 6, simplify the expression. Assume that denomina
tors are not zero.
5.
6.
In Exercises 7 and 8, write the number in scientific notation.
7.
The mean distance from Pluto to the Sun is about
3,680,000,000 miles.
8.
The diameter of a red blood corpuscle is about 0.000007 me
ter.
In Exercises 9 and 10, write the number in decimal form.
9.
Our solar system is about
years old.
10.
The mass of an electron is about
g (gram).
11.
The data in Table P.9 give the Fiscal 2009 final budget for some
Department of Education programs. Using scientific notation
and no calculator, write the amount in dollars for the programs.
9.1094
*
10

28
5
*
10
9
1
3
x
2
y
3
2

2
1
uv
2
2
3
v
2
u
3
2
x
3
+
4
x
2
2
1
x
2

x
2
2,
q
Table P.9
Fiscal 2009 Budget
Program
Amount
Title 1 district grants
$14.5 billion
Title 1 school improvement grants
$545.6 million
IDEA (Individuals with Disabilities
$11.5 billion
Education Act) state grants
Teacher Incentive Fund
$97 million
Head Start
$7.1 billion
Source: U.S. Departments of Education, Health and Human
Services as reported in Education Week, May 13, 2009.
(a)
Title 1 district grants
(b)
Title 1 school improvement grants
(c)
IDEA state grants
(d)
Teacher Incentive Fund
(e)
Head Start
12.
Decimal Form
Find the decimal form for
. State
whether it repeats or terminates.

5/11
In Exercises 13 and 14, find
(a)
the distance between the points and
(b)
the midpoint of the line segment determined by the points.
13.
and 14
14.
1
and
2
In Exercises 15 and 16, show that the figure determined by the points
is the indicated type.
15.
Right triangle:
,
1
3, 11
2
,
1
7, 9
2
16.
Equilateral triangle:
1
0, 1
2
,
1
4, 1
2
,
In Exercises 17 and 18, find the standard form equation for the circle.
17.
Center
1
0, 0
2
, radius 2
18.
Center
radius 4
In Exercises 19 and 20, find the center and radius of the circle.
19.
20.
21.
(a)
Find the length of the sides of
the triangle in the figure.
(b)
Writing to Learn
Show
that the triangle is a right trian
gle.
22.
Distance and Absolute Value
Use absolute value
notation to write the statement that the distance between
z
and
is less than or equal to 1.
23.
Finding a Line Segment with Given Midpoint
Let
1
3, 5
2
be the midpoint of the line segment with endpoints
and
1
a
,
b
2
. Determine
a
and
b
.
24.
Finding Slope
Find the slope of the line through the
points
25.
Finding PointSlope Form Equation
Find an
equation in pointslope form for the line through the point
with slope
26.
Find an equation of the line through the points
and
in the general form
In Exercises 2732, find an equation in slopeintercept form for the line.
27.
The line through
with slope
28.
The line through the points
and
1
3, 2)
29.
The line through
1
, 4
2
with slope
30.
The line
31.
The line through
and parallel to the line
32.
The line through
1
2,
2
and perpendicular to the line
2
x
+
5
y
=
3

3
2
x
+
5
y
=
3
1
2,

3
2
3
x

4
y
=
7
m
=
0

2
1

1,

4
2
m
=
4/5
1
3,

2
2
Ax
+
By
+
C
=
0.
1
2,

5
2
1

5, 4
2
m
= 
2/3.
1
2,

1
2
1

1,

2
2
and
1
4,

5
2
.
1

1, 1
2

3
x
2
+
y
2
=
1
(
x
+
5)
2
+
(
y
+
4)
2
=
9
1
5,

3
2
,
1
2, 1

2
2
3
2
1

2, 1
2
1
5,

1

4, 3
2

5
y
x
(5, 6)
(3, 2)
(1, 2)