solve. write your answer in interval notation.riesg036/doc/doc/math1005exam2pursuitf09.pdf1 solve....
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1
Solve. Write your answer in interval notation.
3(2 1) 2( 4) 7 2(3 4 )x x x
1
3(2 1) 2( 4) 7 2(3 4 )
6 3 2 8 7 6 8
4 5 8 13
5 4 13
8 4
2
2
( , 2]
x x x
x x x
x x
x
x
x
x
1
Solve for x.
26
3 4
x x
1
26
3 4
LCD (3)(4) 12
2(12) 6 (12)
3 4
4(2 ) 6(12) (3)
8 72 3
11 72
72
11
x x
x x
x x
x x
x
x
1
Solve for x.
2
5 1 8
3 2 6x x x x
1
2
5 1 8
3 2 6
5 1 8
3 2 ( 3)( 2)
LCD ( 3)( 2) 3, 2
5 1 8( 3)( 2) ( 3)( 2)
3 2 ( 3)( 2)
5( 2) 1( 3) 8
5 10 3 8
6 7 8
6 15
15 5
6 2
x x x x
x x x x
x x x x
x x x xx x x x
x x
x x
x
x
x
1
Solve. Write your answer in interval notation.
5 2 1 3x
1
5 2 1 3
6 2 2
3 1
[ 1,3)
x
x
x
1
Solve for x.
3 1 1
2 2 6 3 3
x x
x x
1
3 1 1 3 1 1
2 2 6 3 3 2( 1) 6 3( 1)
3 1 1 3 1
2( 1) 6 3 2( 1) 2
LCD 6( 1) 1
3 16( 1) 6( 1)
2( 1) 2
3( 3) 3( 1)
3 1
3 1
no solution
x x x x
x x x x
x x
x x
x x
xx x
x
x x
x x
2
Solve
3 4 7 8x
2
3 4 7 8
3 4 15
4 5
4 5 or 4 5
9 or 1
check!
x
x
x
x x
x x
2
Solve. Write your answer in interval notation.
2 3 5 0x
2
2 3 5 0
2 3 5
2 3 5 or 2 3 5
2 8 or 2 2
4 or 1
( , 1) (4, )
x
x
x x
x x
x x
2
Solve
5 6x x
2
2
2
5 6
5 6
5 6 0
( 2)( 3) 0
2 or 3
check!
x x
x x
x x
x x
x x
2
Solve. Write your answer in interval notation.
13 1 6 0
2x
2
1 13 1 6 0 3 1 6
2 2
11 2
2
12 1 2
2
13 1
2
6 2
[ 6,2]
x x
x
x
x
x
2
Solve
3 4 2x x
2
3 4 2
3 4 2
3 4 4 4 4
3 4 4
3 4 4
34
4
94
16
73 check!
16
x x
x x
x x x
x x x
x
x
x
x
3
Simplify
( 2 3 )(1 5 )i i
3
2( 2 3 )(1 5 ) 2 10 3 15
2 13 15( 1)
2 13 15
13 13
i i i i i
i
i
i
3
Simplify
2 6
5 3
i
i
3
2
2 6 (2 6 ) (5 3 )
5 3 (5 3 ) (5 3 )
10 6 30 18
25 9
10 36 18
34
8 36
34
8 36
34 34
4 18
17 17
i i i
i i i
i i i
i
i
i
i
3
Simplify and write instandard form.
3 3 6
3
2
3 3 6 3 3 6
3 3 3 6
( 1)(3) 3 2
3 3 2
i i
i i
i
i
3
Solve
2/3 1/3 2 0x x
3
2/3 1/3
1 23 3
1/3 2 1/3
1/3
2
1/3 1/3
1/3 3 3 1/3 3 3
2 0
( )2
( ) 2 0
let
2 0
( 2)( 1) 0
2 0 or 1 0
2 or 1
2 or 1
( ) (2) or ( ) ( 1)
8 or 1
check
x x
x x
u x
u u
u u
u u
u u
x x
x x
x x
3
Solve.
2 4 13 0x x
3
2
2
2 2 242 2
2 2
2
completing the square
4 13 0
4 13
( ) ( ) ( 2)
4 ( 2) 13 4
( 2) 9
2 9
2 3
2 3
b
x x
x x
x x
x
x
x i
x i
2
2
quadratic formula
4 13 0
1, 4, 13
( 4) ( 4) 4(1)(13)
2(1)
4 16 52
2
4 36 4 6
2 2
4 6
2 2
2 3
x x
a b c
x
i
i
x i
3
Solve.
2(5 3 ) 7 0x
3
2
2
(5 3 ) 7 0
(5 3 ) 7
5 3 7
3 5 7
5 7
3
x
x
x
x
x
4
Write the equation of the circle in standard form.Give the center and radius.
2 2 8 6 24 0x y x y
4
2 2
2 2
2 2 282 2
2 2 262 2
2 2 2 2
2 2
8 6 24 0
( 8 ) ( 6 ) 24
for the group: ( ) ( ) ( 4) 16
for the group: ( ) ( ) (3) 9
( 8 ( 4) ) ( 6 (3) ) 24 16 9
( 4) ( 3) 49
center: (4, 3)
radius: 49 7
b
b
x y x y
x x y y
x
y
x x y y
x y
4
Given the equation of the circle, identify the center and radius, and sketch thegraph.
2 2( 1) 4x y
4
2 2( 1) 4
center: (1,0)
radius: 4 2
x y
5 4 3 2 1 1 2 3 4 5x
4
2
2
4
y
4
Find the distance betweenthe points.
( 1, 2) and (4,1)
4
2 2
2 2
2 2
2 2
( 1, 2) and (4,1)
( 1 4) ( 2 1)
( 5) ( 3) 25 9 34
OR
(4 ( 1)) (1 ( 2))
(5) (3) 25 9 34
d
d
4
Write the equation of the circle in standard form giventhe center of and radius of 5.
(1,6)
4
2 2 2
2 2 2
2 2
center : (1,6)
5
( ) ( )
( 1) ( 6) 5
( 1) ( 6) 25
r
x h y k r
x y
x y
4
Find the midpoint of the line segment connected by the points
912 2
( , 1) and ( , 4)
4
912 2
912 2
102
( , 1) and ( , 4)
1 ( 4)midpt ,
2 2
5 5 5, , (2.5, 2.5)
2 2 2 2
5
Graph the line using intercepts
2 3 6 0x y
5
2 3 6 0
int :
2 3(0) 6 0
2 6
3
int :
2(0) 3 6 0
3 6
2
x y
x
x
x
x
y
y
y
y
5 4 3 2 1 1 2 3 4 5x
6
4
2
2
4
6
y
5
Write the equation in slope intercept form of the line passing through the point and perpendicular to the line
( 3,6)
13
4y x
5
1 13 3
4,
So the slope of our line is 3,
and we have the point ( 3,6)
6 3( 3) (pt-slope form)
6 3 9
3 3 (slope-int form)
y x m
m
y x
y x
y x
5
Identify the slope of each equation aspositive, negative, zero, or undefined.Then classify the equation as increasing,decreasing, horizontal, or vertical.
12
25
a)
b) 3
c) 6
d) 4 10
x
y x
y
y x
5
12
25
a)
slope undefined, vertical line
b) 3
positive slope, increasing graph
c) 6
zero slope, horizontal line
d) 4 10
negative slope, decreasing graph
x
y x
y
y x
5
Write the equation of the linein point-slope form for the line passing through (4,-7) and parallel to the line
2 4 0x y
5
2 4 0
2 4, 2
our line has 2 and point (4, 7)
( 7) 2( 4)
7 2( 4)
x y
y x m
m
y x
y x
5
Test the equation for symmetry across the x-axis,y-axis, and the origin.
2 25 2 4x x y
5
2 2
2 2
2 2
2 2
2 2
2 2
2 2
5 2 4
:
5 2 4( )
5 2 4 sym across
:
5( ) 2( ) 4
5 2 4 no sym across
:
5( ) 2( ) 4( )
5 2 4 no sym thru
x x y
x axis
x x y
x x y x axis
y axis
x x y
x x y y axis
origin
x x y
x x y origin
5
Write the equation of theline passing through points
(2, 5) and (3,0)
5
(2, 5) and (3,0)
5 0 55
2 3 1
point-slope form:
0 5( 3) or 5 5( 2)
slope-intercept form:
5 15
standard form:
5 15 or 5 15
m
y x y x
y x
x y x y
6
A car rental agency charges $20 per day and $0.12 per mile. How many miles can be driven to have a cost of at least $32 and at most $44?
6
Let number of miles driven
32 20 0.12 44
12 0.12 24
100 200
x
x
x
x
The number of miles driven should bebetween 100 and 200, inclusive.
6
You invest a total of $6,000 into asavings account and a money market account. The savings account earns 2% annual interest and the money market account earns 5% annual interest. If youearn $255 in interest, how much money did you have in each account.
6
interest earned in savings acct
6000 interest earned in money market acct
x
x
0.02 0.05(6000 ) 255
0.02 300 0.05 255
0.03 300 255
0.03 45
1500
x x
x x
x
x
x
6000 6000 1500 4500x
$1500 in savings$4500 in money market
6
The length of Pam’s living room is 5m less than 2 times the width of the room. If the perimeter of the room is 70m, what are thedimensions of the living room?
6
width of living room
2 5 length of the living room
x
x
width is 13.3 ftlength is 2(13.3)-5=21.6 ft
P=2length+2width
70 2(2 5) 2
70 4 10 2
70 6 10
80 6
80
6
13.3
x x
x x
x
x
x
x
6
The area of a rectangular garden is 1120 square feet. The length of the garden is 4 less than 3 timesthe width. Find the dimensions of the garden.
6
2
2
3 4
( )( )
1120 (3 4)
1120 3 4
0 3 4 1120
0 ( 20)(3 56)
20 0 or 3 56 0
5620 or can't have negative width
3
so width is 20 and length is 3(2
x width
x length
area length width
x x
x x
x x
x x
x x
x x
ft
0) 4 56 ft
6
Gym A charges $10 for a membershipplus $1 per visit. Gym B charges $5 for a membership plus $1.50 per visit.After how many visits will the costsbe the same? What is the cost?
6
# visits
Gym A cost = Gym B cost
10 1 5 1.5
5 1.5
5 0.5
10
The cost is the same after 10 visits.
The cost will be 10 1(10) $20
or could use 5 1.5(10) $20
x
x x
x x
x
x