Transcript ch.1 active learning

Active Learning Lecture Slides
For use with Classroom Response Systems
Chapter 1
Graphs,
Equations,
and
Inequalities
© 2009 Pearson Education, Inc.
All rights reserved.
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 1
Find the distance between the d(P1, P2) between
the points P1(–4, –1) and P2(5, –4).
a. 3 10
b. 72 2
c. 72
d. 12
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Slide 1 - 2
Find the distance between the d(P1, P2) between
the points P1(–4, –1) and P2(5, –4).
a. 3 10
b. 72 2
c. 72
d. 12
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Slide 1 - 3
Find the midpoint of the line segment joining
points P1(0.3, 0.9) and P2(1.7, 1.4).
a. (1.15, 1)
b. (1, 1.15)
c. (0.7, 0.25)
d. (0.25, 0.7)
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Slide 1 - 4
Find the midpoint of the line segment joining
points P1(0.3, 0.9) and P2(1.7, 1.4).
a. (1.15, 1)
b. (1, 1.15)
c. (0.7, 0.25)
d. (0.25, 0.7)
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Slide 1 - 5
Graph y = 3x - 9.
a.
b.
c.
d.
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Slide 1 - 6
Graph y = 3x - 9.
a.
b.
c.
d.
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Slide 1 - 7
Graph 3x2 –2y = 56 using a graphing utility.
a.
b.
c.
d.
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Slide 1 - 8
Graph 3x2 –2y = 56 using a graphing utility.
a.
b.
c.
d.
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Slide 1 - 9
List the intercepts of the graph.
a. (–4, 0), (0, –4), (0, 1), (0, –5)
x
b. (–4, 0), (0, 4), (0, 1), (0, 5)
c. (–4, 0), (1, 0), (–5, 0), (0, –4)
d. (4, 0), (1, 0), (5, 0), (0, –4)
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Slide 1 - 10
List the intercepts of the graph.
a. (–4, 0), (0, –4), (0, 1), (0, –5)
x
b. (–4, 0), (0, 4), (0, 1), (0, 5)
c. (–4, 0), (1, 0), (–5, 0), (0, –4)
d. (4, 0), (1, 0), (5, 0), (0, –4)
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Slide 1 - 11
Use a graphing utility to approximate the
intercepts rounded to two decimal places for
the equation 3x2 – 5y = 34.
a. (0, –6.8), (3.37, 0)
b. (0, –6.8), (–3.36, 0), (3.36, 0)
c. (0, 6.8), (–3.37, 0), (3.37, 0)
d. (0, –6.8), (–3.37, 0), (3.37, 0)
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 12
Use a graphing utility to approximate the
intercepts rounded to two decimal places for
the equation 3x2 – 5y = 34.
a. (0, –6.8), (3.37, 0)
b. (0, –6.8), (–3.36, 0), (3.36, 0)
c. (0, 6.8), (–3.37, 0), (3.37, 0)
d. (0, –6.8), (–3.37, 0), (3.37, 0)
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Slide 1 - 13
Use a graphing utility to approximate the real
solutions, if any, rounded to two decimal
places of the equation x4 – 3x2 + 4x + 15 = 0.
a. {–0.84, –1.93}
b. {2.11, –2.60}
c. {3.94, –1.27}
d. No real solutions
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Slide 1 - 14
Use a graphing utility to approximate the real
solutions, if any, rounded to two decimal
places of the equation x4 – 3x2 + 4x + 15 = 0.
a. {–0.84, –1.93}
b. {2.11, –2.60}
c. {3.94, –1.27}
d. No real solutions
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Slide 1 - 15
Solve.
x  7x  1  x  1
a.
2
b.
7
 
4 
c.
8
d.
8 
 
7
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2
Slide 1 - 16
Solve.
x  7x  1  x  1
a.
2
b.
7
 
4 
c.
8
d.
8 
 
7
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2
Slide 1 - 17
6
1
1


Solve.
5x x  1 x 2x  2 
a.
7
 7
b.  
 2
 7
c.  
 10 
d. No solution
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Slide 1 - 18
6
1
1


Solve.
5x x  1 x 2x  2 
a.
7
 7
b.  
 2
 7
c.  
 10 
d. No solution
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Slide 1 - 19
Going into the final exam, which will count as
three tests, Jerome has test scores of 61, 72, 59,
75, and 77. What score does Jerome need on the
final in order to earn a C, which requires an
average of 70?
a. 82
b.
72
c. 74
d.
76
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 20
Going into the final exam, which will count as
three tests, Jerome has test scores of 61, 72, 59,
75, and 77. What score does Jerome need on the
final in order to earn a C, which requires an
average of 70?
a. 82
b.
72
c. 74
d.
76
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Slide 1 - 21
2
12x
 5x  25  0
Solve.
a.
5 5
 , 
4 3
5 5

b.  ,  
 4 3
c.
5 5
 , 
4 3
 5 5
 , 
 4 3
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d.
Slide 1 - 22
2
12x
 5x  25  0
Solve.
a.
5 5
 , 
4 3
5 5

b.  ,  
 4 3
c.
5 5
 , 
4 3
 5 5
 , 
 4 3
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d.
Slide 1 - 23
Solve the equation by square root method.
2
2x  3  25
a. {–14, 14}
b. {1, 4}
c. {–4, 1}
d. {0, 1}
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Slide 1 - 24
Solve the equation by square root method.
2
2x  3  25
a. {–14, 14}
b. {1, 4}
c. {–4, 1}
d. {0, 1}
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Slide 1 - 25
Solve the equation by completing the square.
1 2 1
1
x  x 0
3
12
6
a.
1 1 
 , 
8 8 
c.
 33 33 
,


8 
 8
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b.
 33  1
33  1 
,


8 
 8
d.
 33  1 33  1 
,


8 
 8
Slide 1 - 26
Solve the equation by completing the square.
1 2 1
1
x  x 0
3
12
6
a.
1 1 
 , 
8 8 
c.
 33 33 
,


8 
 8
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b.
 33  1
33  1 
,


8 
 8
d.
 33  1 33  1 
,


8 
 8
Slide 1 - 27
Solve the equation by using the quadratic
formula.
2x 2  x  5  0
 1 41 1  41 
a. 
,

4
4


1  41 1  41 
,
b. 

2 
 2
 1 41 1  41 
c. 
,

2
2


d.
Copyright © 2009 Pearson Education, Inc.
No solution
Slide 1 - 28
Solve the equation by using the quadratic
formula.
2x 2  x  5  0
 1 41 1  41 
a. 
,

4
4


1  41 1  41 
,
b. 

2 
 2
 1 41 1  41 
c. 
,

2
2


d.
Copyright © 2009 Pearson Education, Inc.
No solution
Slide 1 - 29
A ball is thrown vertically upward from the
top of a building 128 feet tall with an initial
velocity of 112 feet per second. The distance
s (in feet) of the ball form the ground after t
seconds is s = 128 + 112t – 16t2 . After how
many seconds will the ball pass the top of the
building on its way down?
a. 9 sec
b.
128 sec
c. 6 sec
d.
7 sec
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 30
A ball is thrown vertically upward from the
top of a building 128 feet tall with an initial
velocity of 112 feet per second. The distance
s (in feet) of the ball form the ground after t
seconds is s = 128 + 112t – 16t2 . After how
many seconds will the ball pass the top of the
building on its way down?
a. 9 sec
b.
128 sec
c. 6 sec
d.
7 sec
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 31
Multiply. (4 + 6i)(2 – 7i)
a. –34 + 40i
b. 50 + 16i
c. 50 – 16i
d. –42i2 – 16i + 8
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Slide 1 - 32
Multiply. (4 + 6i)(2 – 7i)
a. –34 + 40i
b. 50 + 16i
c. 50 – 16i
d. –42i2 – 16i + 8
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Slide 1 - 33
Given z = 4 – 9i, evaluate zz .
a. –65
b. 16 – 81i2
c. 97
d. 16 – 81i
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Slide 1 - 34
Given z = 4 – 9i, evaluate zz .
a. –65
b. 16 – 81i2
c. 97
d. 16 – 81i
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Slide 1 - 35
Solve the equation in the complex number
system.
x 4  4x 2  5  0
a.
 5i,i
b.

5, 5,i,i
c.

5i, i
d.
 5, 5


Copyright © 2009 Pearson Education, Inc.
Slide 1 - 36
Solve the equation in the complex number
system.
x 4  4x 2  5  0
a.
 5i,i
b.

5, 5,i,i
c.

5i, i
d.
 5, 5


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Slide 1 - 37
Find the real solutions of the equation.
x  2  2x  5  0
2
a.
3,1
b.
3, 1
c.
3
d. No real solution
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Slide 1 - 38
Find the real solutions of the equation.
x  2  2x  5  0
2
a.
3,1
b.
3, 1
c.
3
d. No real solution
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 39
Find the real solutions of the equation.
x 2 3  2x1 3  15  0
a.
5, 3
b.
3, 5
c.
27,125
d.
125, 27
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Slide 1 - 40
Find the real solutions of the equation.
x 2 3  2x1 3  15  0
a.
5, 3
b.
3, 5
c.
27,125
d.
125, 27
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Slide 1 - 41
Solve the equation.
2
x  15x  8  8
a.
16, 15, 0,1
b.
16,16, 1,1
c.
16, 15,1
d.
15, 1, 0,16
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Slide 1 - 42
Solve the equation.
2
x  15x  8  8
a.
16, 15, 0,1
b.
16,16, 1,1
c.
16, 15,1
d.
15, 1, 0,16
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 43
Solve the equation.
x 3  2x 2  9x  18  0
a.
3, 3, 2
b.
9, 2
c.
3, 2
d.
3, 3, 2
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 44
Solve the equation.
x 3  2x 2  9x  18  0
a.
3, 3, 2
b.
9, 2
c.
3, 2
d.
3, 3, 2
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 45
A bank loaned out $65,000, part of it at a rate
of 12% per year and the rest at a rate of 6%
per year. If the interest received was $5580,
how much was loaned at 12%?
a. $28,000
b. $37,000
c. $29,000
d. $36,000
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 46
A bank loaned out $65,000, part of it at a rate
of 12% per year and the rest at a rate of 6%
per year. If the interest received was $5580,
how much was loaned at 12%?
a. $28,000
b. $37,000
c. $29,000
d. $36,000
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 47
How many gallons of a 30% alcohol solution
must be mixed with 60 gallons of a 14%
solution to obtain a solution that is 20%
alcohol?
a. 27 gal
b. 36 gal
c. 7 gal
d. 12 gal
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 48
How many gallons of a 30% alcohol solution
must be mixed with 60 gallons of a 14%
solution to obtain a solution that is 20%
alcohol?
a. 27 gal
b. 36 gal
c. 7 gal
d. 12 gal
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 49
A freight train leaves a station traveling at 32
km/h. Two hours later, a passenger train leaves
the same station traveling in the same direction
at 52 km/h. How long does it take the passenger
train to catch up to the freight train?
a. 5.2 hr
b. 4.2 hr
c. 3.2 hr
d. 2.2 hr
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Slide 1 - 50
A freight train leaves a station traveling at 32
km/h. Two hours later, a passenger train leaves
the same station traveling in the same direction
at 52 km/h. How long does it take the passenger
train to catch up to the freight train?
a. 5.2 hr
b. 4.2 hr
c. 3.2 hr
d. 2.2 hr
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 51
BJ can overhaul a boat’s diesel inboard engine
in 20 hours. His apprentice takes 60 hours to do
the same job. How long would it take them
working together assuming no gain or loss in
efficiency?
a. 12 hr
b. 6 hr
c. 80 hr
d. 15 hr
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 52
BJ can overhaul a boat’s diesel inboard engine
in 20 hours. His apprentice takes 60 hours to do
the same job. How long would it take them
working together assuming no gain or loss in
efficiency?
a. 12 hr
b. 6 hr
c. 80 hr
d. 15 hr
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 53
Express the graph shown using interval
notation and as an inequality involving x.
[
)
–8 –6 –4 –2 0 2 4
a. [–7, –1); –7 ≤ x < –1
b. (–7, –1); –7 < x < –1
c. [–7, –1]; –7 ≤ x ≤ –1
d. (–7, –1]; –7 < x ≤ –1
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 54
Express the graph shown using interval
notation and as an inequality involving x.
[
)
–8 –6 –4 –2 0 2 4
a. [–7, –1); –7 ≤ x < –1
b. (–7, –1); –7 < x < –1
c. [–7, –1]; –7 ≤ x ≤ –1
d. (–7, –1]; –7 < x ≤ –1
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 55
Solve –5(2x + 13) < –15x – 35. Express your
answer in interval notation.
a. (6, ∞)
b. (–∞, 6)
c. (–∞, 4)
d. (–∞, 20)
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Slide 1 - 56
Solve –5(2x + 13) < –15x – 35. Express your
answer in interval notation.
a. (6, ∞)
b. (–∞, 6)
c. (–∞, 4)
d. (–∞, 20)
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 57
Solve –27 ≤ –5x – 2 ≤ –12. Express your
answer in interval notation.
a. (2, 5)
b. [2, 5]
c. [–5, –2]
d. (–5, –2)
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 58
Solve –27 ≤ –5x – 2 ≤ –12. Express your
answer in interval notation.
a. (2, 5)
b. [2, 5]
c. [–5, –2]
d. (–5, –2)
Copyright © 2009 Pearson Education, Inc.
Slide 1 - 59
Solve |x – 6| + 7 ≤ 16. Express your answer
in interval notation.
a. [–3, 16]
b. (–3, 15)
c. [–3, 15]
d.

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Slide 1 - 60
Solve |x – 6| + 7 ≤ 16. Express your answer
in interval notation.
a. [–3, 16]
b. (–3, 15)
c. [–3, 15]
d.

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Slide 1 - 61