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– Second level
Section 5.1.4
• Third level
– Fourth level
» Fifth level
How Can I Use Systems
#5-44 How Tall is Harold
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Dinah –and
Jamal
Second
level were eating as they came
• Third
into Algebra
4 level
class from lunch. Someone had
– Fourth level
left a book on
the
floor and they tripped. As
» Fifth level
they each hit the floor, the food they were
carrying went flying across the room directly
toward Harold who was showing off his latest
dance moves.
#5-44 How Tall is Harold
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• As Jamal
and Dinah watched in horror, Jamal’s
– Second level
cupcake •and
Dinah’s
sandwich splattered Harold
Third
level
right on top–ofFourth
his level
head! Jamal’s cupcake flew on
» Fifth level
a path that would
have landed on the floor 20 feet
away from him if it had not hit Harold. Dinah’s
sandwich flew on a path that would have landed
on the floor 24 feet away from her if it had not hit
Harold. Jamal’s cupcake got up 9 feet high, and
Jamal’s sandwich reached a height of 6 feet
before hitting Harold.
#5-44 How Tall is Harold
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• How– tall
is level
Harold? Show solution in as
Second
• Thirdas
level
many ways
possible.
– Fourth level
» Fifth level
Generate tables of values
one for each person
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–x Second level
y
x
• Third level
0
0
0 level
– Fourth
» Fifth level
12
10
9
24
20
0
y
0
6
0
Now run the Quadratic Regression (choice 5)
on your calculator; remember to store one
equation in Y1 and the other in Y2
Adjust the window of your
calculator
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• Once– you
each formula and you have
Secondknow
level
• Third in
level
stored them
Y1 and Y2, use intersect key
Fourth level
to find the–point
of intersection.
» Fifth level
• What does x coordinate of POI represent?
• What does y coordinate of POI represent?
• Once you know each equation, use the EQV
method to find x and y.
11
y
10
9
8
7
6
H
5
4
3
2
1
-1
-1
x
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
J D
Click of the grid and turn on each function/point series.
#5-45
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• Your–math
class wants to collect money for a field
Second level
trip, so it• decides
Third levelto sell two kinds of candy bags.
– Fourth
level bag costs 4.25 for five
The Chocolate
Lovers
» Fifth level
chocolate truffles
and two caramel turtle candies.
The Combusting Caramel Bag costs 3.50 for eight
caramel turtle candies and two chocolate truffles.
How much does each chocolate truffle and
caramel turtle candy cost?
solution
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• Let x– be
thelevel
cost of Truffles
Second
level
• Let y be• Third
the
cost
of
Caramel
Turtles
– Fourth level
» Fifth of
levelbag write an equation:
Then for each type
5𝑥 + 2𝑦 = 4.25
2𝑥 + 8𝑦 = 3.5
Solution
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• There
are several
methods to solve the
– Second
level
Third
level
systems• of
equations
you just wrote. The
level
following –isFourth
only
one way:
» Fifth level
• 5𝑥 + 2𝑦 = 4.25
Multiply by -2
• 2𝑥 + 8𝑦 = 3.5
Multiply by 5
solution
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• −10𝑥
− 4𝑦level
= −8.5
– Second
• Third level
• 10𝑥 + 40𝑦
=
17.5
– Fourth level
Now combine.
» Fifth level
•
•
•
•
36y=9
y=0.25
Sub in one of the original equations.
5𝑥 + 2(0.25) = 4.25
x=0.75
X=0.75 and y=0.25
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• Now– that
you
Second
level know the price of each kind
• Third
level your work by substituting
of candy,
check
– Fourth level
your answer
into the second equation:
» Fifth level
• 2(0.75)+8(0.25) ? 3.5
• 1.5+2 = 3.5
#5-46 Jobs
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• Lucky
you!level
You are a new college graduate
– Second
• Third
level been offered two jobs.
and have
already
– Fourth level
Each job involves
exactly the same tasks,
» Fifth level
but the salary plans differ, as shown below.
• Job A offers a starting salary of 52,000 per
year with an annual increase of 3,000.
• Job B starts at 36,000 per year with a raise
of 11% per year.
#5-46 Jobs
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• A. Under
what
– Second
level conditions would Job A be a
• Third level
better choice?
When would Job B be a
– Fourth level
better choice?
Use graphs, tables and
» Fifth level
equations to help you justify your answer.
Solution
•
•
•
•
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Let x– be
thelevel
number of years.
Second
level
JOB A:• Third
𝑦– =
52,000
+
3000𝑥
Fourth level
𝑥
» Fifth level
JOB B: 𝑦 = 36,000(1.11)
Graph each… make sure to display the
window you choose.
graph
y f(x)=52000+3000x
80000
g(x)=36000(1.11)x
60000
40000
20000
x
-1
1
2
3
4
5
6
7
8
9
solution
•
•
•
•
•
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By using
the
– Second
levelintersect key:
• Third level
POI=( 6.625,
71876.17)
– Fourth level
Fifth level
What does x »coordinate
of POI represent?
What does y coordinate of POI represent?
So up to 6 years Job A is a better option.
Starting with year 7 Job B is a better option.
graph
y
Option B earns more x>7
52000+3000x<36000(1.11)x
80000
60000
40000
20000
Option A earns more for x<6
52000+3000x>36000(1.11)x
x
-1
1
2
3
4
5
6
7
8
9
#5-46 Jobs
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• B. How
would
– Second
level you change this problem
Third
levelJob B is always a better
slightly• so
that
– Fourth level
choice? How
could you change it so that
» Fifth level
Job A is always better.? If it is not possible
for Job A or Job B to always be the better
choice, explain why not.
On your own:
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• Review and Preview
• Review
your
– Second
level
Third level
• Page 234
notes. •Rewrite
– Fourth level
and fortify
them
if • # 48-53
» Fifth level
needed.
• Update your
vocab list, if
needed.
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– Second level
• Third level
– Fourth level
» Fifth level