Download 4.5 - David Beydler`s Math

Math 50
4.5 – Applications and Problem Solving
1
To solve problems with two or more unknowns:
1. Select a variable to represent one of the unknowns
2. Write expression(s) the other unknown(s) in terms
of the variable.
3. Write an equation using the variable and
expressions from 1 and 2.
4. Solve the equation.
2
To solve problems with two or more unknowns:
1. Select a variable to represent one of the unknowns
2. Write expression(s) the other unknown(s) in terms
of the variable.
3. Write an equation using the variable and
expressions from 1 and 2.
4. Solve the equation.
3
To solve problems with two or more unknowns:
1. Select a variable to represent one of the unknowns
2. Write expression(s) the other unknown(s) in terms
of the variable.
3. Write an equation using the variable and
expressions from 1 and 2.
4. Solve the equation.
4
To solve problems with two or more unknowns:
1. Select a variable to represent one of the unknowns
2. Write expression(s) the other unknown(s) in terms
of the variable.
3. Write an equation using the variable and
expressions from 1 and 2.
4. Solve the equation.
5
Ex 1.
An LCD monitor is to have a rectangular screen with a width that
is 5 inches less than twice the height and a perimeter of 44
inches. What are the dimensions of the screen?
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Ex 1.
An LCD monitor is to have a rectangular screen with a width that
is 5 inches less than twice the height and a perimeter of 44
inches. What are the dimensions of the screen?
7
Ex 1.
An LCD monitor is to have a rectangular screen with a width that
is 5 inches less than twice the height and a perimeter of 44
inches. What are the dimensions of the screen?
8
Ex 1.
An LCD monitor is to have a rectangular screen with a width that
is 5 inches less than twice the height and a perimeter of 44
inches. What are the dimensions of the screen?
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A triangle with all three sides of equal length is
called an __________________.
10
A triangle with all three sides of equal length is
equilateral triangle
called an __________________.
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A triangle with two sides of equal length is
called an _________________.
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A triangle with two sides of equal length is
isosceles triangle
called an _________________.
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Ex 2.
Suppose each of the equal-length sides of an
isosceles triangle is 3 inches more than the base.
The perimeter is 30 inches. What are the
lengths of the base and the sides of equal
length?
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Two angles whose measurements sum to _____
are called _____________________.
15
Two angles whose measurements sum to _____
𝟗𝟎∘
are called _____________________.
16
Two angles whose measurements sum to _____
𝟗𝟎∘
are called _____________________.
complementary angles
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Two angles whose measurements sum to _____
are called _____________________.
ex: ∠𝐵𝑂𝐴 and ∠𝐶𝑂𝐵 are supplementary angles
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Two angles whose measurements sum to _____
𝟏𝟖𝟎∘
are called _____________________.
ex: ∠𝐵𝑂𝐴 and ∠𝐶𝑂𝐵 are supplementary angles
19
Two angles whose measurements sum to _____
𝟏𝟖𝟎∘
are called _____________________.
supplementary angles
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Note: The angles of a triangle sum to _______.
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∘
𝟏𝟖𝟎
Note: The angles of a triangle sum to _______.
∠𝑨 + ∠𝑩 + ∠𝑪 = 𝟏𝟖𝟎∘
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∘
𝟏𝟖𝟎
Note: The angles of a triangle sum to _______.
∠𝑨 + ∠𝑩 + ∠𝑪 = 𝟏𝟖𝟎∘
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∘
𝟏𝟖𝟎
Note: The angles of a triangle sum to _______.
∠𝑨 + ∠𝑩 + ∠𝑪 = 𝟏𝟖𝟎∘
24
∘
𝟏𝟖𝟎
Note: The angles of a triangle sum to _______.
∠𝑨 + ∠𝑩 + ∠𝑪 = 𝟏𝟖𝟎∘
25
∘
𝟏𝟖𝟎
Note: The angles of a triangle sum to _______.
∠𝑨 + ∠𝑩 + ∠𝑪 = 𝟏𝟖𝟎∘
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Ex 3.
Two angles are to be constructed from metal
beams so that they are complementary angles.
One of the angles is to be 6° less than three
times the other angle. What are the angle
measurements?
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Ex 4.
You sell two kinds of drinks: lemonade and
guava juice. Each glass of lemonade costs $3,
and each glass of guava juice costs $5. Suppose
the number of glasses of lemonade you sold one
day was 10 less than twice the number of
glasses of guava juice you sold. Also suppose
that your total sales that day were $190. How
many glasses of each kind of drink did you sell
that day?
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Ex 5.
A farmer has a total of 17 pigs and chickens.
The combined number of legs is 58. How many
pigs and how many chickens are there?
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