Transcript MAC2 Chapter 04 - Math

Mathematics: Applications and Concepts, Course 2 Interactive Chalkboard
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Lesson 4-1 Writing Expressions and Equations
Lesson 4-2 Solving Addition and Subtraction Equations
Lesson 4-3 Solving Multiplication Equations
Lesson 4-4 Solving Two-Step Equations
Lesson 4-5 Inequalities
Lesson 4-6 Functions and Linear Equations
Lesson 4-7 Lines and Slope
Example 1 Write a Phrase as an Expression
Example 2 Write a Sentence as an Equation
Example 3 Write Sentences as Equations
Example 4 Write Sentences as Equations
Write the phrase twenty dollars less the price of a
movie ticket as an algebraic expression.
Words
twenty dollars less the price of
a movie ticket
Variable
Let m represent the price of a
movie ticket.
Equation
Answer:
Write the phrase five more inches of snow than last
year’s snowfall as an algebraic expression.
Answer:
Write the sentence a number less 4 is 12 as an
algebraic equation.
Words
Variable
Equation
Answer:
a number less 4 is 12
Let n represent a number.
Write the sentence eight less than a number is 12 as
an algebraic equation.
Answer:
Write the sentence twice a number is 18 as an
algebraic equation.
Words
Variable
Equation
Answer:
twice a number is 18
Let a represent a number.
Write the sentence four times a number equals 96 as
an algebraic equation.
Answer:
FOOD An average American adult drinks
more soft drinks than any other beverage
each year. Three times the number of
gallons of soft drinks plus 27 is equal to the
total 183 gallons of beverages consumed.
Write an equation that models this situation.
Words
Variable
Three times the number of gallons
of soft drinks plus 27 equals 183.
Let s = the number of gallons of
soft drinks.
Equation
Answer: The equation is
EXERCISE It is estimated that American adults spend
an average of 8 hours per month exercising. This is
26 hours less than twice the number of hours spent
watching television each month. Write an equation
that models this situation.
Answer:
Example 1 Solve an Addition Equation
Example 2 Solve a Subtraction Equation
Example 3 Use an Equation to Solve a Problem
Solve
Method 1 Use symbols.
Write the equation.
Subtract 14 from each side.
Simplify.
Method 2 Use models.
Answer: The solution is 6.
Solve
Answer: –10
Solve
Check your solution.
Method 1 Use symbols.
Write the equation.
Add 8 to each side.
Simplify.
Method 2 Use models.
Check
Write the original equation.
Replace z with 20.
This sentence is true.
Answer: The solution is 20.
Solve
Answer:
Check your solution.
SPORTS If Tiger Woods had scores of –1, –4, and –3
on his first three rounds in a golf tournament, what
would his fourth round score need to be if his final
score was –18?
Words
The sum of the scores for all rounds was –18.
Variable
Let s represent the score for the fourth round.
Equation
scores for the
first three rounds
score for the
fourth round
final score
Write the original equation.
Add 8 to each side.
Simplify.
Check You can check the solution by adding.
Answer: Tiger Woods needs to score –10 for the fourth
round.
HIKING Kyle wants to hike a trail that is 7 miles long.
If he hikes 2, 1, and 2 miles during the first three
hours of his hike, how far would he need to hike in
the fourth hour in order to complete the trail?
Answer: 2 miles
Example 1 Solve Multiplication Equations
Example 2 Solve Multiplication Equations
Example 3 Use an Equation to Solve a Problem
Solve
Check your solution.
Write the equation.
Divide each side of the equation by 3.
Check
Write the original equation.
Replace y with 13. Is this sentence true?
Answer: The solution is 13.
Solve
Answer: 7
Check your solution.
Solve
Check your solution.
Write the equation.
Divide each side of the equation by –4.
Check
Write the original equation.
Replace z with –15. Is this sentence true?
Answer: The solution is –15.
Solve
Answer: 4
Check your solution.
SPORTS At 6,072 feet, California
Screamin’ is the longest steel roller
coaster in the world. The ride takes 2
minutes 30 seconds to complete. Find
the speed of the roller coaster in feet
per second.
Words
Distance is equal to rate times the time.
Variable
d
r
Equation
6,072
r
t
150
Write the equation.
Divide each side of the equation by 150.
Answer: The roller coaster travels at a
speed of 40.48 feet per second.
TRAVEL David is driving on a business trip. He
drives a total of 589 miles at an average speed of 62
miles per hour. How many hours does David spend
driving?
Answer: 9.5 hours
Example 1 Solve a Two-Step Equation
Example 2 Solve a Two-Step Equation
Example 3 Solve a Two-Step Equation
Example 4 Use an Equation to Solve a Problem
Solve
Check your solution.
Write the equation.
Subtract 3 from each side.
Simplify.
Divide each side by 4.
Simplify.
Check
Write the original equation.
Replace x with 4. Is this sentence true?
Answer: The solution is 4.
Solve
Answer: 7
Check your solution.
Solve
. Check your solution.
Write the equation.
Subtract 9 from each side.
Simplify.
Divide each side by –3.
Simplify.
Check
Write the original equation.
Replace c with 2. Is this sentence true?
Answer: The solution is 2.
Solve
Answer: –3
. Check your solution.
Solve
Check your solution.
Write the equation.
Subtract 6 from each side.
Simplify.
Divide each side by 3.
Simplify.
Check
Write the original equation.
Replace t with –2. Is this sentence true?
Answer: The solution is –2.
Solve
Answer: 8
Check your solution.
PARKS There are 76,000 acres of state parkland in
Georgia. This is 4,000 acres more than three times the
number of acres of state parkland in Mississippi. How
many acres of state parkland are there in Mississippi?
Words
Variable
Equation
Let m
the acres of state parkland in
Mississippi.
Three times the number of acres of state
parkland in Mississippi plus 4,000 equals
76,000.
Write the equation.
Subtract 4,000 from each side.
Simplify.
Divide each side by 3.
Simplify.
Answer: There are 24,000 acres of state parkland
in Mississippi.
BASEBALL Matthew had 64 hits during last year’s
baseball season. This was 8 less than twice the
number of hits Gregory had. How many hits did
Gregory have during last year’s baseball season?
Answer: 36 hits
Example 1 Graph Solutions of Inequalities
Example 2 Graph Solutions of Inequalities
Example 3 Graph Solutions of Inequalities
Example 4 Graph Solutions of Inequalities
Example 5 Solve One-Step Inequalities
Example 6 Solve One-Step Inequalities
Example 7 Use an Inequality to Solve a Problem
Graph the inequality
on a number line.
Answer:
The open circle means
that the number is not
included in the solution.
Graph the inequality
Answer:
on a number line.
Graph the inequality
on a number line.
Answer:
The closed circle means
that the number is
included in the solution.
Graph the inequality
Answer:
on a number line.
Graph the inequality
Answer:
on a number line.
Graph the inequality
Answer:
on a number line.
Graph the inequality
Answer:
on a number line.
Graph the inequality
Answer:
on a number line.
Solve
solution.
Check your solution. Then graph the
Write the inequality.
Add 7 to each side.
Simplify.
Check Try 8, a number less than 9.
Write the inequality.
Replace x with 8. Is this sentence true?
Answer: The solution is all numbers less than 9.
Solve
solution.
Answer:
Check your solution. Then graph the
Solve
Graph the solution.
Write the inequality.
Divide each side by 6.
Check this solution.
Answer: The solution is all numbers greater than or
equal to 4.
Solve
Answer:
Graph the solution.
BASEBALL CARDS Jacob is buying uncirculated
baseball cards online. The cards he has chosen are
$6.70 each and the Web site charges a $1.50 service
charge for each sale. If Jacob has no more than $35
to spend, how many cards can he buy?
Let c represent the number of baseball cards Jacob
can buy.
Write the inequality.
Subtract 1.50 from each side.
Simplify.
Divide each side by 6.70.
Answer: Jacob can buy no more than 5 baseball cards.
BOWLING Danielle is going bowling.
The charge for renting shoes is $1.25
and each game costs $2.25. If Danielle
has no more than $8 to spend on
bowling, how many games can she
play?
Answer: no more than 3
Example 1 Make a Function Table
Example 2 Graph Solutions of Linear Equations
Example 3 Represent Real-World Functions
WORK Asha makes $6.00 an hour working at a
grocery store. Make a function table that shows
Asha’s total earnings for working 1, 2, 3, and 4 hours.
Input
Function
Output
Number of
Hours
Multiply by 6
1
61
6
2
62
12
3
63
18
4
64
24
Total
Earnings
($)
MOVIE RENTAL Dave goes to the video store to rent
a movie. The cost per movie is $3.50. Make a function
table that shows the amount Dave would pay for
renting 1, 2, 3, and 4 movies.
Answer:
Input
Function Rule
Output
Number of
Movies
Multiply by 3.50
Total
Cost ($)
1
3.50  1
3.50
2
3.50  2
7.00
3
3.50  3
10.50
4
3.50  4
14.00
Graph
Select any four values for the input x. We chose 2, 1, 0,
and –1. Substitute these values for x to find the output y.
(2, 5)
(0, 3)
(1, 4)
(–1, 2)
Answer: Four solutions are
(2, 5), (1, 4), (0, 3), and (–1, 2).
Graph
Answer:
ANIMALS Blue whales can reach a speed of 30
miles per hour in bursts when in danger. The
equation
describes the distance d that a
whale traveling at that speed can travel in time t.
Represent this function with a graph.
Step 1
Select any four values for t. Select only positive
numbers because t represents time. Make a
function table.
t
30t
d
(t, d)
2 30(2) 60
(2, 60)
3
30(3)
90
(3, 90)
5
6
30(5) 150
30(6) 180
(5, 150)
(6, 180)
Step 2
Answer:
Graph the ordered pairs and draw a line through
the points.
TRAVEL Susie takes a car trip traveling at an average
speed of 55 miles per hour. The equation
describes the distance d that Susie travels in time t.
Represent this function with a graph.
Answer:
Example 1 Positive Slope
Example 2 Negative Slope
Example 3 Negative Slope
Example 4 Compare Slopes
Find the slope of the line.
2 units right
4 units up
Answer: The slope of
the line is 2.
Find the slope of the line.
Answer:
Find the slope of the line.
5 units left
5 units up
Answer: The slope of
the line is –1.
Find the slope of the line.
Answer: –2
Find the slope of the line.
3 units down
Answer: The slope of
4 units right
the line is
Find the slope of the line.
Answer:
MULTIPLE- CHOICE TEST ITEM The Americans with
Disabilities Act states that the maximum slope of a ramp in
new construction shall be
this requirement?
A
B
C
D
rise: 30 in.; run: 300 in.
rise: 30 in.; run: 360 in.
rise: 30 in.; run: 380 in.
rise: 30 in.; run: 400 in.
. Which ramp does not meet
Read the Test Item
The rise corresponds to the vertical change, or
change in y.
The run corresponds to the horizontal change, or
change in x.
Solve the Test Item
Find the slope of each ramp.
The only ramp with a slope greater than
Answer: A
is Ramp A.
MULTIPLE- CHOICE TEST ITEM The architects building a
new baseball stadium want all of the ramps in the stadium
to have the same slope. Which of the following ramps has
a different slope from the others?
A
B
C
D
rise: 50 ft; run: 700 ft
rise: 30 ft; run: 420 ft
rise: 40 ft; run: 480 ft
rise: 60 ft; run: 840 ft
Answer: C
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