Advanced Algebra 1 Midterm Exam Review

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Advanced Algebra 1Midterm Exam Review
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Chapter 1

• Equations

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Lesson Quiz Part I
Give two ways to write each algebraic expression
in words. 1. j 3 2. 4p 3. Mark is 5 years
older than Juan, who is y years old. Write an
expression for Marks age.
The difference of j and 3 3 less than j.
4 times p The product of 4 and p.
y 5
4
Lesson Quiz Part II
Evaluate each expression for c 6, d 5, and e
10. 4. 5. c d Shemika practices
basketball for 2 hours each day.
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6. Write an expression for the number of hours
she practices in d days. 7. Find the number of
hours she practices in 5, 12, and 20 days.
2d
10 hours 24 hours 40 hours
5
Lesson Quiz
Solve each equation. 1. r 4 8 2. 3. m
13 58 4. 0.75 n 0.6 5. 5 c 22 6. This
year a high school had 578 sophomores enrolled.
This is 89 less than the number enrolled last
year. Write and solve an equation to find the
number of sophomores enrolled last year.
4
45
0.15
27
s 89 578 s 667
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Lesson Quiz Part 1
Solve each equation. 1. 2. 3. 8y 4 4.
126 ?9q 5. 6.
21
2.8
14
40
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Lesson Quiz Part 2
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Lesson Quiz Part 1
Solve each equation. 1. 4y 8 2 2. 3. 2y
29 8y 5 4. 3(x 9) 30 5. x (12 x)
38 6.
8
4
19
25
9
9
Lesson Quiz Part 2
7. If 3b (6 b) 22, find the value of
7b. 8. Josie bought 4 cases of sports drinks for
an upcoming meet. After talking to her coach,
she bought 3 more cases and spent an additional
6.95 on other items. Her receipts totaled
74.15. Write and solve an equation to find how
much each case of sports drinks cost.
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4c 3c 6.95 74.15 9.60
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Lesson Quiz
Solve each equation. 1. 7x 2 5x 8 2.
4(2x 5) 5x 4 3. 6 7(a 1) 3(2
a) 4. 4(3x 1) 7x 6 5x 2 5. 6. A
painting company charges 250 base plus 16 per
hour. Another painting company charges 210 base
plus 18 per hour. How long is a job for which
the two companies costs are the same?
8
3
all real numbers
1
20 hours
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Lesson Quiz Part 1
Solve for the indicated variable. 1. 2. 3.
2x 7y 14 for y 4.
for h
P R C for C
C R P
for m
m x(k 6 )
5.
for C
C Rt S
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Lesson Quiz Part 2
Eulers formula, V E F 2, relates the
number of vertices V, the number of edges E, and
the number of faces F of a polyhedron.
6. Solve Eulers formula for F.
F 2 V E
7. How many faces does a polyhedron with 8
vertices and 12 edges have?
6
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Lesson Quiz
Solve each equation. 1. 15 x 2. 2x 7
14 3. x 1 9 9 4. 5 x 3 2
5. 7 x 8 6
15, 15
0, 14
1
6, 4
no solution
6. Inline skates typically have wheels with a
diameter of 74 mm. The wheels are manufactured so
that the diameters vary from this value by at
most 0.1 mm. Write and solve an absolute-value
equation to find the minimum and maximum
diameters of the wheels.
x 74 0.1 73.9 mm 74.1 mm
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Lesson Quiz Part 1
1. In a school, the ratio of boys to girls is
43. There are 216 boys. How many girls are there?
162
Find each unit rate. Round to the nearest
hundredth if necessary.
2. Nuts cost 10.75 for 3 pounds.
3.58/lb
3. Sue washes 25 cars in 5 hours.
5 cars/h
4. A car travels 180 miles in 4 hours. What is
the cars speed in feet per minute?
3960 ft/min
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Lesson Quiz Part 2
Solve each proportion.
5.
6
16
6.
7. A scale model of a car is 9 inches long. The
scale is 118. How many inches long is the car it
represents?
162 in.
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Lesson Quiz Part 1
Solve for the indicated variable. 1. 2. 3.
2x 7y 14 for y 4.
for h
P R C for C
C R P
for m
m x(k 6 )
5.
for C
C Rt S
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Lesson Quiz Part 2
Eulers formula, V E F 2, relates the
number of vertices V, the number of edges E, and
the number of faces F of a polyhedron.
6. Solve Eulers formula for F.
F 2 V E
7. How many faces does a polyhedron with 8
vertices and 12 edges have?
6
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Chapter 2

• Inequalities

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Lesson Quiz Part I
1. Describe the solutions of 7 lt x 4.
all real numbers greater than 3
2. Graph h 4.75
Write the inequality shown by each graph.
x 3
3.
4.
x lt 5.5
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Lesson Quiz Part II
5. A cell phone plan offers free minutes for no
more than 250 minutes per month. Define a
variable and write an inequality for the possible
number of free minutes. Graph the solution.
Let m number of minutes
0 m 250
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Lesson Quiz Part I
Solve each inequality and graph the solutions.
1. 13 lt x 7
x gt 6
2. 6 h 15
h 21
3. 6.7 y 2.1
y 8.8
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Lesson Quiz Part II
4. A certain restaurant has room for 120
customers. On one night, there are 72 customers
dining. Write and solve an inequality to show how
many more people can eat at the restaurant.
x 72 120 x 48, where x is a natural number
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Lesson Quiz
Solve each inequality and graph the solutions.
1. 8x lt 24
x lt 3
2. 5x 30
x 6
4.
3.
x gt 20
x 6
5. A soccer coach plans to order more shirts for
her team. Each shirt costs 9.85. She has 77
left in her uniform budget. What are the possible
number of shirts she can buy?
0, 1, 2, 3, 4, 5, 6, or 7 shirts
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Lesson Quiz Part I
Solve each inequality and graph the solutions.
1. 13 2x 21
x 4
2. 11 2 lt 3p
p gt 3
t gt 7
3. 23 lt 2(3 t)
4.
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Lesson Quiz Part II
5. A video store has two movie rental plans. Plan
A includes a 25 membership fee plus 1.25 for
each movie rental. Plan B costs 40 for unlimited
movie rentals. For what number of movie rentals
is plan B less than plan A?
more than 12 movies
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Lesson Quiz Part I
Solve each inequality and graph the solutions.
1. t lt 5t 24
t gt 6
2. 5x 9 4.1x 81
x 80
b lt 13
3. 4b 4(1 b) gt b 9
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Lesson Quiz Part II
4. Rick bought a photo printer and supplies for
186.90, which will allow him to print photos for
0.29 each. A photo store charges 0.55 to print
each photo. How many photos must Rick print
before his total cost is less than getting prints
made at the photo store?
Rick must print more than 718 photos.
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Lesson Quiz Part III
Solve each inequality.
5. 2y 2 2(y 7)
no solutions
6. 2(6r 5) lt 3(4r 2)
all real numbers
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Lesson Quiz Part I
1. The target heart rate during exercise for a 15
year-old is between 154 and 174 beats per minute
inclusive. Write a compound inequality to show
the heart rates that are within the target range.
Graph the solutions.
154 h 174
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Lesson Quiz Part II
Solve each compound inequality and graph the
solutions.
2. 2 2w 4 12
1 w 4
3. 3 r gt -2 OR 3 r lt -7
r gt 5 OR r lt 10
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Lesson Quiz Part III
Write the compound inequality shown by each graph.
4.
x lt -7 OR x 0
5.
-2 a lt 4
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Chapter 3

• Functions

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Lesson Quiz Part I
1. Write a possible situation for the given graph.
Possible Situation The level of water in a
bucket stays constant. A steady rain raises the
level. The rain slows down. Someone dumps the
bucket.
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Lesson Quiz Part II
2. A pet store is selling puppies for 50 each.
It has 8 puppies to sell. Sketch a graph for this
situation.
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Lesson Quiz Part I
1. Express the relation (2, 5), (1, 4), (1,
3), (2, 4) as a table, as a graph, and as a
mapping diagram.
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Lesson Quiz Part II
2. Give the domain and range of the relation.
D 3 x 2 R 2 y 4
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Lesson Quiz Part III
3. Give the domain and range of the relation.
Tell whether the relation is a function. Explain.
D 5, 10, 15 R 2, 4, 6, 8 The relation is
not a function since 5 is paired with 2 and 4.
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Lesson Quiz Part I
Identify the independent and dependent variables.
Write a rule in function notation for each
situation.
1. A buffet charges 8.95 per person.
independent number of people dependent
cost f(p) 8.95p
2. A moving company charges 130 for weekly truck
rental plus 1.50 per mile.
independent miles dependent cost f(m) 130
1.50m
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Lesson Quiz Part II
Evaluate each function for the given input values.
3. For g(t) , find g(t) when t 20 and
when t 12.
g(20) 2 g(12) 6
4. For f(x) 6x 1, find f(x) when x 3.5 and
when x 5.
f(3.5) 20 f(5) 31
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Lesson Quiz Part III
Write a function to describe the situation. Find
a reasonable domain and range for the function.
5. A theater can be rented for exactly 2, 3, or 4
hours. The cost is a 100 deposit plus 200 per
hour.
f(h) 200h 100 Domain 2, 3, 4 Range 500,
700, 900
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Lesson Quiz Part I
1. Graph the function for the given domain.
3x y 4 D 1, 0, 1, 2
2. Graph the function y x 3.
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Lesson Quiz Part II
3. The function y 3x describes the distance (in
inches) a giant tortoise walks in x seconds.
Graph the function. Use the graph to estimate how
many inches the tortoise will walk in 5.5
seconds.
About 16.5 in.
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Lesson Quiz Part I
For Items 1 and 2, identify the correlation you
would expect to see between each pair of data
sets. Explain.
1. The outside temperature in the summer and the
cost of the electric bill
Positive correlation as the outside temperature
increases, the electric bill increases because of
the use of the air conditioner.
2. The price of a car and the number of
passengers it seats
No correlation a very expensive car could seat
only 2 passengers.
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Lesson Quiz Part II
3. The scatter plot shows the number of orders
placed for flowers before Valentines Day at one
shop. Based on this relationship, predict the
number of flower orders placed on February 12.
about 45
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Lesson Quiz Part I
Determine whether each sequence appears to be an
arithmetic sequence. If so, find the common
difference and the next three terms in the
sequence.
1. 3, 9, 27, 81,
not arithmetic
2. 5, 6.5, 8, 9.5,
arithmetic 1.5 11, 12.5, 14
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Lesson Quiz Part II
Find the indicated term of each arithmetic
sequence.
3. 23rd term 4, 7, 10, 13,
70
4. 40th term 2, 7, 12, 17,
197
5. 7th term a1 12, d 2
0
89
6. 34th term a1 3.2, d 2.6
7. Zelle has knitted 61 rows of a scarf. Each day
she adds 17 more rows. How many rows total has
Zelle knitted 16 days later?
333 rows
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Chapter 4

• Linear Functions

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Lesson Quiz Part I
Tell whether each set of ordered pairs satisfies
a linear function. Explain.
1. (3, 10), (1, 9), (1, 7), (3, 4), (5, 0)
No a constant change of 2 in x corresponds to
different changes in y.
2. (3, 4), (5, 7), (7, 10), (9, 13), (11, 16)
Yes a constant change of 2 in x corresponds to
a constant change of 3 in y.
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Lesson Quiz Part II
Tell whether each function is linear. If so,
graph the function.
3. y 3 2x
no
yes
4. 3y 12
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Lesson Quiz Part III
5. The cost of a can of iced-tea mix at Save More
Grocery is 4.75. The function f(x) 4.75x gives
the cost of x cans of iced-tea mix. Graph this
function and give its domain and range.
D 0, 1, 2, 3, R 0, 4.75, 9.50,
14.25,
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Lesson Quiz Part I
1. An amateur filmmaker has 6000 to make a film
that costs 75/h to produce. The function f(x)
6000 75x gives the amount of money left to make
the film after x hours of production. Graph this
function and find the intercepts. What does each
intercept represent?
x-int. 80 number of hours it takes to spend all
the money
y-int. 6000 the initial amount of money
available.
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Lesson Quiz Part II
2. Use intercepts to graph the line described by
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Lesson Quiz Part I
Name each of the following.
1. The table shows the number of bikes made by a
company for certain years. Find the rate of
change for each time period. During which time
period did the number of bikes increase at the
fastest rate?
1 to 2 3 2 to 5 4 5 to 7 0 7 to 11 3.5
from years 2 to 5
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Lesson Quiz Part II
Find the slope of each line.
2.
3.
undefined
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Lesson Quiz
1. Find the slope of the line that contains (5,
3) and (1, 4).
2. Find the slope of the line. Then tell what the
slope represents.
50 speed of bus is 50 mi/h
3. Find the slope of the line described by x 2y
8.
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Lesson Quiz Part I
Tell whether each equation represents a direct
variation. If so, identify the constant of
variation.
1. 2y 6x
yes 3
no
2. 3x 4y 7
Tell whether each relationship is a direct
variation. Explain.
3.
4.
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Lesson Quiz Part II
5. The value of y varies directly with x, and y
8 when x 20. Find y when x 4.
1.6
6. Apples cost 0.80 per pound. The equation y
0.8x describes the cost y of x pounds of apples.
Graph this direct variation.
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Lesson Quiz Part I
Write the equation that describes each line in
the slope-intercept form.
1. slope 3, y-intercept 2
y 3x 2
2. slope 0, y-intercept
3. slope , (2, 7) is on the line
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Lesson Quiz Part II
Write each equation in slope-intercept form. Then
graph the line described by the equation.
4. 6x 2y 10
5. x y 6
y x 6
y 3x 5
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Lesson Quiz Part I
Write an equation in slope-intercept form for the
line with the given slope that contains the given
point.
1. Slope 1 (0, 9)
y x 9
2. Slope (3, 6)
Write an equation in slope-intercept form for the
line through the two points.
3. (1, 7) and (2, 1)
y 2x 5
4. (0, 4) and (7, 2)
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Lesson Quiz Part II
5. The cost to take a taxi from the airport is a
linear function of the distance driven. The cost
for 5, 10, and 20 miles are shown in the table.
Write an equation in slope-intercept form that
represents the function.
y 1.6x 6
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Lesson Quiz Part I
Write an equation is slope-intercept form for the
line described.
1. contains the point (8, 12) and is parallel to
2. contains the point (4, 3) and is
perpendicular to y 4x 5
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Lesson Quiz Part II
3. Show that WXYZ is a rectangle.
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Lesson Quiz Part I
Describe the transformation from the graph of
f(x) to the graph of g(x). 1. f(x) 4x, g(x) x
2. 3. 4.
rotated about (0, 0) (less steep)
f(x) x 1, g(x) x 6
translated 7 units up
f(x) x, g(x) 2x
rotated about (0, 0) (steeper)
f(x) 5x, g(x) 5x
reflected across the y-axis, rot. about (0, 0)
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Lesson Quiz Part II
5. f(x) x, g(x) x 4 6.
translated 4 units down
f(x) 3x, g(x) x 1
rotated about (0, 0) (less steep), translated 1
unit up
7. A cashier gets a 50 bonus for working on a
holiday plus 9/h. The total holiday salary is
given by the function f(x) 9x 50. How will
the graph change if the bonus is raised to 75?
if the hourly rate is raised to 12/h?
translate 25 units up rotated about (0, 50)
(steeper)
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Chapter 5

• System of Equations and Inequalities

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Lesson Quiz Part I
Tell whether the ordered pair is a solution of
the given system. 1. (3, 1) 2. (2,
4)
no
yes
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Lesson Quiz Part II
Solve the system by graphing. 3. 4. Joy has
5 collectable stamps and will buy 2 more each
month. Ronald has 25 collectable stamps and will
sell 3 each month. After how many months will
they have the same number of stamps?
How many will that be?
y 2x 9
(2, 5)
y 4x 3
4 months
13 stamps
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Lesson Quiz Part I
Solve each system by substitution. 1. 2.
3.
y 2x
(2, 4)
x 6y 11
(1, 2)
3x 2y 1
3x y 1
x y 4
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Lesson Quiz Part II
4. Plumber A charges 60 an hour. Plumber B
charges 40 to visit your home plus 55 for each
hour. For how many hours will the total cost for
each plumber be the same? How much will that cost
be? If a customer thinks they will need a plumber
for 5 hours, which plumber should the customer
hire? Explain.
8 hours 480 plumber A plumber A is cheaper
for less than 8 hours.
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Lesson Quiz
Solve each system by elimination. 1. 2. 3.

2x y 25
(11, 3)
3y 2x 13
3x 4y 18
(2, 3)
x 2y 4
2x 3y 15
(3, 7)
3x 2y 23
4. Harlan has 44 to buy 7 pairs of socks.
Athletic socks cost 5 per pair. Dress socks cost
8 per pair. How many pairs of each can Harlan
buy?
4 pairs of athletic socks and 3 pairs of dress
socks
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Lesson Quiz Part I
Solve and classify each system. 1. 2. 3.
infinitely many solutions consistent, dependent
y 5x 1
5x y 1 0
no solutions inconsistent
y 4 x
x y 1
y 3(x 1)
consistent, independent
y x 2
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Lesson Quiz Part II
4. If the pattern in the table continues, when
will the sales for Hats Off equal sales for Tops?
never
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Lesson Quiz Part I
1. You can spend at most 12.00 for drinks at a
picnic. Iced tea costs 1.50 a gallon, and
lemonade costs 2.00 per gallon. Write an
inequality to describe the situation. Graph the
solutions, describe reasonable solutions, and
then give two possible combinations of drinks you
could buy.
1.50x 2.00y 12.00
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Lesson Quiz Part I
1.50x 2.00y 12.00
Only whole number solutions are reasonable.
Possible answer (2 gal tea, 3 gal lemonade) and
(4 gal tea, 1 gal lemonde)
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Lesson Quiz Part II
2. Write an inequality to represent the graph.
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Lesson Quiz Part I
y lt x 2
1. Graph .
5x 2y 10
Give two ordered pairs that are solutions and two
that are not solutions.
Possible answer solutions (4, 4), (8, 6) not
solutions (0, 0), (2, 3)
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Lesson Quiz Part II
2. Dee has at most 150 to spend on restocking
dolls and trains at her toy store. Dolls cost
7.50 and trains cost 5.00. Dee needs no more
than 10 trains and she needs at least 8 dolls.
Show and describe all possible combinations of
dolls and trains that Dee can buy. List two
possible combinations.
80
Lesson Quiz Part II Continued
Reasonable answers must be whole numbers.
Possible answer (12 dolls, 6 trains) and (16
dolls, 4 trains)
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