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Math Problems
Algebra 1
Write a linear function: word problems
A gas station charges
9
9
9
$
\$
$
for a drive-through car wash.
\newline
Write an equation that shows how the total car wash earnings,
y
y
y
, depends on the number of cars washed,
x
x
x
.
\newline
Do not include dollar signs in the equation.
\newline
y = ____
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Carlos is a receptionist at a law firm. He spends
2
2
2
minutes routing each phone call as it comes in. Write an equation that shows how the total number of minutes Carlos spends routing calls,
y
y
y
, depends on the number of calls,
x
x
x
.
\newline
y = ____
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Brody is excited to start singing lessons. His teacher says he will learn
2
2
2
vocal pieces each month. Write an equation that shows the relationship between the number of months Brody takes voice lessons,
x
x
x
, and the number of pieces he knows,
y
y
y
.
\newline
y = ____
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There are
28
28
28
women and
21
21
21
men attending online webinar. what is the ratio of women to the total number of people ?
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Esther the clown does a face painting at the city carnival, she paints
7
7
7
faces every
21
21
21
minutes and spends the same amount of time painting each face. Write an equation that relates
f
f
f
, the number of faces she paints, and
m
m
m
, the time she spends painting in minutes.
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A clothier who only makes shirts and pants can make a shirt in
4
4
4
hours and a pair of pants in
6
6
6
hours. Which of the following equations shows the number of shirts,
s
s
s
, and the number of pants,
p
p
p
, that the clothier can make in a
40
40
40
hour work week?
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Video games create a sense of motion by displaying still images, called frames, in rapid succession. A popular video game displays
60
60
60
frames per second. Which of the following equations shows the total number of frames,
f
f
f
, that the video game will display in
s
s
s
seconds?
\newline
Choose
1
1
1
answer:
\newline
(A)
f
=
s
+
60
f=s+60
f
=
s
+
60
\newline
(B)
f
=
s
60
f=\frac{s}{60}
f
=
60
s
\newline
(C)
f
=
60
s
f=\frac{60}{s}
f
=
s
60
\newline
(D)
f
=
60
s
f=60s
f
=
60
s
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A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly and at a constant rate. After
8
8
8
months, he weighed
138
138
138
kilograms. He started at
90
90
90
kilograms.Let
y
y
y
represent the sumo wrestler's weight (in kilograms) after
x
x
x
months.
\newline
Complete the equation for the relationship between the weight and number of months.
\newline
y
=
□
y=\square
y
=
□
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Kayden is a stunt driver. One time, during a gig where she escaped from a building about to explode(!), she drove at a constant speed to get to the safe zone that was
160
160
160
meters away. After
3
3
3
seconds of driving, she was
85
85
85
meters away from the safe zone.
\newline
Let
y
y
y
represent the distance (in meters) from the safe zone after
x
x
x
seconds.
\newline
Complete the equation for the relationship between the distance and number of seconds.
\newline
y
=
□
y=\square
y
=
□
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A manufacturing plant earner
$
80
\$80
$80
per man-hour of labor when it opened. Each year, the plant earns an additional
5
%
5\%
5%
per man-hour. Write a function that gives the amount
A
(
t
)
A(t)
A
(
t
)
that the plant earns per man-hour
t
t
t
years after it opens.
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Zoey goes to a store and buys an item that costs
x
x
x
dollars. She has a coupon for
20
%
20 \%
20%
off, and then a
7
%
7 \%
7%
tax is added to the discounted price. Write an expression in terms of
x
x
x
that represents the total amount that Zoey paid at the register.
\newline
Answer:
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Deondra goes to a store and buys an item that costs
x
x
x
dollars. She has a coupon for
35
%
35 \%
35%
off, and then a
5
%
5 \%
5%
tax is added to the discounted price. Write an expression in terms of
x
x
x
that represents the total amount that Deondra paid at the register.
\newline
Answer:
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24
24
24
\newline
Question
\newline
What are the critical points for the plane curve defined by the equations
x
(
t
)
=
cot
t
,
y
(
t
)
=
sin
t
x(t)=\cot t, y(t)=\sin t
x
(
t
)
=
cot
t
,
y
(
t
)
=
sin
t
, and
0
<
t
<
π
0<t<\pi
0
<
t
<
π
? Write your answer as a list of values of
t
t
t
, separated by commas. For example, if you found
t
=
1
t=1
t
=
1
or
t
=
2
t=2
t
=
2
, you would enter
1
1
1
,
2
2
2
.
\newline
Provide your answer below:
\newline
FEEDBACK
\newline
MORE INSTRUCTION
\newline
SUBMIT
\newline
aluations
\newline
\& Policy
\newline
Content attribution
\newline
I Grades
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Each student in Mr. Ricardo's class has one camera that holds
320
320
320
pictures. He asks each student to delete
1
4
\frac{1}{4}
4
1
of the pictures and turn in the rest. Which of the following functions best represents the number of pictures,
p
p
p
, that Mr. Ricardo will collect depending on the number of cameras,
c
c
c
, that his students have?
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A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. After
11
11
11
months, he weighed
140
140
140
kilograms. He gained weight at a rate of
5.5
5.5
5.5
kilograms per month.
\newline
Let
y
y
y
represent the sumo wrestler's weight (in kilograms) after
x
x
x
months.
\newline
Complete the equation for the relationship between the weight and number of months.
\newline
y
=
□
y=\square
y
=
□
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A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. After
11
11
11
months, he weighed
140
140
140
kilograms. He gained weight at a rate of
5.5
5.5
5.5
kilograms per month.
\newline
Let
y
y
y
represent the sumo wrestler's weight (in kilograms) after
x
x
x
months.
\newline
Complete the equation for the relationship between the weight and number of months.
\newline
y
=
□
y=\square
y
=
□
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Solve the following equation for
b
b
b
. Be sure to take into account whether a letter is capitalized or not.
\newline
f
b
−
h
b
=
D
f b-h b=D
f
b
−
hb
=
D
\newline
Answer:
b
=
b=
b
=
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Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
B
+
a
=
D
B+a=D
B
+
a
=
D
\newline
Answer:
a
=
a=
a
=
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Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
m
=
a
+
9
m=a+9
m
=
a
+
9
\newline
Answer:
a
=
a=
a
=
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Fabio and Carlos play on a basketball team together. In the last game, Fabio had
7
7
7
points less than
2
2
2
times as many points as Carlos. Fabio scored
31
31
31
points in the game. Write an equation to determine the number of points Carlos scored in the last game. Find the number of points Carlos scored in the last game.
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A paintball court charges an initial entrance fee plus a fixed price per ball.
\newline
The variable
p
p
p
models the total price (in dollars) as a function of
n
n
n
, the number of balls used.
\newline
p
=
0.80
n
+
5.50
p = 0.80n + 5.50
p
=
0.80
n
+
5.50
\newline
What is the entrance fee?
\newline
$
\$
$
□
\square
□
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Charong has
21
21
21
cousins. If
12
12
12
of Charong's cousins live in the same city as Charong does, what is the ratio of the number of Charong's cousins who live in the same city as Charong does to the total number of cousins Charong has?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
:
7
3:7
3
:
7
\newline
(B)
4
:
7
4:7
4
:
7
\newline
(C)
4
:
11
4:11
4
:
11
\newline
(D)
7
:
4
7:4
7
:
4
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A habitat of prairie dogs can support
m
m
m
dogs at most.
\newline
The habitat's population,
p
p
p
, grows proportionally to the product of the current population and the difference between
m
m
m
and
p
p
p
.
\newline
Which equation describes this relationship?
\newline
Choose
1
1
1
answer:
\newline
(A)
d
p
d
t
=
k
p
(
m
−
p
)
\frac{d p}{d t}=k p(m-p)
d
t
d
p
=
k
p
(
m
−
p
)
\newline
(B)
d
p
d
t
=
k
m
m
−
p
\frac{d p}{d t}=\frac{k m}{m-p}
d
t
d
p
=
m
−
p
km
\newline
(C)
d
p
d
t
=
k
p
m
−
p
\frac{d p}{d t}=\frac{k p}{m-p}
d
t
d
p
=
m
−
p
k
p
\newline
(D)
d
p
d
t
=
k
m
(
m
−
p
)
\frac{d p}{d t}=k m(m-p)
d
t
d
p
=
km
(
m
−
p
)
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A habitat of prairie dogs can support
m
m
m
dogs at most.
\newline
The habitat's population,
p
p
p
, grows proportionally to the product of the current population and the difference between
m
m
m
and
p
p
p
.
\newline
Which equation describes this relationship?
\newline
Choose
1
1
1
answer:
\newline
(A)
d
p
d
t
=
k
p
m
−
p
\frac{d p}{d t}=\frac{k p}{m-p}
d
t
d
p
=
m
−
p
k
p
\newline
(B)
d
p
d
t
=
k
m
(
m
−
p
)
\frac{d p}{d t}=k m(m-p)
d
t
d
p
=
km
(
m
−
p
)
\newline
(C)
d
p
d
t
=
k
p
(
m
−
p
)
\frac{d p}{d t}=k p(m-p)
d
t
d
p
=
k
p
(
m
−
p
)
\newline
(D)
d
p
d
t
=
k
m
m
−
p
\frac{d p}{d t}=\frac{k m}{m-p}
d
t
d
p
=
m
−
p
km
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The population of a town grows at a rate of
r
(
t
)
r(t)
r
(
t
)
people per year (where
t
t
t
is time in years).
\newline
What does
∫
2
4
r
(
t
)
d
t
\int_{2}^{4} r(t) d t
∫
2
4
r
(
t
)
d
t
represent?
\newline
Choose
1
1
1
answer:
\newline
(A) The change in number of people between the second and the fourth year.
\newline
(B) The time it took for the town to grow from a population of
2
2
2
people to a population of
4
4
4
people.
\newline
(C) The number of people in the town on the fourth year.
\newline
(D) The average rate at which the population grew between the second and the fourth year.
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Jessica is a custodian at Oracle Arena. She waxes
20
m
2
20 \mathrm{~m}^{2}
20
m
2
of the floor in
3
5
\frac{3}{5}
5
3
of an hour. Jessica waxes the floor at a constant rate.
\newline
At this rate, how many square meters can she wax per hour?
\newline
m
2
\mathrm{m}^{2}
m
2
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Yusef earned a total of
180
180
180
dollars from drawing
12
12
12
identically-priced pictures at a festival.
\newline
Write an equation to describe the relationship between
p
p
p
, the number of pictures, and
e
e
e
, the total earnings.
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Mariana wears her winter coat when the temperature is colder than
−
4
∘
C
-4^{\circ} \mathrm{C}
−
4
∘
C
.
\newline
Write an inequality that describes
t
t
t
, temperatures at which Mariana wears her winter coat.
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P
(
t
)
=
400
(
1.5
)
t
P(t)=400(1.5)^{t}
P
(
t
)
=
400
(
1.5
)
t
\newline
Biologists stocked a lake with a new species of fish. The number of the new species of fish in the lake,
P
(
t
)
,
t
P(t), t
P
(
t
)
,
t
years after being stocked, is shown. How many fish did the biologists initially add to the lake?
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A charity organization had to sell a few tickets to their fundraiser just to cover necessary production costs. After selling
10
10
10
tickets, they were still at a net loss of
$
800
\$ 800
$800
(due to the production costs). They sold each ticket for
$
70
\$ 70
$70
.
\newline
Let
y
y
y
represent the net profit (in dollars) when they have sold
x
x
x
tickets.
\newline
Complete the equation for the relationship between the net profit and number of tickets sold.
\newline
y
=
□
y=\square
y
=
□
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T
=
1200
−
0.06
c
T=1200-0.06 c
T
=
1200
−
0.06
c
\newline
A print shop copies and prints documents in large volume for its customers. For a particular copy machine, the equation gives the amount of toner,
T
T
T
, in grams, left after making
c
c
c
copies. How many grams of toner are used per copy?
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Naoya read a book cover to cover in a single session, at a rate of
55
55
55
pages per hour. After
4
4
4
hours, he had
350
350
350
pages left to read.
\newline
Let
y
y
y
represent the number of pages left to read after
x
x
x
hours.
\newline
Complete the equation for the relationship between the number of pages left and number of hours.
\newline
y
=
y=
y
=
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