Resources

Resources

Interpreting Linear Expressions

A particular type of cell triples in number every hour. Which function can be used to find the number of cells present at the end of

h

hours if there are initially

6

of these cells?

\newline

f(h)=6 x^{h}

\newline

f(h)=6(3)^{h}

\newline

f(h)=3(6)^{h}

\newline

f(h)=3(6 h)

the rectangle below has an area of

x^2+8x+15

square meters and a width of

x+3

meters. What expression represents the length of the rectangle

the rectangle below has an area of

x^2-7x+10

square meters and a width of

x-5

meters. What expression represents the length of the rectangle?

n

pairs of couple, how many handshake will be there given couple does not make handshake with themselves

Water is filling a pool. The function

W

gives the pool's water level (in meters) after

t

\newline

What is the best interpretation for the following statement?

\newline

The slope of the line tangent to the graph of

W

t=5

0

1

\newline

1

C

gives the costs (in dollars) of producing

x

liters of a certain sauce.

\newline

What is the best interpretation for the following statement?

\newline

The slope of the line tangent to the graph of

C

x=12

4

\newline

1

C

gives the costs (in dollars) of producing

\boldsymbol{x}

liters of a certain sauce.

\newline

What is the best interpretation for the following statement?

\newline

The slope of the line tangent to the graph of

C

x=12

4

Gaia is driving her truck from Paris to Lyon. The function

D

gives the total distance Gaia has driven (in kilometers) after

t

\newline

What is the best interpretation for the following statement?

\newline

The slope of the line tangent to the graph of

D

t=3

90

The Golden Gate Bridge is a suspension bridge that consists of two cables hung from two towers of equal height that are approximately

1280\,\text{m}

apart. The height of the cable above the ground, in meters, can be modeled by the quadratic function

h(x) = 0.000371(x-640)^2

x

is the distance in meters measured from the left tower. Which of the following approximately equivalent expressions displays the height of the tower as a constant or coefficient?

The Golden Gate Bridge is a suspension bridge that consists of two cables hung from two towers of equal height that are approximately

1280\,\text{m}

apart. The height of the cable above the ground, in meters, can be modeled by the quadratic function

h(I) = 0.000371(x-640)^2

a

is the distance in meters measured from the left tower. Which of the following approximately equivalent expressions displays the height of the tower as a constant or coefficient?

\frac{1}{2}bh

gives the area of a triangle where

b

is the base of the triangle and

h

is the height of the triangle. what is the area of the triangle with a base of

7\,\text{cm}

and a height of

4\,\text{cm}

Suppose that the mean systolic blood pressure for women over age seventy is

131 \mathrm{mmHg}

(millimeters of mercury), with a standard deviation of

6 \mathrm{mmHg}

. Suppose that the blood pressures are normally distributed. Complete the following statements.

\newline

(a) Approximately

99.7 \%

of women over seventy have blood pressures between

\square \mathrm{mmHg}

\square \mathrm{mmHg}

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(b) Approximately ? V of women over seventy have blood pressures between

119

\mathrm{mmHg}

143 \mathrm{mmHg}

The population of fish in a pond grew over a five-year period according to the function

\newline

P(t)=20(2.50)^{\frac{t}{5}},

\newline

t

represents time in years. Move the options to the spaces to rewrite

\newline

P(t)

in an equivalent form that reveals the annual growth rate of the fish.

\newline

\newline

0.50

\newline

1.20

\newline

1.82

\newline

2.50

\newline

4

\newline

20

\newline

t

0

The population of fish in a pond grew over a five.year period according to the function

P(t)=20(2.50)^{\frac{t}{5}}

t

represents time in years. Move the options to the spaces to rewrite

P(t)

in an equivalent form that reveals the annual growth rate of the fish.

\newline

P(t)=\underline{(-)^{t}}

\newline

0

50

\newline

1

20

\newline

1

82

\newline

2

50

\newline

4

\newline

20

\newline

100

D=1,874-0.55 t

\newline

D

, in meters, between an antarctic glacier and the coast

t

days after January

1

2010

is approximated by the equation. How does the distance between the glacier and the coast change over time?

\newline

1

\newline

(A) The glacier moves

0

55

meters per day closer to the shore.

\newline

(B) The glacier moves

1

874

meters per day closer to the shore.

\newline

(C) The glacier moves

0

55

meters per day further from the shore.

\newline

(D) The glacier moves

1

874

meters per day further from the shore.

D

in millions of miles of the voyager

1

space craft from the sun

m

months after January

1

2015

is approximately by the equation

D=27.4m+12,100

. What is the best interpretation of

27.4

as shown in the given equation?

A once-popular children's doll is slowly declining in popularity. The quartic function

\newline

f(x)=0.002 x^{4}+0.025 x^{3}-0.364 x^{2}-7.243 x+86.993

\newline

x

is the number of years since

1993

, can be used to estimate the number of dolls of this type that were sold (in thousands) during a given year from

1993

2003

. Estimate how many dolls were sold in

1997

h=16,890-3.4t

\newline

h

, in feet, of a mountain at a time,

t

, measured in thousands of years from the present is given by the equation. What is the best interpretation of

16,890

as shown in the given equation?

\newline

1

\newline

(A) The height of the mountain is presently

16,890

\newline

(B) The height of the mountain will reach

0

16,890

years from now.

\newline

(C) The height of the mountain increases by

16,890

feet every thousand years.

\newline

(D) The height of the mountain decreases by

16,890

feet every thousand years.

5^{1.15^x}

gives the area, in square meters, of forest damaged by a fire as a function of minutes since the fire was discovered. How many square meters of forest was damaged when the fire was discovered?

Fiona's Fashion Store is world renowned for its buttoned uniforms.

\newline

A collection of

36

42

jackets contains

842

buttons. A collection of

6

7

jackets contains

137

buttons. Each shirt has the same number of buttons, and each jacket has the same number of buttons.

\newline

How many buttons are there in a Fiona's Fashion shirt, and how many buttons are there in a jacket?

\newline

1

\newline

(A) There is not enough information to determine the exact number of buttons in a shirt or jacket.

\newline

(B) The given information describes an impossible situation.

\newline

10

buttons in a single shirt and

11

buttons in a single jacket.

\newline

11

buttons in a single shirt and

10

buttons in a single jacket.

A habitat of prairie dogs can support

m

dogs at most. The habitat's population,

p

, grows proportionally to the product of the current population and the difference between

m

p

. Which equation describes this relationship?

A sequence starts at

10

. The term-to-term rule is to subtract

3

then multiply by

2

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a) Work out the fourth term of the sequence.

\newline

b) Is this sequence increasing, decreasing or neither?

A research probe needs to be

0.5

meters under the ground. It is known that the probe must be traveling

140

meters per second at impact to reach a depth of

0.5

meters. If the probe is dropped from

10b^2

(b is constant) meters above the ground and the distance traveled is given by the function

s(t) = 4.9t^2

. Find the value of

b

and the height the probe should be dropped from.

Caleb is going to throw a ball from the top floor of his middle school. The function

h(t)=-16t^{2}+16t+192

models the height,

h

, of the ball above the ground as a function of time

t

. Find the time(s) when the ball's height is

192

feet. The ball has a height of

192

t=

seconds. (If there is more than one answer, express your answers separated by commas)

A researcher is cooling a metal. She cools the metal so that the temperature of the metal drops at a constant rate. After

15

minutes of cooling, the metal is

470^{\circ}C

39

minutes, the metal is

230^{\circ}C

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(a) Choose the statement that best describes how the time and the temperature of the metal are related. Then fill in the blank.

\newline

As time increases, the temperature of the metal decreases.

\newline

The temperature of the metal decreases at a rate of

\square^{\circ}C

\newline

As time increases, the temperature of the metal increases.

\newline

The temperature of the metal increases at a rate of

\square^{\circ}C

\newline

(b) What was the temperature of the metal when the researcher started cooling it?

\newline

\square^{\circ}C

18

3

2

69

\newline

\newline

1

3

\newline

0

1

\newline

\newline

The amount of a particular pollutant

p

from a power plant in the air above the plant depends on the wind speed

s

, among other things, with the relationship between

p

s

approximated by

p=32-0.02s^{2}

s

in miles per hour. a. Find the value(s) of

s

p=0

\newline

p=0

mean in this application?

\newline

c. What solution to

0=32-0.02s^{2}

makes sense in the context of this application?

\newline

a. The value(s) of

s

p=0

s

2

\newline

(Simplify your answer. Use a comma to separate answers as needed.)

A_y = \frac{3}{4}X \quad x - 5y = 0

For what value of

a

does the system of linear equations in the variables

x

y

have infinitely many solutions?

A_y = \frac{3}{4}X

x - 5y = 0

For what value of

a

does the system of linear equations in the variables

x

y

have infinitely many solutions?

Noa drove from the Dead Sea up to Jerusalem. When she arrived in Jerusalem after

1.5

hours of driving, her altitude was

710

meters above sea level. Her altitude increased at a constant rate of

740

meters per hour.

\newline

y

represent Noa's altitude (in meters) relative to sea level after

x

\newline

Complete the equation for the relationship between the altitude and number of hours.

P(t)=1,800(1.004)^{t}

\newline

The function models

P

, the amount of money, in dollars, in Yara's savings account

t

years after she opened the account with an initial deposit of

\$ 1,800

. How much money is in Yara's account

5

years after her initial deposit if she makes no deposits or withdraws in that time?

Kiran has a collection of vintage action figures that is worth

\$ 320

. If the collection appreciates at a rate of

14.8 \%

per year, which equation represents the value of the collection after

8

\newline

V=320(1+0.148)

\newline

V=320(1.148)^{8}

\newline

V=320(0.148)^{8}

\newline

V=320(1-0.148)^{8}

A town has a population of

118

600

and grows at a rate of

5 \%

every year. Which equation represents the town's population after

4

\newline

P=118,600(1+0.05)^{4}

\newline

P=118,600(1+0.05)

\newline

P=118,600(0.05)^{4}

\newline

P=118,600(0.95)^{4}

In a lab experiment, a population of

500

bacteria is able to triple every hour. Which equation matches the number of bacteria in the population after

4

\newline

B=500(1+3)^{4}

\newline

B=3(500)^{4}

\newline

B=3(1+500)^{4}

\newline

B=500(3)(3)(3)(3)

A town has a population of

27

000

and shrinks at a rate of

8 \%

every year. Which equation represents the town's population after

7

\newline

P=27,000(0.2)^{7}

\newline

P=27,000(0.92)^{7}

\newline

P=27,000(1-0.08)(1-0.08)(1-0.08)

\newline

P=27,000(0.08)^{7}

The formula gives the volume of a right square pyramid of height

h

and square base of side length

s

. If the side length of a right square pyramid increases by

30\%

while the height remains constant, what happens to the volume?

P = 23 + 10(h - 1)

People start waiting in line for the release of the newest cell phone at

5

a.m. The equation gives the number of people,

P

, in line between the hours,

h

6

11

a.m., when the doors open. Assume that

6

a.m. is when time

h = 1

. What does the

23

mean in the equation?

5.5 B+4R=28

The given equation models the cost if Amit picks

B

pounds of blueberries and

R

pounds of raspberries at a farm where blueberries cost

\$5.50

per pound and raspberries cost

\$4.00

per pound. According to the equation, how much does Amit spend in total on both types of berries? Choose

1

(A) \$\$9.50

\$22.00

\$28.00

\$56.00

Lauren launches a toy rocket from a platform. The height of the rocket in feet is given by

h(t)=-16 t^{2}+48 t+28

t

represents the time in seconds after launch. What is the appropriate domain for this situation?

\newline

For the function

f

f(0) = 86

, and for each increase in

x

1

f(x)

80\%

. What is the value of

f(2)

Water leaking onto a floor forms a circular pool. The area of the pool increases at a rate of

16\,\text{picm}^{2}/\text{min}

. How fast is the radius of the pool increasing when the radius is

7\,\text{cm}

A perfect cube shaped ice cube melts so that the length of its sides are decreasing at a rate of

2\frac{\text{in}}{\text{sec}}

. Assume that the block retains its cube shape as it melts. At what rate is the volume of the ice cube changing when the sides are

7\text{in}

Chase signed up for a streaming music service where there's a fixed cost for monthly membership and a cost per song downloaded. His total cost per month is given by the equation

c=7.99+1.25 x

x

represents the number of songs he downloads and

c

represents the total cost, in dollars and cents. What could the number

7

99

represent in the equation?

\newline

The total cost per month assuming one song is downloaded.

\newline

The cost to download

100

\newline

The change in the total cost for every one additional download.

\newline

The base cost of the streaming service per month.

Nakeisha is driving on a long road trip. She wrote an equation to represent how many gallons of gas she has left in her tank,

g=11-0.45 h

g

represents the number of gallons and

h

represents time in hours. What is the meaning of the

g

h=1

\newline

The number of gallons of gas initially in the tank.

\newline

The change in the number of gallons of gas in the tank for every one additional hour.

\newline

The number of gallons in the tank after one hour.

\newline

The number of gallons in the tank when the trip ends.

At the beginning of spring, Lily planted a small sunflower in her backyard. The sunflower's height in inches,

h

w

weeks, is given by the equation

h=4 w+18

. What could the number

4

represent in the equation?

\newline

The sunflower's height after one week.

\newline

The rate of change in the sunflower's height.

\newline

The sunflower's final height

\newline

The sunflower's height when it was planted.

Jose's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation

y=67+6.6 x

y

represents the expected quiz score and

x

represents hours spent on homework that week. What is the meaning of the

y

x=1

\newline

A student's expected quiz score if they spent

73

6

hours on their homework.

\newline

The change in expected quiz score for every additional one hour students spend on their homework.

\newline

A student's expected quiz score if they spent

1

hour on their homework.

\newline

A student's expected quiz score if they spent no time on their homework.

At the beginning of spring, Anand planted a small sunflower in his backyard. The sunflower's height in inches,

h

w

weeks, is given by the equation

h=3.75 w+18

. What could the number

3

75

represent in the equation?

\newline

The rate of change in the sunflower's height.

\newline

The sunflower's final height

\newline

The sunflower's height after one week.

\newline

The sunflower's height when it was planted.

Ajay is preheating his oven before using it to bake. Ajay wants to predict the final temperature after

x

minutes. He wrote the equation

y=45 x+79

y

represents the final temperature in degrees Fahrenheit. What is the meaning of the

y

x=1

\newline

The oven's temperature after

1

\newline

The change in minutes for every change of one degree Fahrenheit.

\newline

The rate of change in the oven's temperature over time.

\newline

The time when the oven's temperature is

0^{\circ}

Melissa and Rachel like to make funny hats. Melissa has made

20

zebra-printed hats, and Rachel has made

h

striped hats. Together they have made a total of

42

\newline

Write an equation to describe this situation.

\newline

1350(1.05)^t

models the average wages, in dollars, in the US as a function of the number of years since

1930

\newline

1.05

represent in this expression?

\newline

1

\newline

(A) The average wages double every

1.05

\newline

(B) The average wages in the US were about

\newline

\$1.05

1930

\newline

(C) The average wages in the US increase by about

\newline

5\%

The amount in moles,

m

, of a reactant

s

seconds after the start of a chemical reaction is given by the equation

m= 0.15(8.6-s)

. Which of the following is the best interpretation of the number

0.15

\newline

(A) The initial amount of reactant was

0.15

\newline

(B) The amount of reactant decreases by

0.15

moles per second.

\newline

(C) No reactant remains

0.15

seconds after the start of the chemical reaction.

\newline

(D) The amount of reactant begins to decrease

0.15

seconds after the start of the chemical reaction.

...