Resources

Resources

Evaluate two-variable equations: word problems

The quotient of a number,

z

21

42

. Which equation and value of

z

represent this relationship?

\newline

\frac{1}{21} z=42

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21 z=42

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\frac{1}{21} z=42

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21 z=42

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z=2

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z=2

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z=882

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z=882

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\newline

The position of an object moving in a straight line, in kilometers, can be modeled by the function

s(

t

is measured in days. The velocity of the object is

2

kilometers per day when

t=5

. Selected values of

s(t)

are shown in the table below. Use a linear approximation when

t=5

to estimate the position of the object at time

t=4.8

. Use proper units.

\newline

\begin{tabular}{|c|c|c|c|c|c|c|}

\newline

t

0

5

8

13

18

20

\newline

s(t)

30

40

55

80

90

100

\newline

\newline

Rafael purchased his car for

\$12,000

. The value of Rafael's car depreciates over time, decreasing by

10\%

every year. Which of the following graphs could model this relationship if

t

is elapsed time in years, and

V

is the value of Rafael's car in thousands of dollars?

12

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An unknown metal has been found and the following experimental results have been tabulated in the table below. The table contains the grams of the unknown metal and the volume in milliliters of water displacement. Find a linear model that express volume as a function of the mass.

\newline

Round your answers to

3

\newline

\begin{tabular}{|r|r|}

\newline

\hline grams & Volume in

\mathrm{ml}

\newline

18

141

3

\newline

19

5

153

1

\newline

21

168

1

\newline

22

5

178

4

\newline

24

184

6

\newline

25

5

202

2

\newline

27

214

1

\newline

\newline

\newline

=

\square

x+

\square

x

is the grams of the unknown metal

\newline

\square

Message instructor

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Submit Question

c

more crackers than Brooke. Brooke ate only

8

crackers. Write an expression that shows how many crackers Mason ate.

8-c

A passenger is riding a Ferris wheel The graph shows the height, in feet. of the passenger as a function of time

A store sells all compact discs for

\$14.99

. The following equation represents the revenue,

y

, (in dollars) generated by selling

x

\newline

y=14.99x

(x \geq 0)

\newline

0

4

\newline

1

4

\newline

y=\square

x=8

The table shows the most commonly spoken five languages in the world by native and non-native speakers, in millions, according to the

2013

SIL Ethnologue. If the relative frequency of Spanish non-native speakers to all non-native speakers was

4.8 \%

, approximately how many non-native Spanish speakers, in millions, were there in

2013 ?

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1

\newline

20

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59

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119

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594

The table shows

x

y

values for a quadratic function. Based on the table, which of the following statements is true?

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\newline

x

\newline

y

\newline

\newline

-4

\newline

-6

\newline

\newline

-3

\newline

-2

\newline

\newline

-2

\newline

1

\newline

\newline

y

0

\newline

1

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y

2

\newline

-2

\newline

\newline

1

\newline

-6

\newline

\newline

a. The graph of the function has

y

6

x

\newline

b. The graph of the function has

y

6

x

\newline

c. The graph of the function has

1

x

- intercept and

1

x

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d. The graph of the function has no

x

Use the shell method to find the volume of the solid generated by revolving the shaded region about the

x

\newline

Set up the integral that gives the volume of the solid.

\newline

The volume of the solid generated by revolving the shaded region about the

x

\square

cubic units. (Type an exact answer, using

\pi

Given the cone dimensions below:

\newline

cone's slant height

=20 \mathrm{~m}

\newline

=12 \mathrm{~m}

\newline

Find the height of the cone and the cone's volume.

\newline

=

\qquad

\newline

=

The internal temperature, in degrees Celsius, of an electric, convection oven was measured over a two-minute interval. The data Is shown below, where

t

is measured in minutes.

\newline

\begin{tabular}{|c|c|c|c|c|c|c|}

\newline

t

0

0

5

1

1

5

2

\newline

{ }^{\circ} \mathrm{C}

18

29

677

48

929

80

670

133

003

\newline

\newline

\newline

Which of the following models best represents this situation as a function of time?

\newline

Elimination Tool

\newline

Setect one answer

\newline

C(t)=56.2 x+5.856

\newline

C(t)=18 e^{t}

\newline

C(t)=18^{t}+17

A party store sells tablecloths for

\$1

5

\$5

10

\$8

. Is the relationship between the number of tablecloths purchased and total cost a linear relationship?

\newline

\newline

\newline

\newline

Now, justify your answer.

\newline

\newline

(A)Tablecloths cost a constant amount,

\$1

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(B)The three money amounts don't increase by a constant amount.

\newline

(C)The three quantities of tablecloths don't increase by a constant amount.

\newline

(D)The cost per tablecloth can vary, depending on how many you buy.

It's the end of the summer, and Sandeep is draining his family's swimming pool. The function

y = -600x + 12,000

represents the total number of gallons in the pool,

y

, as a function of the number of hours the pool has been draining,

x

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What is true about the function?

\newline

\newline

(A)It is nonlinear because it decreases at a constant rate.

\newline

(B)It is nonlinear because it is always decreasing.

\newline

(C)It is linear because it decreases at a constant rate.

\newline

(D)It is linear because it is always decreasing.

A cafeteria purchases milk from one of three providers each week, depending on what other items need to be purchased. The probability of shopping at each store and the cost of one gallon of milk are shown in the table below

\newline

\newline

Probability and Milk Cost by Store

\newline

\newline

\newline

\newline

Milk Cost per Gallon

\newline

\newline

\newline

30\%

\newline

\$300

\newline

\newline

\newline

10\%

\newline

\$350

\newline

\newline

\newline

60\%

\newline

\$275

\newline

\newline

The cafeteria should budget

\$

on average for one gallon of milk

A store manager adjusts the price of an item each week that the item goes unsold. The price of the unsold item, in dollars, after

\newline

x

weeks can be modeled by the exponential function

\newline

f(x)=320(0.90)^{x}

\newline

Select ONE correct answer in each box to complete each sentence.

\newline

The initial price of the item before the store manager made any adjustments was

\newline

\newline

\$288

\newline

\newline

\$320

\newline

\newline

\$352

\newline

The price of the item

\newline

\newline

\newline

\newline

110\%

T

0

25q

+ 87

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Manon's statistics professor puts a bonus question on every test, which adds

0.25

points to a student's overall grade at the end of the term. The equation gives Manon's current overall grade,

T

, after taking into account

q

extra credit questions answered correctly. What does the

87

mean in this equation?

\newline

1

\newline

(A) Manon must get an

87

or above to pass.

\newline

(B) Manon's average is an

87

before adding the extra credit.

\newline

(C) After adding in her extra credit, Manon's average is an

87

\newline

(D) Manon's professor gave

87

opportunities for extra credit this term.

w=\sqrt{108w}

\newline

What is the sum of all solutions to the given equation?

During a mayoral election, candidate A spent

\$960,000

on her campaign, and candidate B spent

\$720,000

on her campaign. What is the ratio of candidate A's campaign spending to candidate B's campaign spending?

\newline

1

\newline

3:4

\newline

4:3

\newline

7:9

\newline

9:7

Dina is conducting a study on the amount of electricity used per person in the country of Qatar. She finds that from the year

2000

2008

, the amount of electricity used per person grew by an average of

6\%

from one year to the next. Let

e(t)

be the amount of electricity used per person in kilowatt-hours and

t

the number of years after

2000

. If the amount of electricity used per person in

2000

was approximately

12,300

kilowatt-hours, which of the following mathematical models will give Dana how much electricity was used per person between

2000

2008

Fernando built a robot to filter air and water efficiently. He expects the robot to filter more than

512

liters of air and water while using less than

9

Joules of energy.

\newline

A

represents the number of minutes the robot filters air, and

\newline

W

represents the number of minutes the robot filters water.

\newline

21A + 14W > 512

represents the number of minutes the robot filters air and water to filter more than

512

liters of air and water.

\newline

0.36A + 0.6W < 9

represents the number of minutes the robot filters air and water while using less than

9

Joules of energy.

\newline

Does the robot meet both of Fernando's expectations by filtering air for

15

minutes and filtering water for

5

Hanson is at a ball game with his family. He goes to the concession stand to buy soft pretzels and water bottles for everyone. A water bottle costs

2\$

, and a pretzel costs

3.50\$

16

items and spends

47\$

\newline

This system of equations can be used to represent the situation:

\newline

x + y = 16

\newline

2x + 3.5y = 47

\newline

Which statement is correct?

\newline

(A) In the system of equations,

x

represents the amount of money Hanson spends on pretzels, and

y

represents the amount of money he spends on water bottles.

\newline

(B) In the system of equations,

x

represents the number of water bottles Hanson buys, and

y

represents the number of pretzels he buys.

\newline

(C) In the system of equations,

x

represents the number of pretzels Hanson buys, and

y

represents the number of water bottles he buys.

\newline

(D) In the system of equations,

x

represents the amount of money Hanson spends on water bottles, and

y

represents the amount of money he spends on pretzels.

\newline

How much money does Hanson spend on pretzels?

\newline

3.50\$

2

3.50\$

3

Susan set up a lemonade stand to raise money for a children's hospital. She's selling cups of lemonade for

2.50

\$

each and brownies for

1.50

\$

each. She sells

280

items and raises

540

\$

. This system of equations can be used to represent the situation:

\newline

x + y = 280

\newline

2.5x + 1.5y = 540

\newline

Which statement is correct?

\newline

(A) In the system of equations,

x

represents the amount of money Susan raises from selling brownies, and

\$

0

represents the amount of money she raises from selling lemonade.

\newline

(B) In the system of equations,

x

represents the number of brownies Susan sells, and

\$

0

represents the number of cups of lemonade she sells.

\newline

(C) In the system of equations,

x

represents the number of cups of lemonade Susan sells, and

\$

0

represents the number of brownies she sells.

\newline

(D) In the system of equations,

x

represents the amount of money Susan raises from selling lemonade, and

\$

0

represents the amount of money she raises from selling brownies.

\newline

How much money does Susan raise from selling lemonade?

\newline

\$

During the youth baseball season, Carter grills and sells hamburgers and hot dogs at the Hillview baseball field. On Saturday, he sold

30

25

hot dogs and earned a total of

\$195

. On Sunday, he sold

15

20

hot dogs and earned a total of

\$120

\newline

This system of equations can be used to represent the situation.

\newline

\newline

Complete the sentence.

\newline

How much does Carter charge for a hot dog?

\newline

\$

Mr. Lee wants to hire a balloon artist for the carnival day at school, and he is considering two companies that each charge a fixed hourly rate. A balloon artist from The Amusing Muse charges

\$549

3

hours. This equation describes how much a balloon artist from Laugh Time Parties charges. In the equation,

y

represents the cost in dollars for

x

\newline

\newline

y = 190x

\newline

Which company charges more per hour?

\newline

\newline

(A)The Amusing Muse

\newline

(B)Laugh Time Parties

\newline

How much would that company charge for

2

\newline

\$

Supriya makes papadums to sell in her food truck. She uses

12 \mathrm{oz}

of dough to make each batch.

\newline

60 \mathrm{oz}

of dough and wants to know how many batches she can make.

\newline

Write a multiplication equation to describe the situation.

\newline

dough for one batch

\newline

number of batches

\newline

total amount of dough

Translate the sentence into an equation.

\newline

8

times a number and

9

2

\newline

Use the variable

b

for the unknown number.

y

years old. His father is twenty five years older than Chebii. The sum of their ages is

84

years. Form an equation that can be used to calculate their ages.

Capital SD Links

\newline

myapps.classlink.c

\newline

Desmos |Scientific.

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6

14

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7

15

1

point) I Question Attempt:

1

2

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Lashonda has a part-time job and gets paid the same amount each hour. For each hour she works, she puts

\$9

aside for her mom. Lashonda works

3

hours a day and the total amount she keeps each day is

\$18

. How much does she get paid each hour?

\newline

(a) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then fill in the blanks with the numbers

9

3

18

h

represent the amount (in dollars) Lashonda gets paid each hour.

\newline

\square

\newline

(h+ \square )= \square

\newline

\square(h-\square)= \square

\newline

(b) Solve the equation in part (a) to find the amount (in dollars) Lashonda gets paid each hour.

\newline

h=\square

\newline

\newline

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2024

McGraw Hill LLC. All Rights Reserved.

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27

A. Get the shortest path on the given graph below, find the shortest path between Point A (Node A) to Point J (Node J). (

10

\newline

Design Analysis and Algorithms - Activity \#

1

\newline

B. Get the permutation and combination of the given below. (

5

\newline

1

. A company is developing a new mobile application and needs to select a team of

\mathbf{4}

developers from a pool of

\mathbf{2 0}

skilled individuals. How many different teams can be formed, assuming each team member has a distinct role in the development process?

\newline

2

. A cybersecurity expert is creating a passcode for a secure facility. The passcode must be

8

characters long, consisting of

2

uppercase letters,

2

lowercase letters,

2

2

special characters. How many unique passcodes can be generated following these requirements?

Cyce city charges an initial price of \$\(15\) plus \$\(0\).\(75\) per hour for bike rentals, which is represented by the expression \$\(15\)\(-0\).\(75\)h. Complete each statement to describe the terms. The variable \(h\) represents ? The constant \(15\) represents ? The variable term \(0.75h\) represents ?

The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using

14

HCF of water is

\$39.89

, and the cost for using

51

\$100.94

. What is the cost for using

21

The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for

40

minutes of calls is

\$15.60

and the monthly cost for

62

\$18.46

. What is the monthly cost for

56

minutes of calls?

The ratio boys : girls in a park is

\newline

1:4

\newline

65

girls leave and the ratio becomes

\newline

4:3

\newline

Work out how many boys there are in the park.

\newline

\square

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Calculator Permitted

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Get Video Help on this Topic

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45 \%

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Costcorp sells packets of mints to shop owners.

\newline

On Monday three shop owners buy mints from Costcorp. Each shop owner buys small packets, medium packets and large packets of mints.

\newline

400

packets of mints.

\newline

32 \%

are small packets.

\newline

40 \%

are large packets.

\newline

500

packets of mints.

\newline

\frac{3}{10}

are small packets.

\newline

\frac{1}{10}

are large packets.

\newline

150

small packets of mints so that

\newline

number of small packets : number of medium packets

=3: 4

\newline

Work out the total number of medium packets of mints these shop owners buy.

\newline

5

\newline

\square

10

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10

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What does the law of large numbers state about the mean,

\bar{x}

, of observed values, when the number of observations drawn at

\newline

All of the choices are correct.

\newline

\bar{x}

, tends to get closer to the population mean,

\mu

\newline

\bar{x}

, tends to get smaller.

\newline

\bar{x}

, tends to get larger.

Three friends drove radio controlled cars around a track. The table below shows the number of laps completed by each person and the time it took.

\newline

\begin{tabular}{|l|c|c|c|}

\newline

\hline & Diane & Karen & Elsa \\

\newline

\hline Time (minutes) &

5

3

6

\newline

\hline Number of laps &

40

18

60

\newline

\newline

\newline

Write the number of laps completed per minute for each person. Then determine who drove the fastest.

\newline

Number of laps completed per minute by Diane:

\square

\newline

Number of laps completed per minute by Karen:

\square

\newline

Number of laps completed per minute by Elsa:

\square

\newline

Select the person who drove the fastest.

\newline

\newline

\newline

Three gardeners trimmed bushes in a large courtyard. The table below shows the number of bushes each of them trimmed and how much spent.

\newline

\begin{tabular}{|c|c|c|c|}

\newline

\hline & \begin{tabular}{c}

\newline

\newline

\newline

\end{tabular} & \begin{tabular}{c}

\newline

\newline

\newline

\end{tabular} & \begin{tabular}{c}

\newline

\newline

\newline

\end{tabular} \\

\newline

\hline Number of bushes &

8

4

9

\newline

\hline Time (minutes) &

48

16

45

\newline

\newline

\newline

Write the time it took per bush for each gardener. Then determine who trimmed bushes the fastest.

\newline

Time taken per bush for the first gardener:

\square

\newline

Time taken per bush for the second gardener:

\square

\newline

Time taken per bush for the third gardener:

\square

\newline

Select the gardener who trimmed bushes the fastest.

\newline

\newline

Second gardener

\newline

1.4 \times 10^{5}

bacteria are measured to be in a dirt sample that weighs

1

gram. Use scientific notation to express the number of bacteria that would be in a sample weighing

4

\newline

\square \times 10^ \square

\newline

\newline

\newline

1

5

Slope-intercept form: write an equation from a graph

9 \mathrm{GW}

\newline

Write the equation of this line in slope-intercept form.

\newline

Write your answer using integers, proper fractions, and improper fractions in simplest form.

\newline

y=1

Mrs. Avery makes note of the different types of plants in her garden and creates a bar graph to display the data.

\newline

MRS. AVERY'S GARDEN

\newline

1

: There are one-fourth the number of peppers as there are lettuce plants.

\newline

2

: The number of lettuce and pepper plants is equal to the number of tomato and strawberry plants.

\newline

3

: Fifty percent of the plants are lettuce plants.

1.05S + 1.02B

predicts the end-of-year value of a financial portfolio, where

S

is the value of stocks in dollars and

B

is the value of bonds in dollars in the portfolio at the beginning of the year. What is the predicted end-of-year value, in dollars, of a portfolio that begins the year with

S

dollars in stocks and

B

dollars in bonds?

24

. A loaf of bread costs

\$ 2.50

and appler cosest

\$ 1.29

per pound. Write a linear function to represent the price of a loaf of bread and some apples. Graph the function on a separate sheet of paper. How much will you pay if you buy

3

pounds of apples?

\qquad

\newline

=5 x

\newline

bout the relationship

The image shows the distances in kilometers between three cities.

\newline

How much closer is it to travel from Aurora to Clifton directly than from Aurora to Clifton through Burlington?

\newline

\square

\newline

Show Calculator

\sqrt{12}

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5

Find a value using two-variable equations

46 Q

\newline

Learn with an example

\newline

\newline

\newline

Use the equation

a=h+8

to find the value of

a

h=3

\newline

a=

\newline

\square

\newline

\newline

\newline

Not feeling ready yet? These can help

\newline

Evaluate yariable expressions with whole numbers

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The Information for two pzy-as-yc -go cell phone companles is glven.

\newline

\newline

35

\$ 10

\newline

What is the unit rate in dollas: er hour for each company?

\newline

The unit rate in dolls is per \& ir for On Call is

\$

\square

per hour and the unit rate In dollars per hour for Talk Time is \$ \( \square \) per hour.\(\newline\)Which company offers the better deal? Complete the explanation.\(\newline\)The company which offers the better deal is \( \square \) (select) because their rate per hour is lower.\(\newline\)Another company offers a rate of \( \$ 0.06 \) per minute. How would you find the unit rate per hour?\(\newline\)\( \square \) \(0\).\(06\) by \(60\) because there are \(60\) minutes in \(1\) hour.\(\newline\)Is the rate for this company a better deal than On Call or Talk Time? Complete the explanation.\(\newline\)The unit rate is \( \$ 3.60 \) per hour, so it \( \square \)\(\newline\)\( \square \) a better deal.

\newline

4

4

1

point) | Question Attempt:

5

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\checkmark 2

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\checkmark 3

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4

\newline

catter plot shows the number of hours worked,

x

, and the amount of money spent on entertainment,

y

24

\newline

Write an approximate equation of the line of best fit for the data. It doesn't have to be the exact line of best fit.

\newline

Using your equation from part (a), predict the money spent on entertainment for a student who works

10

\newline

te that you can use the graphing tools to help you approximate the line.

\newline

(a) Write an approximate equation of the line of best fit.

\newline

y=

\newline

\square

\newline

(b) Using your equation from part (a), predict the money spent on entertainment for a student who works

10

\newline

5 \square

\newline

\newline

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2024

MeGrow Hill LLC. AU Rights Reservert

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3

3

5

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online.fullsall.edu

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System of Equations Word Problem

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Francisco, the trainer, has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday, there were

5

clients who did Plan A and

6

who did Plan B. On Thursday, there were

3

clients who did Plan A and

2

who did Plan B. Felipe trained his Wednesday clients for a total of

7

hours and his Thursday clients

f

3

hours. How long does each of the workout plans last?

\newline

\cdot 4

\newline

Plan A workout:

0

75

\newline

Plan B workout:

0

5

\newline

Plan A workout:

0

5

1

\newline

1

\newline

Which of the following must be true before two matrices

A

B

can be multiplied?

\newline

The number of rows in

A=

The number of rows in

B

\newline

The number of columns in

A=

The number of rows in

B

\newline

The number of rows in

A=

The number of columns in

B

\newline

The number of columns in

A=

The number of columns in

B

20

-meter-long fence that she plans to use to enclose a rectangular garden of width

w

. The fencing will be placed around all four sides of the garden so that its area is

18.75

\newline

Write an equation in terms of

w

that models the situation.

...