Catarina and Tom want to buy a rug for a room that is 8 by 12. They want to leave an even strip of flooring uncovered around the edges of the room. How wide a stip will have if they buy a rug with an area of 32 square feet

Answers

Answer 1

Answer:

The length of the strip is 4ft

Explanation:

Given

Room dimension: 8 by 12

Rug Area: 32

Required

Determine the width of the strip

Since it is an even strip. Represent the width with w.

So, the rug area [tex](in\ terms\ of\ the\ room\ dimension)[/tex] is:

[tex]Area = (8 - w) * (12 - w)[/tex]

Substitute 32 for Area

[tex]32 = (8 - w) * (12 - w)[/tex]

Expand

[tex]32 = 8(12 - w) -w(12 - w)[/tex]

Open brackets

[tex]32 = 96 - 8w -12w + w^2[/tex]

Collect Like Terms

[tex]w^2 - 12w - 8w -32 + 96 = 0[/tex]

[tex]w^2 - 20w+64 = 0[/tex]

Expand

[tex]w^2 - 16w - 4w + 64 = 0[/tex]

Factorize

[tex]w(w - 16) - 4(w - 16) = 0[/tex]

[tex](w - 4)(w - 16) = 0[/tex]

[tex]w - 4 = 0\ \ or\ w-16=0[/tex]

[tex]w = 4\ \ or\ w=16[/tex]

But w can't be greater than the any of the dimension of the room (8 or 12).

So:

[tex]w = 4[/tex]

Hence, the length of the strip is 4ft


Related Questions

what was one result of the Black Death?​

Answers

Answer:

The Black Death caused 75-200 million deaths. The World economy also dropped drastically, causing many to go into poverty. However, North and South America were unaffected, as the European had not colonized or explored the Americas at the time.

Please help with this.

Answers

Answer: A. Many Ethnic Albanians lost their homes

Explanation:

In the Kosovo Conflict of 1998 - 1999 that saw Serbia go up against Kosovo which was a region that it claimed, hundreds of thousands of Ethnic Albanians fled the country and even though some came back, many lost their homes.

The Serbian leadership as well as many Serbs did not like that Albanians numbered so much in Kosovo because Albanians were Muslims and Serbians were Christians majorly. Kosovo to Serbia is a sacred place and so the leadership of Serbia wanted as few Albanians there as possible.

Athens suffered a great defeat in the Second Peloponnesian War after it attempted to conquer what Spartan ally?
A. Corinth
B. Aegina
C. Thebes
D. Syracuse

Answers

Answer: A. Corinth

Explanation:

Under the Treaty of Versailles, which country had to accept full responsibility for the war and
pay huge amounts of damages caused during the war?

Answers

Germany had to pay and accept full responsibility

Which company had a monopoly in tea sales?

Answers

Answer:

British East India Company Tea

The Tea Act: The Catalyst of the Boston Tea Party. The Tea Act, passed by Parliament on May 10, 1773, granted the British East India Company Tea a monopoly on tea sales in the American colonies.

Explanation:

I hope this helped u!!

British east company
PLATO4LIFE took the test

The meatpacking industry was located in____

Answers

Answer: Chicago

Explanation:  Largest of all was the meat-packing industry in Chicago. It spread through acres of stockyards, feed lots, slaughterhouses, and meat-processing plants. Together with the nearby housing area where the workers lived, this part of Chicago was known as Packingtown.

what is opportunity cost?​

Answers

the loss of potential gain from other alternatives when one alternative is chosen.

80 POINTS! ANSWER AT LEAST 2 OF THESE!
1.What was one of the major events of the Cold War and how did it impact Soviet/U.S. relations?

2.Why did Africa become the site of so many proxy wars during the post-war era?

3.How did the conflict in Israel and Palestine emerge from competing national movements?

4.Who were some of the nationalist leaders in the post-war era, and how did they impact their societies?

5.How did the post-World War II world change life and economics in the United States?

Answers

Answer:

1. The Cold War shaped American foreign policy and political ideology, impacted the domestic economy and the presidency, and affected the personal lives of Americans creating a climate of expected conformity and normalcy. By the end of the 1950's, dissent slowly increased reaching a climax by the late 1960's.

2. they became the site of many proxy wars as result of the soviet union and the united states pulling strings in the newly, easily manipulative governments. ... the united states obviously wouldn't have this so they stopped it by supporting the non-communists and the soviet union backed the pro-communists.

Explanation:

Answer:

1. 5 Key Cold War Events

Containment of Russia. ...

Arms Race Between the United States & Russia. ...

Development of the Hydrogen Bomb. ...

Space exploration. ...

Fall of the Berlin Wall.

2. They became the site of many proxy wars as result of the soviet union and the united states pulling strings in the newly, easily manipulative governments. ... the united states obviously wouldn't have this so they stopped it by supporting the non-communists and the soviet union backed the pro-communists.

explain a likely cultural effect of pilgrims on the location shown in image 1

Answers

Answer:

There is no image.

Explanation:

The absence and presence of sculptures, as well as the geometric patterns of religious temples, are cultural effects of travelers on the site seen in image 1.

What is image?

A visual depiction is referred to as an “images.” Vector graphics and raster graphics are the two subcategories of an image. JPEG, PNG, and bitmap are the image file types. The image is the shown to the picture, photo, drawing, and they interpret the audience.

Jerusalem is a sacred site for Muslims, Jews, and Christians because they all worship the same God. Because the Gods of these three faiths are not represented by sculptures, there are no carvings at the time depicted in the image. The temple in Gaya is triangular in form and features slanted, pointy lines.

As a result, the absence and presence of sculptures, as well as the geometric patterns of religious temples.

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Please helppp I need help ASAP...

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The answer is B for this problem “Individuals” to “themselves”.

When and why the number of electoral votes of a state have changed?

Answers

Answer:

The number of electoral votes can constantly change. This is because the number of votes a state gets is the number of representatives and senators in congress. Since the number of representatives is based on the population it can change. Every ten years the US takes a census to see the population of each state, then based of the results decides how many representatives every state gets, this then changes the number of votes every state gets. For example, in 1960 there were only 537 electoral colleges in the US, currently, there are 538.

5. A
Is a toll road built for easy travel and for
shipment of goods

Answers

Answer: No, Toll Roads are typically implemented to help recoup the costs of road construction and maintenance.

Which phrases are used to describe the division between the free and non-free regions of Europe?​

Answers

Answer: Europe is the western peninsula of the giant "supercontinent" of Eurasia. Europe is divided from Asia by a series of watersheds, including the Ural River and the Caspian and Black Seas.

Explanation:

Answer:

Answer

1

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Answer: Europe is the western peninsula of the giant "supercontinent" of Eurasia. Europe is divided from Asia by a series of watersheds, including the Ural River and the Caspian and Black Seas.

Explanation:

what does patrick henry declare in this speech

Answers

Answer:

Give me liberty, or give me deathhhh

Explanation:

Answer:“Give me liberty, or give me death!”

Explanation: Patrick Henry was one of the Founding Fathers of the United States and the first governor of Virginia. ... His rousing speeches—which included a 1775 speech to the Virginia legislature in which he famously declared, “Give me liberty, or give me death!”—fired up America's fight for independence.Oct 24, 2019

How did the Greeks probably transport most of their trade goods?


A. Overland along the coast

B. By ship along sea coasts

C. Overland along existing trade routes

D. By ship along rivers and lakes

Answers

Answer:

by ship along sea coast

Explanation:

i dont really know but i think thats the answer

Answer: B. By ship along sea coasts

Explanation:

Many ancient civilizations based their profits on agriculture. Greece did not have much space for agricultural production, so the Greeks focused on trade. The trade was mainly based along the shores of the Mediterranean. The Greeks traded in many items. However, one of the main elements of the ancient Greek economy was the fish trade.

Is the belief that some acts are always right or always wrong

Answers

A belief that some acts are always right or always wrong. Moral Relativism. A belief that a decision may be right even if it is not in keeping with our own ethical standards.

Which feature of eastern Europe's physical geography connects Russia and
Belarus to the Black Sea?
A. The Dnieper
B. The Dinaric Alps
C. The Baltic Sea
D. The Great Hungarian Plain

Answers

A. The Dniester connects Belarus to the Black Sea

Answer:

A. The Dnieper

Explanation:

did the test !!

Which best explains why Great Britain, France, and Russia formed the Triple Entente?

They hoped to help each other imperialize Africa and counter the power of the Triple Alliance on that continent.
They feared the rising military power of Germany and sought to counter the power of the Triple Alliance.
They wanted to prevent conflict in the Balkans and convince the Triple Alliance not to interfere in the region.
They sought to surround Germany on two sides and convince the Triple Alliance not to expand its power.

Answers

Answer:

They feared the rising military power of Germany and sought to counter the power of the Triple Alliance.

Explanation:

The Triple Alliance, otherwise known as Triple Entente is an agreement reached by Great Britain, France and Russia that they would each remain neutrals in wars between each other and help defend each other when attacked by external forces.

The best explanation as to why Great Britain, France, and Russia formed the Triple Entente was that they feared the growing power of Germany and sought to enter an alliance with each other.

Answer:

b

Explanation:

Which definition best matches the term historical argument? A. A source of information about the past created during that period O B. A statement that describes the key point of an argumentative essay C. An attempt to discredit a historian by highlighting potential bias O D. An opinion about the past supported by historical evidence​

Answers

Answer:

D I think?

Explanation:

A. would be historical evidence

B. isn't just related to history, moreso English

C. is just trying to take away the statement someone's made about the past because it shows opinion

D. would be an argument supported by history

Definition that best matches the term historical argument is historic evidence is an opinion about the past supported by historical evidence​. Option (d) is correct.

What do you mean by Argument?

Arguments are statements backed by justifications and facts. There are five very pertinent qualities of argument: Argumentation happens in groups. Two or more people engaging in an argument must respond to each other's claims and arguments.

An explanation of the how or why a prior event occurred is given by a historical argument. A thesis statement, which must be clear, verifiable, and capable of being argued, introduces the argument.

To support their arguments, historians turn to primary, secondary, and oral histories. They must decide which pieces of evidence are the most crucial and reliable.

Therefore, Option (d) is correct. Definition that best matches the term historical argument is historic evidence is an opinion about the past supported by historical evidence​.

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Question 1
What were some of the political consequences of the Great Depression in Europe and the United States? Put the responses in the correct
buckets.

Answers

Answer:

The most important political consequence of the Great Depression was of course the rise of right‐wing authoritarianism in Germany, Austria, Central, and Eastern Europe, and Latin America

Explanation:

Immigrants around 1900 helped build what?
A) Erie Canal
B) World Trade Center
C) Skyscraper buildmgs
D) Madison Square Garden
E) B and C

Answers

Answer:

C) Skyscraper buildings

In document c, examines British naval expenses in 1914 do the Germans have a reason to worry about freedom of the seas?

Answers

Answer:

Answer Expert Verified Assuming that this is referring to the same document that was posted before with this question, the correct response would be "yes, they did" since this showed that countries such as the United States could supply war materials and other goods to countries at war with Germany by sea.

how were mexican citizens' lives affected by the leadership of Antonio Lopez de Santa Anna?

Answers

Answer: After Texans had tried to achieve representation in the Mexican legislature, Santa Anna threw out the Mexican democratic constitution and established a dictatorship, which prompted the Texans to revolt.

citizens were silenced and weren't really protected by the army

During Reconstruction, African Americans:
A. lived in a society in which they attempted to become full citizens, in spite of the efforts of white Southerners.
B. had no opportunity for schooling.
C.were able to become independent farmers by purchasing their own land.
D. lived in fully integrated urban societies.
E. left the South in overwhelming numbers.

Answers

Answer:

E: left the South in overwhelming numbers:

Explanation:

What did the declining demand for cotton lead to?

A) It made finding work in the textile industry difficult

B)It forced mill workers to become farmers

C)It fueled other types of industries

D) It created more jobs for farmers in urban areas

Answers

Answer:

While it was true that the cotton gin reduced the labor of removing seeds, it did not reduce the need for slaves to grow and pick the cotton. In fact, the opposite occurred. Cotton growing became so profitable for the planters that it greatly increased their demand for both land and slave labor.

in my. opinion

Answer: b I think

Explanation:

SS.8.final
Question: 1-4
Which factor contributed most to the industrial advantages the North had over the South at the beginning
of the Civil War?
O The lack of natural resources in the South
o The South's dependence on European goods
o The strength of the labor movement in the South
o The profitability of the Southern cash-crop economy
Next
Previous
O

Answers

Answer:

The South's dependence on European goods

Explanation:

The factor that contributed most to the industrial advantages the North had over the South at the beginning of the Civil War was "The South's dependence on European goods"

This is evident in the fact that the North has the seaport and the European goods on which the south depended would have to pass through the seaport in the North, in which they put outrightly blocked. Thereby, the South was unable to import goods and weapons from the Europeans.

In August of 1945, the American dropped atomic bombs on which of the following Japanese cities? Hiroshima and Beijing, Beijing and Tokyo, Hiroshima and Nagasaki

Answers

Answer:

Hiroshima and Nagasaki

Hiroshima and Nagasaki

Select THREE purposes of the Articles of Confederation, the United States' first
constitution
to provide protection for the 13 states against foreign invasion
to establish a weak king who would obey the will of the people
to create a strong central government that would keep the states in line
to declare the colonies independent from foreign nations
to create an organized government to manage the American Revolution
to establish the 13 colonies as the United States of America

Answers

Answer:

to create a strong central government

to create an organized government to manage the American Revolution

to establish the 13 colonies as the United States of America

to provide protection for the 13 states against foreign invasion

Explanation:

I'm in middle school and I know this

2. What do you think are the risks involved in being an entrepreneur or inventor?

Answers

Answer:

Personally, I think some of the risks of being an entreperneur or an inventor is that if your product doesn't work, succeed, or even sell, you've wasted all of the money and time that you put into it. It's a risky business, as there is no way to say with 100% certainty that your product will earn an income.

Explanation:

Hope this helps!

1. What was the biggest problem that farmers faced?
burning their crops for fuel
no crops to barter with
losing their land
low prices for their crops

Answers

Answer:

The correct answer is Losing their land (i just took the test)

Explanation:

Among the options provided, the biggest problem that farmers faced was low prices for their crops. Thus, option C is the correct option.

During various periods in history, farmers have struggled with economic challenges due to fluctuations in market prices for their agricultural products. Factors such as oversupply, changes in consumer demand, and the absence of effective price controls have resulted in farmers receiving inadequate compensation for their crops.

This issue often leads to financial instability, debt, and even the loss of farms. While the other options mentioned may have been challenges faced by some farmers, the low prices for their crops have been a persistent and widespread concern impacting agricultural communities.

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