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Dennis_Churaev [7]
2 years ago
6

A rectangular floor measures $a$ feet by $b$ feet, where $a$ and $b$ are positive integers with $b > a$. An artist paints a r

ectangle on the floor with the sides of the rectangle parallel to the sides of the floor. The unpainted part of the floor forms a border of width 1 foot around the painted rectangle and occupies half the area of the entire floor. How many possibilities are there for the ordered pair $(a,b)$?
Business
1 answer:
DENIUS [597]2 years ago
8 0

The number of possibilities that are there for the ordered pair is 2.

<h3>Calculation and Parameters
</h3>

Because the unpainted part of the floor covers 1/2 of the area, then the painted rectangle covers 1/2 of the area as well.

Given that the border width is 1 foot, the dimensions of the rectangle are a-2 by b-2.

Making an equation:

ab= 2((a-2)(b-2))

ab= 2ab-4a-4b+8

ab-4a-4b+8=0

If we apply Simon's Favorite Factoring Trick,

ab-4a-4b+16= 8

(a-4)(b-4)= 8

Since b > a, then we have the possibilities

(a-4) = 1 and (b-4) = 8, or (a-4) = 2 and (b-4) = 4.

(5, 12) or (6,8) which gives us 2 possibilities.

Read more about possibilities here:

brainly.com/question/25870256

#SPJ1

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8 0
1 year ago
You supply a good at a price of $5. You also earn a profit at this price. This means that your marginal cost could be _____.
Fed [463]
<span>You supply a good at a price of $5. You also earn a profit at this price. This means that your marginal cost could be less than $5.
Hope it helps.
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3 0
3 years ago
State whether the following actions will increase or decrease GDP: a. An individual sells her house on her own. b. An individual
statuscvo [17]

Answer:

a. An individual sells her house on her own.  

         GDP is not affected.

b. An individual sells his house through a broker.

         GDP is not affected.  

c. Government increases Social Security payments.  

          GDP is not affected.

d. Stock prices rise by 20 percent.

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Explanation:

Selling a house by an individual does not affect the Gross Domestic Product of a Country.  

Selling a house by a broker will also not affect the Gross Domestic Product of a Country.

When a Government increases the social security payments, this result in transfer of money from government to social security account but it does not generate any goods are services in the country.

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3 years ago
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