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Maurinko [17]
2 years ago
15

George has opened a new store and he is monitoring its success closely. He has found that this store's revenue each month can be

modeled by r(x) = x² + 5x + 14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by c(x) = x² - 4x + 5 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars. What does (r-c) (5) mean about George's new store?​
A. the new store will sell 5400 items in its fifth month in business
B. The new store will have a profit of $5400 after its fifth month in business
C. The new store will have a profit of $900 after its fifth month in business
D. The new store will sell 900 items In its fifth month in business
Mathematics
1 answer:
makvit [3.9K]2 years ago
6 0

Answer:

The new store will have a profit of $5400 after its fifth month.

(R-C)(x) = (x²+5x+14)-(x²-4x+5) = x²-x²+5x--4x+14-5 = 5x+4x+14-5=9x+9

(Use 5 for x)

(R-C)(5) = 9(5) + 9 = 45+9 = 54

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160 - 20·x + 16·x - 2·x² ≥ 130

160 - 4·x - 2·x² ≥ 130

<h3>What is  inequalities?</h3>

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality. When comparing two numbers on a number line, it is most frequently used to compare their sizes.

<h3>According to the given information:</h3>

Each buffet costs $10.

Every hour, there are 16 clients that choose the buffet.

The number of patrons declines by two each hour for every $1 increase in the buffet price.

The hourly minimum wage necessary is $130.

The circumstance has two expressions: one for the price and one for the customers.

let:

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Customers will hear the following term when costs rise by an amount x;

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(10 + x) × (16 - 2·x) ≥ 130

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160 - 20·x + 16·x - 2·x² ≥ 130

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Type the cost expression on the first line and the customer expression on the second line:

160 - 20·x + 16·x - 2·x² ≥ 130

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