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zhuklara
1 month ago
12

What are the vertical and horizontal asymptotes for the function f (x) = StartFraction 3 x squared Over x squared minus 4 EndFra

ction?

Mathematics
2 answers:
Leona [12.6K]1 month ago
7 0

Answer:

The vertical asymptotes are at x = 2 and x = -2.

The horizontal asymptote is located at y = 3.

Step-by-step explanation:

Given the function

f(x)=\dfrac{3x^2}{x^2-4}

Transform it into the following:

f(x)\\ \\=\dfrac{3x^2}{x^2-4}\\ \\=3\dfrac{x^2-4+4}{x^2-4}\\ \\=3\left(1+\dfrac{4}{x^2-4}\right)\\ \\=3+\dfrac{12}{(x-2)(x+2)}

This function is not defined when the denominator equals zero. This occurs when x = 2 or x = -2, resulting in two vertical asymptotes located at x = 2 and x = -2.

<pThe horizontal asymptote is determined to be y = 3.

lawyer [12.5K]1 month ago
6 0

Answer:

A

Step-by-step explanation:

This is the first item listed on Edgeniuty (an unreliable site).

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Serena estimates that she can paint 60 square feet of wall space every half -hour .Write a equations for the relationship with t
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Response: Therefore, the connection with i hours being the independent variable is y=120i

Serena is unable to paint 400 square feet of wall area within 3.5 hours.

Detailed explanation:

It's provided that

The area she can paint = 60 square feet

Time taken = half an hour = 30 minutes = 0.5 hours

Applying the "Unitary method, it leads to

In 0.5 hours, she is capable of painting = 60 square feet

In 1 hour, she can paint = \dfrac{60}{0.5}=120\ sq.\ feet

In i hours, she is able to paint = 120\times i\ sq.\ feet=120i\ sq.\ feet

Let’s denote the total area she can paint as 'y'.

Thus, the connection with i hours treated as the independent variable would be

y=120i

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Substituting y = 400 and i = 3.5 hours helps us determine if they are equivalent.

400= 120\times 3.5\\\\400\neq 420

Therefore, Serena cannot paint 400 square feet of wall space in 3.5 hours.

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25 days ago
Last year, sales at a book store increased from $5,000 to $10,000. This year, sales decreased to $5,000 from $10,000. What perce
Svet_ta [12734]
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1 month ago
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Barry has 17 more than two-thirds of the number of cards in his brother’s baseball card collection. If x represents the number o
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Step-by-step explanation:

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19 days ago
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Answer:

First, it's essential to define the equation that characterizes the function.

The investment is $200 with an interest rate of 5%, where y represents the money after x periods.

After one period, the amount of money grows to 200 plus 5% interest, resulting in 200 + 5%(200) = 200 (1 +5%) = 200 (1 + 0.05) = 200 (1.05)

After two periods, the total is 200(1.05)*(1.05) = 200 (1.05)^2

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Step-by-step explanation:

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