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miss Akunina [59]
3 years ago
11

State the horizontal asymptote of the rational function. For full credit, explain the reasoning you used to find the horizontal

asymptote. (5 points)
f(x)= x^2+3x-2/x-2
Mathematics
1 answer:
Rzqust [24]3 years ago
5 0

So here are the rules of horizontal asymptotes:

  • Degree of Numerator > Degree of Denominator: No horizontal asymptote
  • Degree of Numerator = Degree of Denominator: y=\frac{\textsf{leading coefficient of numerator}}{\textsf{leading coefficient of denominator}}
  • Degree of Numerator < Degree of Denominator: y = 0

Looking at the rational function, since the degree of the numerator is 2 and the degree of the denominator is 1 (and 2 > 1), this means that <u>this function has no horizontal asymptote.</u>

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b option is right

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faltersainse [42]

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Step-by-step explanation:

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salma purchased a prepaid phone card for $20. long distance calls cost 24 cents a minute using this card. salma used her card on
suter [353]
We can set up an equation to solve this problem, but first we need to write out what we know.

$20 overall
$0.24 every minute
$13.52 remaining on the card

Now that we know our information, we can set it up in an equation. 

20 - 0.24x = 13.52

The 20 represents $20 overall when she first got the phone card.
We are then subtracting $20 from how must it costs a minute (which is 24 cents). The 'x' indicates the number we are trying to find (how many minutes her call lasted). Lastly, 13.52 is the result of everything, since she has $13.52 remaining on the card.

We can now solve the equation:

20 - 0.24x = 13.52
-0.24x = 13.52 - 20 /// subtract 20 from each side
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x = 27 /// divide each side by -0.24

Our solution is: x = 27.

-----

An easier way to solve this problem would be to first, subtract the total amount of money she had on the card when she first got it, and then the remaining total she ended up with.

$20 - $13.52 = $6.48

So, she spent a total of $6.48 on long distance calls, but since we are looking for how many minutes, we need to divide the total she spent and how much it costs per minute.

6.48 ÷ 24 = 27

We receive the same amount of minutes spent just like we did the last way we solved.

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Salma spent 27 minutes on the phone. 
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Step-by-step explanation:

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