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Nataly_w [17]
3 years ago
12

What are the vertical asymptotes of the function f(x) = 2x + 8 / x2 + 5x + 6?

Mathematics
1 answer:
Irina18 [472]3 years ago
4 0
I'm assuming the function is f(x) = (2x+8)/(x^2+5x+6). If so, make sure to use parenthesis to indicate that you're dividing all of "2x+8" over all of "x^2+5x+6" as one big fraction. Otherwise, things are ambiguous and it leads to confusion.

Side Note: x^2 means "x squared"

Factor the numerator: 2x+8 = 2(x+4)
Factor the denominator: x^2+5x+6 = (x+2)(x+3)

There are no common factors between the numerator and denominator. So there is nothing to cancel out. 

Recall that you cannot divide by zero. Something like 1/0 is undefined. 
We need to find the x values that cause the denominator to be zero.
Set the denominator equal to zero and solve for x
x^2+5x+6 = 0
(x+2)(x+3) = 0
x+2 = 0 or x+3 = 0
x = -2 or x = -3

The x values x = -2 or x = -3 will lead to the denominator being zero. This means that the vertical asymptotes are x = -2 or x = -3 as shown by the blue dashed vertical lines in the attached image.

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NOYHING

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3 years ago
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A car travels at a constant speed. What is the car's speed between checkpoints, expressed as a unit rate? Checkpoint A 1:00 PM T
storchak [24]
Average speed  

Average speed between the checkpoints  
distance between the checkpoints
divided by
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Distance between the checkpoints = 
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Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.43cm and a standard deviation
malfutka [58]

Answer:

Approximately 68% of the apples have diameters that are between 7.08cm and 7.78cm.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 7.43cm, standard deviation of 0.35cm.

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Within 1 standard deviation of the mean, so approximately 68% of the apples have diameters that are between 7.08cm and 7.78cm.

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Answer: =248x

Step-by-step explanation: Hope this help :D

Let's simplify step-by-step.

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Combine Like Terms:

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=(40x+208x)

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3 years ago
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