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marysya [2.9K]
3 years ago
15

At which values of x does the graph of the function F(x) have a vertical asymptote? Check all that apply. f(x)=x+4/x^2+5x-24

Mathematics
1 answer:
mr Goodwill [35]3 years ago
3 0

Answer:

x = -8   &   at x = 3

Step-by-step explanation:

This is a rational function.

We can get the values of x at which vertical asymptotes occur by setting the denominator equal to 0 and solving for x.

Let's do this:

x^2+5x-24=0\\(x+8)(x-3)=0\\x=-8,3

Hence, vertical asymptotes occur at x = -8 & at x = 3

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What are the next three terms in the sequence 4, -1, -6, -11, ...?
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Answer:

In summary, "the next three terms" are {-16, -21, -26}

Step-by-step explanation:

Note that the common difference separating the terms of 4, -1, -6, -11, ... is -5.  Each new term is found by combining the previous term with -5.

Thus, the applicable formula is a(n) = 4-5(n-1).

We should test this.  Take the term -6 and determine whether or not this formula correctly predicts the next term:  -11:

a(4) = 4-5(4-1) = 4 - 5(3) = 4 - 15 = -11 (yes).

We have the first four terms and need the 5th, 6th and 7th terms.

The fifth term, a(5), is 4-5(5-1) = 4-20 = -16

The sixth term is a(6) = 4-5(6-1) = -21

The seventh term is a(7) = 4 -5(6) = -26

In summary, "the next three terms" are {-16, -21, -26}

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