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Serjik [45]
3 years ago
9

Explain why f(x) = x^2+4x+3/x^2-x-2 is not continuous at x = -1.

Mathematics
1 answer:
liberstina [14]3 years ago
3 0

Answer:

The value of x = -1 makes the denominator of the function equal to zero. That is why this value is not included in the domain of f(x)

Step-by-step explanation:

We have the following expression

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

Since the division between zero is not defined then the function f(x) can not include the values of x that make the denominator of the function zero.

Now we search that values of x make 0 the denominator factoring the polynomial x^2-x-2

We need two numbers that when adding them get as a result -1 and when multiplying those numbers, obtain -2 as a result.

These numbers are -2 and 1

Then the factors are:

(x-2) (x + 1)

We do the same with the numerator

x^2+4x+3

We need two numbers that when adding them get as a result 4 and when multiplying those numbers, obtain 3 as a result.

These numbers are 3 and 1

Then the factors are:

(x+3)(x + 1)

Therefore

f(x) = \frac{(x+3)(x+1)}{(x-2)(x+1)}

Note that \frac{(x+1)}{(x+1)}=1 only if x \neq -1

So since x = -1 is not included in the domain the function has a discontinuity in x = -1

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Step-by-step explanation:

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Answer:

41.4 in

Step-by-step explanation:

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3 years ago
A student claims that x=3 and 2+3i are the zeros of a quadratic function. Explain why this is incorrect
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Step-by-step explanation:

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3 years ago
The SAT scores have an average of 1200 with a standard deviation of 60. A sample of 36 scores is selected. a) What is the probab
erastova [34]

Answer:

the probability that the sample mean will be larger than 1224 is  0.0082

Step-by-step explanation:

Given that:

The SAT scores have an average of 1200

with a  standard deviation of 60

also; a sample of 36 scores is selected

The objective is to determine  the probability that the sample mean will be larger than 1224

Assuming X to be the random variable that represents the SAT score of each student.

This implies that  ;

S \sim N ( 1200,60)

the probability that the sample mean will be larger than 1224 will now be:

P(\overline X > 1224) = P(\dfrac{\overline X - \mu }{\dfrac{\sigma}{\sqrt{n}} }> \dfrac{}{}\dfrac{1224- \mu }{\dfrac{\sigma}{\sqrt{n}} })

P(\overline X > 1224) = P(Z > \dfrac{1224- 1200 }{\dfrac{60}{\sqrt{36}} })

P(\overline X > 1224) = P(Z > \dfrac{24 }{\dfrac{60}{6} })

P(\overline X > 1224) = P(Z > \dfrac{24 }{10} })

P(\overline X > 1224) = P(Z > 2.4 })

P(\overline X > 1224) =1 -  P(Z \leq 2.4 })

From Excel Table ; Using the formula (=NORMDIST(2.4))

P(\overline X > 1224) = 1 -  0.9918

P(\overline X > 1224) = 0.0082

Hence;  the probability that the sample mean will be larger than 1224 is  0.0082

4 0
3 years ago
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