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Vladimir79 [104]
3 years ago
6

Which of the following is the graph of the rational function? y=x^2+2x-8/x^2-9

Mathematics
1 answer:
rusak2 [61]3 years ago
7 0
Notice that we can simplify both numerator and denominator of our rational function. In the numerator we have a quadratic expression of the form ax^2+bx+c. To to simplify it, we are going to find tow numbers that add to 2 and multiply to -8; those numbers are 4 and -2.
x^2+2x-8=(x+4)(x-2)
In the denominator we have a difference of squares:
x^2-9=x^2-3^2=(x+3)(x-3)

Now we can rewrite our function:
y= \frac{x^2+2x-8}{x^2-9} = \frac{(x+4)(x-2)}{(x+3)(x-3)}

From the simplified form of our rational function we can infer that its graph has two vertical asymptotes at x=3 and x-3

We can conclude that the graphic of our rational function is: 

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Given f(x)=cos c and g(x)=cot x, what are the domain and range of f(g(x))?
ololo11 [35]

Answer:

Alternative C is the correct answer

Step-by-step explanation:

The first step is to determine the composite function;

f[g(x)]

f[g(x)]=cos[cot(x)]

We then employ a graphing utility to determine the range and the domain of the new function.

The range is the set of y-values for which the function is defined. In this case it is;

[-1,1]

On the other hand, the domain refers to the set of the x-values for which the function is real and defined. In this case; it is the set of real numbers x except x does not equal npi for all integers n.

8 0
3 years ago
Which of the following functions are an example of exponential growth ?
yanalaym [24]

Answer:

i don't know maybe D. 2 and 3

8 0
3 years ago
Point b is the midpoint of ac-. if ab= 4x+2 and ac=10x-6, find the length of ac
Natasha2012 [34]

let's bear in mind that B is the midpoint and thus it cuts a segment into two equal halves.

\bf \underset{\leftarrow \qquad \textit{\large 10x-6}\qquad \to }{\boxed{A}\stackrel{4x+2}{\rule[0.35em]{10em}{0.25pt}} B\stackrel{\underline{4x+2}}{\rule[0.35em]{10em}{0.25pt}\boxed{C}}} \\\\\\ AC=AB+BC\implies 10x-6=(4x+2)+(4x+2)\implies 10x-6=8x+4 \\\\\\ 2x-6=4\implies 2x=10\implies x=\cfrac{10}{2}\implies x= 5 \\\\[-0.35em] ~\dotfill\\\\ AC=(4x+2)+(4x+2)\implies AC=[4(5)+2]+[4(5)+2] \\\\\\ AC=22+22\implies AC=44

3 0
3 years ago
Which arc is a minor arc?
egoroff_w [7]

Answer: The answer you selected PS is correct.

Step-by-step explanation: A minor arc is a arc that is less than or equal to 180 degrees. PS looks to be exactly 180 degrees or at least close to it.

3 0
3 years ago
Read 2 more answers
Fifteen SmartCars were randomly selected and the highway mileage of each was noted The analysis yielded a mean of 47 miles per g
laiz [17]

Answer: a. 47 plusminus (1.753*(5 ÷ 3.8730)

Step-by-step explanation:

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation = 5

n = number of samples = 15

z represents the test statistic

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the test statistic score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 15 - 1 = 14

Since confidence level = 90% = 0.90, α = 1 - CL = 1 – 0.90 = 0.1

α/2 = 0.1/2 = 0.05

the area to the right of z0.05 is 0.05 and the area to the left of z0.05 is 1 - 0.05 = 0.95

Looking at the t distribution table,

z = 1.753

Margin of error = 1.753(5 ÷ 3.8730)

Confidence interval = 47 ± 1.753(5 ÷ 3.8730)

8 0
3 years ago
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