Find the domain of the rational function.

C(x) = x+9/X^2 -16

Answers

Answer 1

Answer:

Domain = {x : x ≠ 4 , -4}  or  (-∞ , -4) ∪ (-4 , 4) ∪ (4 , ∞)

Step-by-step explanation:

TO FIND :-

Domain of [tex]C(x) = \frac{x + 9}{x^2 - 16}[/tex]

SOLUTION :-

Domain of a function is a value for which the function is valid.

The function [tex]C(x) = \frac{x + 9}{x^2 - 16}[/tex] is valid until the denominator is 0.

So make sure that the denominator must not be 0.

[tex]=> x^2 - 16 > 0[/tex]

Find the values of x for which the denominator becomes 0. To find it , you'll have to solve the above inequality.

Add 16 to both the sides

[tex]=>x^2 - 16 + 16 > 0 + 16[/tex]

[tex]=> x^2 > 16[/tex]

[tex]=> x > \sqrt{16}[/tex]

[tex]=> \boxed{x > 4} \: or \:\boxed{x > -4}[/tex]

We can say that 4 & -4 can't be domains because these values will make the function undefined.

Now try putting values of x such that -4 < x < 4. You'll observe that the function will be valid for all those values of x between -4 & 4.

CONCLUSION :-

The function will be valid for any value of 'x' except 4 & -4. So in :-

Interval notation , it can be written as → (-∞ , -4) ∪ (-4 , 4) ∪ (4 , ∞)

Set builder notation , it can be written as → {x : x ≠ 4 , -4}


Related Questions

What is the least common multiple of 4, 6, and 12?

Answers

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

12,24,36,48,60,72...

12 is the smallest common multiple so LCM of 4,6 and 12 is 12

Researchers at two universities found that airlines are doing a better job of getting passengers to their destinations on time. Company A and Company B Airlines were among the leaders in on-time arrivals with both having 88% of their flights arriving on time. But for the 12% of flights that were delayed, how many minutes were these flights late

Answers

Complete question :

Formulate the hypothesis that can be used to test for a difference between the population mean minutes late for delayed flights by these two airlines. (Let μ1 = population mean minutes late for delayed Company A flights and μ2 = population mean minutes late for delayed Company B flights.)

(b) What is the sample mean number of minutes late for delayed flights for each of these two airlines?

(c) Calculate the test statistic. (Round your answer to three decimal places.)

What is the p-value? (Round your answer to four decimal places.)

Answers:

H0: μ1 − μ2 = 0

H1: μ1 − μ2 ≠ 0

Test statistic = - 0.314

Pvalue = 0.7550

Step-by-step explanation:

Mean, xbar = Σx / n

Standard deviation, s = √(Σ(x-xbar) / n-1)

Company A :

Sample size, n = 25

Mean, x1 = 50.6

Standard deviation, s1 = 26.57

Company B :

Mean, x2 = 52.82

Sample size, n2 = 20

Standard deviation, s2 = 20.02

Mean, xbar = Σx / n

Standard deviation, s = √(Σ(x-xbar) / n-1)

Company A :

Sample size, n = 25

Mean, x1 = 50.6

Standard deviation, s1 = 26.57

Company B :

Mean, x2 = 52.85

Sample size, n2 = 20

Standard deviation, s2 = 20.02

The hypothesis :

H0: μ1 − μ2 = 0

H1: μ1 − μ2 ≠ 0

The test statistic :

Test statistic:

t = (x1 - x2)/[√(s²p(1/n1 + 1/n2 )]

Pooled variance = s²p

s²p = ((n1-1)*s1² + (n2-1)*s2² )/(n1+n2-2)

s²p = (24*26.57^2) + (19*20.02^2) / 43

s²p = 571. 125

√(s²p(1/n1 + 1/n2) ;

√572.125(1/25 + 1/20) = 7.169

x1 - x2 ; 50.6 - 52.85 = - 2.25

Test statistic = - 2.25 / 7.169

Test statistic = - 0.314

Using the Pvalue from t score calculator :

Pvalue(-0.314, 43) = 0.755

Pvalue > α ; We fail to reject the Null

what is the answer for this one?



2x + 3 = 9. x

Answers

Answer:

3/7

Step-by-step explanation:

You want to seperate the numbers from the variable.

Use limits to find the area of the shaded region in the graph y = x2.
a.
7 units²
c.
4 units²
b.
9 units²
d.
6 units ²

Answers

Answer:

B. 9 Units squared

Step-by-step explanation:

Edge 2021

Question:
a spinner has 8 equally sized sections, six of the selections are green.

a. What is the probability that the spinner will land on green?
1. ____ out of 8, or _/4, or ____%
b. Use words to describe the probability / It is ____ that the spinner will land on green.

Answers

1a. 6 out of 8, 3/4, or 75%
1b. It is likely that the spinner will land on green.

Color Frequency
Blue
57
Black
84
Silver
183
Red
168
Green
64
If there were 6 times as many of each color car in the parking lot, how
many silver cars would be in the parking lot?

Answers

6 x 183 = 1098

So there will need to be 1098 cars.

PEASE HELP ASAP!!! The sum of two numbers is 58.
The difference of those two numbers
is 28. Find both numbers.

Answers

Answer:

y=15

x=43

(any variable can be used, I used x and y to make it easier to show)

Step-by-step explanation:

x+y=58

x-y=28

get x by its self

x=58-y

then subsitute into the other equation

(58-y)-y=28

58-2y=28

-2y=-30

y=15

sub. again

x+15=58

x=43

It’s 15 and 43 skkwowuwbe

Given the following data, what is the probability that a car will have a V8 or a manual transmission?
A- 70.06%
B-110.71%
C-76.07%
D-60.71%

Answers

Answer is c hope this helps

Two trains leave stations 456 miles apart at the same time and travel toward each other. One train travels at 105 miles per hour while the other travels at 105miles per hour. How long will it take for the two trains to meet?

Answers

Answer:

let x=distance 105 mph train traveled

(456-x)=distance 85 mph train traveled

Travel time = distance/speed (equal in both directions)

 

x/105=(456-x)/85

85x=105*456-105x

190x=105*456

x=105*456/190=252 miles

travel time=252/105=2.4 hrs

ans:

The two trains will meet in 2.4 hrs

Step-by-step explanation:

there brainliest pls

A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 533 randomly selected Americans surveyed, 351 were in favor of the initiative. Round answers to 4 decimal places where possible.

Answers

Answer:

The 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative is (0.6247, 0.6923).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

Of the 533 randomly selected Americans surveyed, 351 were in favor of the initiative.

This means that [tex]n = 533, \pi = \frac{351}{533} = 0.6585[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6585 - 1.645\sqrt{\frac{0.6585*0.3415}{533}} = 0.6247[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6585 + 1.645\sqrt{\frac{0.6585*0.3415}{533}} = 0.6923[/tex]

The 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative is (0.6247, 0.6923).

Ms. Hernandez has $100 to spend on parking and admission to the zoo. The parking will cost $10 and the
admission tickets will cost $15 per person, including tax. Write and solve an equation that can be used to
determine the number of people that she can bring to the zoo, including herself.
Show your work

Answers

Answer:

6

Step-by-step explanation:

First subtract 10 from 100 and get 90. Then divide 90 by 15 and you'll get 6. Therefore, Ms. Hernandez can bring 6 people including herself.

Find the slope of the line that passes through the
points (-4, 7) and (3,-2)

Answers

Answer:

-9/7

Step-by-step

Slope Formula:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

We can plug in the numbers 7 and -2 for the y and -4 and 3 for x

[tex]\frac{7-(-2)}{-4-3} =\frac{9}{-7}[/tex]

Find derivative of y=(-3x^5+1)^3

Answers

Use the chain rule:

[tex]\frac{\mathrm dy}{\mathrm dx}=3(-3x^5+1)^2\frac{\mathrm d[-3x^5+1]}{\mathrm dx}=3(-3x^5+1)^2(-15x^4)=\boxed{-45x^4(1-3x^5)^2}[/tex]

as a customer enters a grocery store, they are handed a coupon worth up to $5 in savings.

Answers

Answer:

is c

Step-by-step explanation:

How many tenths are in 8.32?

Answers

Answer:

3 tenths

Step-by-step explanation:

What is the range of this absolute value function?

Answers

Answer:

im pretty sure the answer is A

What is the volume of this composite solid?​

Answers

Step-by-step explanation:

5×9×12=540

6×9×12÷2=324

324+540=864

Answer:

C. 1188 cubic meters

Step-by-step explanation:

"To find the volume, we must multiply the length x width x height"

The shape is too big so we must break it into another shape

Let's solve the bottom shape that looks like a rectangle!

Length: 12 m

Width: 9 m

Height: 5 m

Volume = 540 m

Now the top shape!

Length: 12 m

Width: 9 m

Height: 6 m

Volume = 648 m

Now we need to add both of the volume shapes!

648 + 540 = 1188 cubic meters

Jamie will plot (9, 5) on a coordinate plane. She knows the last step is to put a point where two lines intersect. Which two steps should she use first

Answers

Answer:

i got g

Step-by-step explanation:

Answer:

Step-by-step explanation:

G and h

Consider the following graph of y = f (x).
I need help

Answers

Answer:

Step-by-step explanation:

a)   -1, 1, 5

b)   -3

c)   -1 to 6

d)    -3  to 2

e)  for a value, we need an input between or equal to -1 to 6,  what ever that x value is,  find it on the graph, then see what the y value is at that point.  That's your value of f    

What is 5C3?
A. 35
B. 10
C. 14
D. 28

Answers

Answer: B. 10

-5C3 or 5 choose 3 refers to how many combinations are possible from 5 items, taken 3 at a time. To calculate combinations, we will use the formula nCr = n! / r! ... * (n - r)!, where n represents the total number of items, and r represents the number of items being chosen at a time.

-10 is the total number of all possible combinations for choosing 3 elements at a time from 5 distinct elements without considering the order of elements in statistics & probability surveys or experiments. The number of combinations for sample space 5 CHOOSE 3 can also be written as 5C3 in the format of nCr or nCk.

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

Solve -7 2/3+(-5 1/2)+8 3/4=

Answers

Answer:

-53/12

Step-by-step explanation:

Answer:

Exact Form: -53/12

decimal form: -4.416

mixed number -4 5/12

Step-by-step explanation:

convert mixed numbers into improper fractions: -2 3/3 +(5 1/2)+ 8 3/4

convert mixed numbers into improper fractions: =11/2  =[tex]-\frac{23}{3}+\left(-\frac{11}{2}\right)+\frac{35}{4}[/tex] =

[tex]-\frac{23}{3}+\left-\frac{11}{2}\right+\frac{35}{4}[/tex][tex]=-\frac{92}{12}-\frac{66}{12}+\frac{105}{12}[/tex]

[tex]\frac{-92-66+105}{12}[/tex]

add/subtract the numbers: -92-66+105=-53

-53/12

apply the fraction rule: [tex]\frac{-a}{b} = -\frac{a}{b\\}[/tex]

[tex]=-\frac{53}{12}\\[/tex]

There are 5 red balls, 3 blue balls and 2 green balls in a box. Suzie takes at random a ball from the box and gives it to her friend. She then takes at random another ball from the box.

Answers

What is the question, because this is not complete.

Solve for n.
n + 184 = –375

Answers

Answer:

n=-559

Step-by-step explanation:

Answer:

n=-559

Step-by-step explanation:

you need to get n by itself so you subtract 184 from both side n=-375-184 then simplify it to n= -559 leaving you with the answer.

hope this helped

What equation models the volume for a rectangular prism that is 4 cm long, 4cm wide, and 0.1 m tall A. V = 42 x 10 B. V = 10 x (4 + 4) C. V = 400 x 4 D. V = (4 x 4) + 10

Answers

Answer:

It's 160

I think you have a typo in d. If you do, the answer is d) V=(4 x 4) x 10

meaning a x 10 versus a + 10 as typed.

Step-by-step explanation:

.1m=10cm

volume = 4 x 4 x 10 = 160

question in picture ​

Answers

Answers:

cos(A) = 0.8480

tan(B) = 1.6

=============================================

Explanation:

Before we can compute cos(A), we'll need to find the hypotenuse.

Use the pythagorean theorem.

a^2 + b^2 = c^2

8^2 + 5^2 = c^2

89 = c^2

c^2 = 89

c = sqrt(89)

The hypotenuse is exactly sqrt(89) units long.

This will allow us to find the cos(A) value

cos(angle) = adjacent/hypotenuse

cos(A) = AC/AB

cos(A) = 8/sqrt(89)

cos(A) = 0.84799830400509 which is approximate

cos(A) = 0.8480 when rounding to four decimal places

-------------------------

For the tangent ratio, we won't use the hypotenuse. Instead, we use the opposite and adjacent sides like so:

tan(angle) = opposite/adjacent

tan(B) = AC/BC

tan(B) = 8/5

tan(B) = 1.6

Suppose the function S ( t ) = 2.5 cos ( 0.017 t − 1.35 ) + 7 models the amount of snowfall for a year in Anchorage, Alaska, where t = 1 is the first day of the year. Based on the function, what is the range of snowfall for Anchorage?

Answers

Answer:

4.5 to 9.5

Step-by-step explanation:

Reflect P (-5,10) over the x-axis. What are the coordinates of the reflected point? What quadrant is the reflected point in?

Answers

Answer:

(-5,-10)

it is in quadrant 3 (quadrant III)

Step-by-step explanation:

Mark as Brainliest

Answer:

(-5,-10) In Quadrant III

Step-by-step explanation:

When reflecting a point accross the x-axis, the y-coordinate of the point changes signs

Ex. Positive to Negative and vice versa

Therefore, (-5,10) reflected accross the x-axis becomes (-5,-10)

Since both x and y coordinates are negative, the point falls in the third quadrant, or Quadrant III

Choose impossible,unlikely,as likely as not, or certain to describe the event. The spinner lands on numbers 2,3,or 4.

Answers

2 is the right answer

The event can be unlikely.

What is Probability?

A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.

As per the given data:

We have to find out whether the event that a spinner lands on the numbers 2, 3, or 4 is impossible,unlikely,as likely as not, or certain.

The event cannot be impossible because there is a chance that it might actually stop on any of the three numbers 2, 3, or 4.

The event can be unlikely because it's not confirmed that it will always stop on any of the three numbers 2, 3, or 4.

The event cannot be as likely as not because the probability of the event happening and not happening is not the same.

The event cannot be certain because it's not confirmed that it will always stop on any of the three numbers 2, 3, or 4.

Hence, The event can be unlikely.

To learn more on Probability, click:

brainly.com/question/30034780

#SPJ2

PLEASE HELP ME
The following data set shows the pulse rate of some goats at a farm:

75, 76, 77, 76, 77, 76, 78, 75, 78, 76, 79, 76, 78, 76, 77, 76


Which dot plot best represents the data?


dot plot with 2 dots over 75, 8 dots over 76, 3 dots over 77, 3 dots over 78, no dot over 79

dot plot with 2 dots over 75, 7 dots over 76, 3 dots over 77, 3 dots over 78, 1 dot over 79

dot plot with 1 dot over 75, 8 dots over 76, 3 dots over 77, 3 dots over 78, 1 dot over 79

dot plot with 2 dots over 75, 6 dots over 76, 3 dots over 77, 3 dots over 78, 1 dot over 79

Answers

Answer: The answer is the 3rd one

Answer: B) dot plot with 2 dots over 75, 7 dots over 76, 3 dots over 77, 3 dots over 78, 1 dot over 79

Step-by-step explanation: took the test, hope this helps c:

What is the volume of this figure? Pls help this is due Thursday 11:45

Answers

Answer:

The answer for this question is 49 cubic inches

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