Question 19 of 25
f(x)=√x-6. Find the inverse of f(x) and its domain.

Answers

Answer 1

Answer:

f¯¹(x)=x²+12x+36

Step-by-step explanation:

[tex]f(x) = \sqrt{x} - 6 \\ substitute \: y \: for \: f {}^{ - 1} (x) \\ y = \sqrt{x} - 6 \\ interchange \: x \: and \: y \\ x = \sqrt{y} - 6 \\ swap \: the \: side \: of \: the \: equation \\ \sqrt{y } - 6 = x \\ move \: the \: constant \: to \: the \: right \: hand \: side \\ \sqrt{y} = x + 6 \\ square \: both \: sides \: of \: the \: equation \\ y = x {}^{2} + 12x + 36 \\ substitute \: f \frac{}{ -1} (x) \: for \: y \\ f {}^{ - 1} (x) = x {}^{2} + 12x + 36 \\ domain \: x∈R[/tex]


Related Questions

Your warehouse had 51 cases of Happy Cola at the start of your shift. A truck arrived this morning with another 25 cases of Happy Cola. How many cases of Happy Cola do you have now?

Answers

Answer:

76 cases

Step-by-step explanation:

original 51 plus the 21 new is equal to 76 total

An equation is shown below:

8(2x − 14) + 13 = 4x − 27

Part A: Write the steps you will use to solve the equation, and explain each step. (6 points)

Part B: What value of x makes the equation true? (4 points)

Amd please show the work.

Answers

Step-by-step explanation:

first distribute the first equation

8(2x) - 8(14) +13 = 4x -27

16x - 112 +13 = 4x -27

then combine like terms

16x - 99 = 4x -27

subtract 4x from both sides

12x - 99 = -27

add 99 to both sides

12x = 72

divide both sides 12 to isolate the x

x = 72/12 = 6

Solve for x in equation x^2-10x25=35

Answers

Answer:   b

Step-by-step explanation:

x= 5+√35 and 5-√35

Jordan and Beth are mixing yellow and blue paint to make green paint.
They are both using the same shades of yellow and blue paint.
A green paint made with a higher proportion of blue produces a darker green
Jordan mixes the yellow and blue paint in the ratio of 5:2.
Beth mixes the yellow and blue paint in the ratio of 18:7.
Who has the darker green paint?

Answers

Answer:

Jordan

Step-by-step explanation:

Jordan 5:2 -> 10:4, 15:6   20:8  25:10  50:20  60:24  70:28

Beth  18:7->  36:14  54:21  72:28

When Both of them add 28 of BLUE paint, Jordan adds only 70 yellow paint, while Beth uses 72 yellow paint. This would make Jordan's green darker.

Answer:

HI RACHEL

Step-by-step explanation:

so you do 1 + 1 which equalls to -8

then you do 7 - 9 which qualls 67

LOOL

What is the y-intercept of the Function

Answers

Answer:

(0, 3)

General Formulas and Concepts:

Algebra I

Reading a Cartesian planeCoordinates (x, y)The y-intercept is the y value when x = 0. Another way to reword that is when the graph crosses the y-axis.

Step-by-step explanation:

According to the graph, when x = 0, we see that y = 3. Therefore, our y-intercept is (0, 3).

Dave divided 3/5 of a gallon of plant fertilizer evenly among 6 smaller bottles. How many gallons did he put in each bottle?

Whoever answers first gets brainliest please help

Answers

Answer:

Brothers Sorry I don't

Step-by-step explanation:

Please give thanks to all my answers and please mark as brilliant and please follow me

The equation of a line XY is (y-3)=3/2(x-4) what is the slope of the line perpendicular to XY?

Answers

Answer:

It must be 3/2.........

Answer: -2/3

Step-by-step explanation:

I wrote the equation y-3=3/2(x-4) in slope-intercept form. It's y=3/2x-5, so the slope is 3/2.

To find the perpendicular slope, I found the opposite reciprocal. The reciprocal of 3/2 is 2/3 and the opposite of 2/3 is -2/3

Darren wants to save 1,125 for his vacation. When he saved 3 times as much as he has already saved, he will need only 27 more. how much has he saved so far​

Answers

Answer:

125

Step-by-step explanation:

the answer is 125. hope helped bye

Find the absolute value.
What is the absolute value of four

Answers

Answer:

whats the graph???

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

When it’s an absolute value no matter what it’s inside the braces ( “ | # | “ ) it’s a positive. While the signs outsides can stay the same

What is the y-intercept of the graph of f ?

Answers

Answer:

(0,4)

Step-by-step explanation:

y intercept is where the line crosses the y axis

Answer:

4

Step-by-step explanation:

Math question, can you guys answer this? 25 points. ​

Answers

Answer:

5. 1/29

Step-by-step explanation:

1/. and the bottom numbers says 30-1 which is 29 soooo 1/29

To test the effectiveness of an exercise program in reducing high blood pressure, 15 participants had their blood pressures recorded before beginning the program and again after completing the program. The difference (after minus before) in blood pressure was recorded for each participant, and the sample mean difference was calculated. A hypothesis test will be conducted to investigate whether there is convincing statistical evidence for a reduction in blood pressure for all who complete the program. Which of the following is the correct set of hypotheses?
A. H0 : bar xD = 0
Ha : bar xD is not equal to 0
B. H0 : bar xD = 0
Ha : bar xD > 0
C. H0 : mu D = 0
Ha : mu D is not equal to 0
D. H0 : mu D = 0
Ha : mu D > 0
E. H0 : mu D = 0
Ha : mu d < 0

Answers

Answer:

E.

H0 : mu D = 0

Ha : mu d < 0

Step-by-step explanation:

The hypothesis is to test if there is a reduction in blood pressure for those who complete the program, this means if the mean difference in blood pressure (that is after - before) is less than 0. Here, the hypothesis is the alternative side while the opposite, that is, there is no difference in blood pressure before and after is the null.

This means :

H0 : μD = 0

Ha : μD < 0

You can use the definitions for null and alternate hypotheses  

The correct set of hypothesis is given by:

Option E.  [tex]H_0: \mu_D = 0[/tex]

[tex]H_a: \mu_D < 0[/tex]

How to form the hypotheses?

There are two hypotheses. First one is  called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.

Null hypothesis is the one which researchers try to disprove.

How to find the correct set of hypothesis for the given situation?

Since the test is to test the effectiveness of the exercise program, thus the wish of the tester is to get the result that effectiveness is there. This will be the alternate hypothesis and the null hypothesis will be that there is no difference in the blood pressure before and after the exercise. Thus, we will test against the null hypothesis.

Since the evidence is to be found for all of the people who completed the program, thus it is hypothesis about population perimeter. The average blood pressure difference of the population is denoted by [tex]\mu_D[/tex] and that of the sample is denoted by [tex]\overline{x}_D[/tex]

Thus, we have:

Null hypothesis = the difference in average blood pressure before and after the program of the population is not changed(thus 0 is the difference) = [tex]H_0: \mu_D = 0[/tex]

Alternate hypothesis = the difference in average blood pressure is reduced(since the test is for seeing if the blood pressure is reduced or not) = [tex]H_a: \mu_D < 0[/tex]

Thus,

The correct set of hypothesis is given by:

Option E.  [tex]H_0: \mu_D = 0[/tex]

[tex]H_a: \mu_D < 0[/tex]

Learn more about null and alternative hypothesis here:

https://brainly.com/question/18831983

If the sum of two numbers is 4 and the sum of their spuares minus three times their product is 76, find the numbers

Answers

Answer:

[tex]Suppose~that~two~numbers~are~x~and~y.\\From~the~first~condition,\\x+y=4.........(1)\\or, y=4-x.......(2)\\From~the~second~condition,\\x^2+y^2-3xy=76\\or, (x+y)^2-2xy-3xy=76\\or, 4^2-5xy=76\\or, -5xy = 76-16\\or, -5xy = 60\\or, xy = -12\\From~eq^n~(2),\\x(4-x)=-12\\or, 4x-x^2=-12\\or, x^2-4x-12=0\\or, x^2 +2x-6x-12=0\\or, x(x+2)-6(x+2) = 0\\or,(x+2)(x-6) = 0\\i.e. x = -2 ~or ~6\\When~ x=-2, y=4-(-2) = 4+2 =6\\When~x=6, y=4-6 = 4-6 = -2\\So,~the~two~numbers~are~-2~and~6.[/tex]

Answer:

-2 and 6

Step-by-step explanation:

Mark the first number as x

and the second number as y

Since x + y = 4

y = 4 - x

// substitute the given value of y into the equation

[tex]x^{2} + y^{2}[/tex] - 3xy = 76

[tex]x^{2}[/tex] + [tex](4-x)^{2}[/tex] - 3 * x * (4 - x) = 76

[tex]x^{2}[/tex]  + 16 - 8x + [tex]x^{2}[/tex]  - 12x + 3[tex]x^{2}[/tex] = 76

[tex]x^{2}[/tex]  + [tex]x^{2}[/tex]  + 3[tex]x^{2}[/tex]  - 20x = 76 - 16

5[tex]x^{2}[/tex]  - 20x = 60

5[tex]x^{2}[/tex]  - 20x - 60 = 0

// divide both sides by 5

[tex]x^{2}[/tex] - 4x - 12 = 0

// write -4 x as a difference, this way it is faster than calculating discriminant

[tex]x^{2}[/tex] + 2x - 6x - 12 = 0

// factor out x and -6 from the expression

x (x +2) - 6 (x +2) = 0

(x - 6) * (x + 2) = 0

// there are two possible cases

1) x - 6 = 0

2) x + 2 = 0

1) x = -2

2) x = 6

// substitute the given value of x into the equation

1) y = 4 - x = 4 - (-2) = 6

2) y = 4 - x = 4 - 6 = -2

Now we get two pairs (-2; 6) and (6; -2), which are the solutions to the system

Since their sequence as the question suggests is irrelevant, the numbers are -2 and 6

How do I write this equation without fractions or decimals?
2-(3/4)x=2/5

Answers

multiply each side by 20
40 - 15x = 8

An iPhone that is marked $500 is marked up 250%.

What is the new price of the iPhone?


$750
$1750
$1250
$1000

Answers

Answer:

1250

Step-by-step explanation:

This would be 500 x 250/100 = 125000/100 = 1250

1. X+4x+6x need help ASAP 10 minutes remaining ​

Answers

Answer:10x …….….....

Answer:

10x^2 or 10x because you are adding x

Sasha ran 2/3 of a 27km race before she stopped to walk. How
many kilometers had she run at that point?

Answers

Answer:

2/3 of 27=18 km

Step-by-step explanation:

Factor the expression 49t4 - 25 using the polynomial identity (x2 - y2) = (x - y)(x + y)

Answers

Answer:

Step-by-step explanation:

49t^4-25

(7t^2-5)(7t^2+5)

a) 8801
+2031
_______​

Answers

Answer:

the answer is 10832

Step-by-step explanation:

you can use a calculator

Answer:

10832

Step-by-step explanation:

Add one digit at the time (from right to left):

1 + 1 = 2

0 + 3 = 3

8 + 0 = 8

8 + 2 = 10

Now we get 10832

solve this 50+50-25×0+2+2​

Answers

4 that’s the answer I think
I believe the answer is 4

which fraction is 16/64 in lowest terms

PLEASE SHOW HOW U DID UR PROBLEM

Answers

Answer:

16/64 simplified to lowest terms is 1/4

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 16 and 64 is 16

Divide both the numerator and denominator by the GCD

16 ÷ 16

64 ÷ 16

Reduced fraction:  

1/ 4

Answer:

1/4

Step-by-step explanation:

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 16 and 64 is 16

Divide both the numerator and denominator by the GCD

16 ÷ 16

64 ÷ 16

Reduced fraction:

1 / 4

Therefore, 16/64 simplified to lowest terms is 1/4.

A marine biologist wants to estimate the average weight of a population of dolphins living in a certain region of the ocean. The biologist will collect a random sample of dolphins and use the sample weights to create the estimate Which of the following is an appropriate method for the biologist to use for inference to the population?
A A one-sample t-interval for a population mean
B A one-sample t-interval for a sample mean
C A one-sample 2-interval for a population proportion
D A matched-pairs t-interval for a mean difference
E A two-sample t-interval for a difference between means

Answers

Answer:

A A one-sample t-interval for a population mean

Step-by-step explanation:

The biologist will collect a random sample of dolphins and use the sample weights to create the estimate.

In a confidence interval, we take the data from the sample and want to estimate it for the entire population, so the interval is for a population mean.

The standard deviation will be taken from the sample, which means that the t-interval is used.

We want for one population, so it is a one sample for the population mean, and the correct answer is given by option A.

5% of a number is 23

1% percent of the same
number is 6.4

Work out 16%​ of the number

Answers

Answer:

73.6

Step-by-step explanation:

Let the number be m

so, 5% × m = 23

5 m = 23100

m = 23 × 100 5

m = 460

16% of that number

16 × 460 = 73.6100

16% of the number is 73.6

b. 3.3 x 0.8 =
3 3
х
8

Answers

Answer: the answer is 2.64 or 264

Explanation: if you multiply 3.3 × 0.8=264 but if you mulyiply 33×8=264

What would be the y- intercept for the function y=3x-6?

Answers

Answer:

the y intercept would be at (0,-6)

Kaitlin has four and two-thirds berry pies. She is going to share it equally among 12 people. How much pies will each person get?

Answers

Answer:

7/18

Step-by-step explanation:

4 2/3=14/3

(14/3)/12=14/36

reduces to

7/18

Bir otobüste bulunan 45 yolcudan
Buna göre bu otobüsteki yolcuların
18'i çocuktur.
yüzde kaçı çocuktur?

Answers

Step-by-step explanation:

bence 27 cunkku yuzd sordugu icin kolaylıklar dilerim iyi günler

What is the least common denominator of the rational expressions below?
1/x^2 - 4/3x^2+15x

Answers

Answer:

The LCD is 3x²

The other two denominators can be factors of 3x²

Step-by-step explanation:

To get the equivalent fractions, divide the original denominator into the LCD, then multiply the original numerator by the quotient.

For the first term: 1/x²

3x² ÷ x² = 3 3×1=3 The equivalent is 3/3x²

Second term: Leave it as it is.

For the third term: 15x

The implied denominator is 1

3x² ÷ 1 = 3x² 3x² × 15 = 135x²

The equivalent is 135x²/3x²

To check the validity, substitute a value for x and calculate the numbers.

For example let x = 3

The original expression becomes

1/3² + 4/3(3²) - 15(3)

1/9 + 4/27 - 45

With the LCD it is

3/27 + 4/27 - 1215/27

Answer:

3x^2(x+5)

Step-by-step explanation:

hope this helps

The table shows the results of a survey of 100 people selected at random
at an airport. Find the experimental probability that a person selected at
random is going to City C.


The experimetal probability that a person selected at random is going to city C is

Answers

Answer:

[tex]\frac{4}{25}[/tex]

Step-by-step explanation:

22/200 simpilfy is 4/25

The experimental probability that a person selected at random is going to city C is P ( C ) = 4/25 = 0.16

What is Probability?

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the experimental probability that a person selected at random is going to city C is P ( C )

Now , the total number of people in the city = 100

The number of people going to city C = 16

So , P ( C ) = number of people going to city C / total number of people in the city

On simplifying , we get

P ( C ) = 16 / 100

P ( C ) = 4/25

P ( C ) = 0.16

Hence , the probability is 0.16

To learn more about probability click :

https://brainly.com/question/17089724

#SPJ2


A store marks a TV down from $499 to $350. Which expression can be used to calculate the percent decrease?

Answers

Answer:

499-350

Step-by-step explanation:

455-350=?

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