Consider function f.
f(1) = 170 – 21
Place the steps for finding /-(s) in the correct order.
y = 171 – 21
I = V7y - 21
1
432 + 3 = 1-1(), where I > 0
1
(1 +21)2 = 77
$(72 – 21) = |-|(s), where a > 0
1
12 + 21 = 7y
12 = 7y - 21
1
42 +3 = 4
1
Answers
Given:
The function is:
[tex]f(x)=\sqrt{7x-21}[/tex]
To find:
The steps of finding the inverse function [tex]f^{-1}(x)[/tex].
Solution:
We have,
[tex]f(x)=\sqrt{7x-21}[/tex]
The steps of finding the inverse function are:
Step 1: Substitute [tex]f(x)=y[/tex].
[tex]y=\sqrt{7x-21}[/tex]
Step 2: Interchange x and y.
[tex]x=\sqrt{7y-21}[/tex]
Step 3: Taking square on both sides, we get
[tex]x^2=7y-21[/tex]
Step 4: Adding 21 on both sides, we get
[tex]x^2+21=7y[/tex]
Step 5: Divide both sides by 7.
[tex]\dfrac{1}{7}x^2+3=y[/tex]
Step 6: Substitute [tex]y=f^{-1}(x)[/tex].
[tex]\dfrac{1}{7}x^2+3=f^{-1}(x)[/tex], where [tex]x\geq 0[/tex].
Therefore, the inverse of the given function is [tex]f^{-1}(x)=\dfrac{1}{7}x^2+3[/tex] and the arrangement of steps is shown above.
Related Questions
What is the z-score of a data value that is 3 standard deviations to the left of the mean?
Answers
Answer:
Step-by-step explanation:
look up z-table
3 std div. = 0.00135
If you can’t see it let me know and I will type it
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PLEASE HELP THIS IS VERY IMPORTANT I WILL GIVE U BRAINLIEST IF ITS CORRECT NO LINKS PLEASE no guessing ;) rip my points i have 6 now ): IM CRYING
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Answer:
5(b+3)
Step-by-step explanation:
you are multiplying the sum of b and 3 by 5
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
evaluate the expression 7^2/ x^2 - 2 for x = 3
Answers
Answer:
7
Step-by-step explanation:
7²/x²-2 when x=3
49/3²-2
49/9-2
49/7
answer=7
The school nurse would like to compare the daily calorie consumption of some teachers to their weight. The data are given below: Calorie 1960 2160 1530 1690 Weight 75 74 78 80 Calorie 1580 1780 2170 1820 1880 Weight 77 85 79 82 78
Answers
Answer:
hinh nh ul a caanbang
Step-by-step explanation:
Calorie consumption increases, and weight tends to increase slightly, but the relationship is not very strong.
How to compare data?To compare the daily calorie consumption of teachers to their weight, we can create a scatter plot of the given data, where the calorie consumption is plotted on the x-axis, and the weight is plotted on the y-axis.
Each point on the scatter plot represents a teacher, and the position of the point shows the teacher's calorie consumption and weight.
From the scatter plot, we can see that there is no clear pattern or trend between the calorie consumption and weight of the teachers. However, we can calculate the correlation coefficient between the two variables to quantify the strength and direction of the relationship.
Using a calculator or a spreadsheet program, we can find that the correlation coefficient between calorie consumption and weight is approximately 0.07, which indicates a weak positive correlation.
This means that as calorie consumption increases, weight tends to increase slightly, but the relationship is not very strong.
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Find the Experimental Probability of Spinning a 4
Answers
Answer:
....................................,..............................,................................,...................................,...........................,..................,......,,,.,.................................
Step-by-step explanation:
42 32 30 32 44 36 45 43 What is the median of this set of data?
Answers
Answer: 39
Step-by-step explanation:
30 32 32 36 42 42 44 45
Please HELP!!!!!
I need help ASAP!!!!!!!
HELP!!!!!!!!
Answers
Answer: Choice C)
The variable y is on one side of the equation. The expression on the other side of the equation shows the relationship between x and y
In other words: y is all by itself on one side, while x is buried in an expression on the other side.
For instance, one such equation could be y = 2x+5.
A bed sheet was sold for $483 thereby gaining 15%. Find the Cost Price of
the bed sheet.
Answers
Gain=15% of x
SP=483$
Profit=SP-CP
CP=SP-Profit
x=483-15x/100
x+15x/100=483
100x+15x/100=483
115x/100=483
x=483*100/115
x=420
So, Cost price of the bed sheet is $420.
In ΔHIJ, the measure of ∠J=90°, JH = 81 feet, and HI = 91 feet. Find the measure of ∠I to the nearest degree.
Answers
Answer:
63°
Step-by-step explanation:
[tex]Sin0=\frac{81}{91}[/tex][tex]x=sin^{-1}(81/91)\\\\[/tex][tex]= 62.887[/tex]≈ 63°༻﹡﹡﹡﹡﹡﹡﹡༺
hope it helps...
have a great day!!
A teacher offers 8 extra credit assignments. what is the domain of this graph?
Answers
Answer:
C
Step-by-step explanation:
This is the shows the constant value on the X-axis
if a plate of car consists of two letters and four digits and one car is chosen at random, then find the probability that the car has the letters at the beginning and at the end.
Answers
Answer:
if u take 1 degree to 78 its answer is 79
Step-by-step explanation:
got it?
The probability that the car has the letters at the beginning and at the end is 1/15.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have,
The plate of car consists of two letters and four digits.
So, there are
= 6!/(4!*2!)
=(6 x 5 x 4!)/4! x 2
= 3 x 4
= 15 ways of arranging
Then, the probability that the car has the letters at the beginning and at the end is 1/15.
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Ronald and Khalil had a 400 meter race Ronalds time was 1 minute and 51 seconds and Khalil time was 2 minutes and 34 seconds how much faster was Ronald time the khalil’s
Answers
Answer:
Ronald ran at a speed of 14.26 km / h, while Khalil did so at a speed of 9.35 km / h.
Step-by-step explanation:
Given that Ronald and Khalil had a 400 meter race, and Ronald's time was 1 minute and 51 seconds, and Khalil's time was 2 minutes and 34 seconds, to determine how much faster was Ronald time the Khalil’s, the following calculation must be performed:
400 x 2.5 = 1000
60 x 60 = 3600
1.51 = 101 x 2.5 = 252.5
2.34 = 154 x 2.5 = 385
252.5 = 1000
3600 = X
3600 x 1000 / 252.5 = X
14,257.43 = X
385 = 1000
3600 = X
3600 x 1000/385 = X
9,350.65 = X
14,257.43 / 1000 = 14.26
9,350.65 / 1000 = 9.35
Thus, Ronald ran at a speed of 14.26 km / h, while Khalil did so at a speed of 9.35 km / h.
✓
In a right angled triangle, the ratio of the acute
Three angles of a triangle are (3x +12). (2x - 38), (x + 10
value of each angle.
tion angle in 4P Find the
Answers
Answer:
[tex](3x + 12) + (2x - 38) + (x + 10) = 180 \degree \\ 6x - 16 = 180 \\ 6x = 196 \\ x = 32.6 \\(3x + 12) : = > 110 \degree \\ (2x - 38) : = > 27.3 \degree \\ (x + 10) : = > 42.6 \degree[/tex]
Facial shaving brushes are either bulb-shaped or fan-shaped. An experiment is to be conducted to determine whether the lather thickness is the same for both types of shaving brushes. In previous studies, it was determined that shaving brush size (small, medium, large) is associated with lather thickness, but shaving brush type (Wolf Whiskers, Maggard Razors, Frank Shaving, and so on) is not associated with lather thickness. How could the experiment BEST be conducted?
a) By blocking on shaving brush size
b) By blocking on shaving brush type
c) By blocking on shaving brush shape
d) By blocking on lather thickness
e) Without blocking
Answers
Answer:
a) By blocking on shaving brush size
Step-by-step explanation:
You block on the variable that the researchers think matters.
The experiment can BEST be conducted by blocking on shaving brush size
What is the reason behind the experiments?An experiment is designed to verify your hypothesis. If your theory is valid, every time a scientific experiment has been conducted, it has the potential to be true.
In this given experiment a technique is used to verify or disprove a theory, as well as assess the effectiveness or likelihood of something that has never been tried before. Experiments show what happens when a specific factor is modified, which sheds light on cause-and-effect relationships.
Since, lather thickness and shaving brush size are related, changing the brush size could have an impact on the experiment's findings.
Therefore, The experiment can be best carried out by limiting the size of the shaving brush.
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Select the correct answer from the choices given
(13 + 4i) + n = 0
What is n?
0
1
–13 + 4i
–13 - 4i
Answers
Answer:
D
B
Step-by-step explanation:
I need the answer. Please help
Answers
=3.14 x 12² x 330 ÷ 360 ≈ 415 ft²
In assessing the validity of any test of hypotheses, it is good practice to a. examine the probability model that serves as a basis for the test by using exploratory data analysis on the data. b. determine exactly how the study was conducted. c. determine what assumptions the researchers made. d. all of the above.
Answers
Answer:
The Correct option is - d. all of the above.
Step-by-step explanation:
To find - In assessing the validity of any test of hypotheses, it is good practice to
a. examine the probability model that serves as a basis for the test by using exploratory data analysis on the data.
b. determine exactly how the study was conducted.
c. determine what assumptions the researchers made.
d. all of the above.
Proof -
All the Given options are correct to study the validity of a hypothesis test.
So,
The Correct option is - d. all of the above.
A library sells 600 books for a fundraiser. The library claims that 60% of the books are fiction how many of these books are fiction.
A 10
B 36
C 360
D 600
ASAP PLS!!!!!
Answers
Answer:
C. 360
Step-by-step explanation:
60% = 0.60
600 x 0.60 = 360
360 fiction books
What is the area of this figure?
Enter your answer in the box.
[_] m²
Answers
Answer: 81 m^2
Step-by-step explanation:
Parallelogram:
9 × 5 = 45
Triangle:
8 × 9 = 72
72 ÷ 2 = 36
Add:
45 + 36 = 81 bro look i even did an explation can u plz mark brainlist
A box contains 3 chocolate chips, 5 oatmeal raisin ,and 4 peanut butter cookies.one cookie is randomly selected.what is the probability that a peanut butter cookie will be selected
Answers
Answer:
1/3 or .333 or 33%
Step-by-step explanation
You take the 4 (peanut butter cookies) divided by the total number of cookies (12)
Select all the correct answers.
Natalie buys a new car. At the end of the first month, the odometer on the car reads 800 miles. From past experience, she expects to drive 900 miles per month.
Select all the functions that can be used to find the number of miles, , recorded on the odometer after n months.
Answers
Answer:
(a) [tex]f(n)= 900n -100[/tex]
(b) [tex]f(1) = 800[/tex]; [tex]f(n) = f(n-1) +900[/tex] for [tex]n \ge 2[/tex]
Step-by-step explanation:
Given
[tex]f(1) = 800[/tex] --- first month
[tex]d = 900[/tex] --- difference in distance covered each month
Required
Find f(n)
To do this, we have:
[tex]a_n = a_1 +d(n -1)[/tex]
Where
[tex]a_1 = f(1) = 800[/tex]
This gives:
[tex]a_n = 800 +900(n -1)[/tex]
[tex]a_n = 800 + 900n - 900[/tex]
Collect like terms
[tex]a_n= 900n +800-900[/tex]
[tex]a_n= 900n -100[/tex]
So, we have:
[tex]f(n)= 900n -100[/tex]
As a recursion, we have:
[tex]f(1) = 800[/tex]
For every other month i.e. [tex]n \ge 2[/tex]
We have:
[tex]f(n) = f(n-1) +900[/tex] for [tex]n \ge 2[/tex]
Which means 900 miles plus distance covered in previous month
Max is mixing oil and gas for his moped. He uses 3.75 liters of gas and 1.5 liters of oil. How many liters of gas are used per liter of oil ?
Answers
Step-by-step explanation:
Recognize youre finding the ratio between litres of gas per litres of oil
per always means a ratio
3.75L gas / 1.5L oil
simplify to get 2.5L gas / 1L oil
If your earned income for 2021 will be $84,686, Calculate what you will pay
in Social Security and Medicare taxes if Social Security is taxed at 6.2% at a
maximum taxable income of $142,800 and Medicare is taxed at 1.45%.
Answers
Answer:
5250.53 social security, 1227.95 Medicare
Step-by-step explanation:
84686x.062=5250.53 in social security
84686x.0145=1227.95 in Medicare
A blue bag has 2 times as many marbles as a red bag. The blue bag has 6 marbles.
How many marbles are in the red bag?
Answers
Answer:
3
Step-by-step explanation:
The density of a quartz crystal is 2.16207 g/cm².
What's the density rounded to the nearest tenth?
Answers
Answer:
2.2 g/cm2
Step-by-step explanation:
well the rule for rounding is 5 and up go up and 4 and down stay the same so 2.16207 would round to 2.2
Answer:
2.2
round up
Step-by-step explanation:
Use fractions to explain why 4.5 x 0.5 equals 2.25.
Answers
Answer:
4 1/2 x 1/2
9/2 x 1/2 = 9/4
9/4 = 2 1/4
Step-by-step explanation:
Vanessa walks her puppy 1/2 of a miles in 20 minutes. How far does she walk her puppy
in 1 hour?
Answers
Which of the following is the solution to the compound inequality below?
3x + 4 213 or 2x-13-11
Answers
Answer:
C. x is greater than or equal to 3 or x is less than or greater than -5
Isabel stacked two wooden blocks as shown. What is the total volume of the stacked blocks?
A. 60 cm3
B. 35 cm3
C. 96 cm3
D. 156 cm3
Answers
9514 1404 393
Answer:
156 cm³
Step-by-step explanation:
The volume of any prism is the product of the base area and the height of the prism. Here, we can take the "base" to be the front face of the assembly, and its "height" to be the 3 cm distance between the front and back faces.
The front face area is the sum of the triangle area and the rectangle area.
A = 1/2bh + LW
A = (1/2)(10 cm)(4 cm) + (16 cm)(2 cm) = 52 cm²
Then the volume is ...
V = Bh = (52 cm²)(3 cm) = 156 cm³ . . . . total volume of the two blocks