Which statement describes the inverse of m(x) = x^2 – 17x?


a. The domain restriction x ≥ StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction minus StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .


b. The domain restriction x ≥ StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction + StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .


c. The domain restriction x ≥ Negative StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction minus StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .


d.The domain restriction x ≥ Negative StartFraction 17 Over 2 EndFraction results in m–1(x) =StartFraction 17 Over 2 EndFraction + StartRoot x + StartFraction 289 Over 4 EndFraction EndRoot .

Answers

Answer 1

Given:

The function is

[tex]m(x)=x^2-17x[/tex]

To find:

The inverse of the given function.

Solution:

We have,

[tex]m(x)=x^2-17x[/tex]

Substitute m(x)=y.

[tex]y=x^2-17x[/tex]

Interchange x and y.

[tex]x=y^2-17y[/tex]

Add square of half of coefficient of y , i.e., [tex]\left(\dfrac{-17}{2}\right)^2[/tex] on both sides,

[tex]x+\left(\dfrac{-17}{2}\right)^2=y^2-17y+\left(\dfrac{-17}{2}\right)^2[/tex]

[tex]x+\left(\dfrac{17}{2}\right)^2=y^2-17y+\left(\dfrac{17}{2}\right)^2[/tex]

[tex]x+\left(\dfrac{17}{2}\right)^2=\left(y-\dfrac{17}{2}\right)^2[/tex]        [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]

Taking square root on both sides.

[tex]\sqrt{x+\left(\dfrac{17}{2}\right)^2}=y-\dfrac{17}{2}[/tex]

Add [tex]\dfrac{17}{2}[/tex] on both sides.

[tex]\sqrt{x+\left(\dfrac{17}{2}\right)^2}+\dfrac{17}{2}=y[/tex]

Substitute [tex]y=m^{-1}(x)[/tex].

[tex]m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}[/tex]

We know that, negative term inside the root is not real number. So,

[tex]x+\left(\dfrac{17}{2}\right)^2\geq 0[/tex]

[tex]x\geq -\left(\dfrac{17}{2}\right)^2[/tex]

Therefore, the restricted domain is [tex]x\geq -\left(\dfrac{17}{2}\right)^2[/tex] and the inverse function is [tex]m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}[/tex].

Hence, option D is correct.

Note: In all the options square of [tex]\dfrac{17}{2}[/tex] is missing in restricted domain.

Answer 2

Answer:

C on edu

Step-by-step explanation:


Related Questions

Each of the following tables defines a relationship between an input x and an output y. Which of the relationships represent functions? Table A x -8 -3 0 6 y 24 4 9 72 Table B x 9 15 24 38 y -14 -16 53 29 Table C x 15 24 24 100 y -16 53 29 7 Table D x -8 6 0 6 y 24 4 9 72 a. Table A and Table C b. Table A and Table B c. Table B and Table C d. Table C and Table D Please select the best answer from the choices provided

Answers

Answer:

I think it's d. C and D

Step-by-step explanation:

it needs to be 20 characters long so don't mind this part

Answer: is B. table A and Table B

Step-by-step explanation:

Part A
Choose a writing prompt from the following list. Then brainstorm a topic by asking the questions in the table. Fill in the
table with the prompt, topic, and answers to the questions:
Recount a personal achievement that you're proud of.
• Describe a place that has helped make you who you are.
• Identify and describe your role model.
Examine something that you're afraid of..
Describe something that motivates you.
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AAEEE 3
Font Sures
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Writing Prompt
Topic
What?
Where?
When?
Who?
Why?
How?
I
I’m

Answers

Answer:

Step-by-step explanation:

you pick your topic

the what is what is your topic

where does your topic take place

who is in your topic or who is it talking about

why did you choose this topic

There are four blue marbles and 6 red marbles. What is the ratio of blue marbles to red marbles. Write the ratio in simplest form

Answers

Answer:

2:3

Step-by-step explanation:

2 is the greatest common factor, so divide both 4 and 6 by 2, which should result as 2:3.

hope this helps :)

I am trying to choose a cellphone plan. Plan A charges $90 per month plus $0.15 per text message sent during the month. Plan B charges $60 per month plus $0.35 per text message sent during the month. In order for Plan A to be cheaper than Plan B, I would have to send how many messages in a month?

Answers

Answer:

258

Step-by-step explanation:

mark brainlest

Answer:

You will need to send 150 texts for them to be the same price

Step-by-step explanation:

A = .15x+90

B=.35x+60

.15x+90=.35x+60

      -60            -60

.15x+30=.35x

-.15x       -.15x

30=.2x

x=150

According to the US Bureau of Labor statistics, the average weekly earning of a production worker in 1997 were $424.5. Suppose a labor researcher wants to test to determine whether this figure is still accurate today .The researcher randomly selected 54 production workers from across the United States and obtained a representative earning statement for one week from each. The resulting sample average is $432.69. Assuming population Standard deviation is 33.90. and a 5% level of significance, To determine whether the mean weekly earnings of the production worker have changed.

Required:
To determine whether the mean weekly earnings of the production worker have changed, what would be the value of test statistics?

Answers

Answer:

test statistic is 1.775

Step-by-step explanation:

Bar x = 432.69

Standard deviation sd = 33.90

N = 54 production workers

Null hypothesis:

H0: μ = 424.5

Alternate hypothesis

H1: μ not equal to 424.5

Test statistic

= 432.69-424.5/sd/√n

= 8.19/33.9/√54

= 8.19/33.9/7.348

8.19/4.6135

= 1.7752

This is the value of our test statistic

When we test this with level of significance 0.05

Critical value z = 1.96

So we conclude that we do not have enough evidence to reject null hypothesis so we accept null and say mean weekly earnings have not changed

Given the domain {-4, 0, 5}, what is the range for the relation 12x + 6y = 24?

A.
{-4, 4, 14}
B.
{2, 4, 9}
C.
{-12, -4, 6}
D.
{12, 4, -6}

Answers

Answer:

The range is {12, 4, -6} ⇒ D

Step-by-step explanation:

The range of the relation is the values of y corresponding to the values given for x which is the domain of the relation

∵ The relation is 12x + 6y = 24

∵ The domain of the function is {-4, 0, 5}

→ That means x = -4, 0, 5, we need to find their corresponding values of y

∴ Substitute the values of x in the relation

x = -4

∴ 12(-4) + 6y = 24

∴ -48 + 6y = 24

→ Add 48 to both sides

∴ -48 + 48 + 6y = 24 + 48

∴ 6y = 72

→ Divide both sides by 6 to find y

∴ [tex]\frac{6y}{6}=\frac{72}{6}[/tex]

y = 12

x = 0

∴ 12(0) + 6y = 24

∴ 0 + 6y = 24

∴ 6y = 24

→ Divide both sides by 6 to find y

∴ [tex]\frac{6y}{6}=\frac{24}{6}[/tex]

y = 4

x = 5

∴ 12(5) + 6y = 24

∴ 60 + 6y = 24

→ Subtract 60 from both sides

∴ 60 - 60 + 6y = 24 - 60

∴ 6y = -36

→ Divide both sides by 6 to find y

∴ [tex]\frac{6y}{6}=\frac{-36}{6}[/tex]

y = -6

∵ The range is the values of y which corresponding to the domain

The range is {12, 4, -6}

The answer is down below have a good day!!!

what are the slopes of the two different lines? are they undefined?

Answers

Answer:

m = (y2 -- y1) / (x2 -- x1)

Step-by-step explanation:

Factorise fully
6x - 8​

Answers

Answer:

2(3x+ 4)

I hope it helps

Pls mark as brainliest

What type of transformation is a translation

Answers

Answer:

A translation, yes.....ok! the answer is below! ;)

In my explanation:

A translation is a type of transformation, it is when there is a plane and an object slides from one place to another without changing it's size, shape, or rotation.

Web explanation:

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or a space by the same distance in a given direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system.

Look at the image below, there is a figure, called the pre-image, and then when it slides the new image is called the image.

Hope this helps!

Have a nice day!

If you find my answers helpful

Pls consider marking my answers as Brainliest! It would mean a lot!

18. Leonardo lives in a 10-storey apartment
building. The building is 121 m tall.
All the storeys have the same height.
How high is each storey?

Answers

Answer:

12.1 m tall

Step-by-step explanation:

First you take 121 and divide it by 10 then you take the end number and add a m

is f(x)=5x^2+6x^3 a polynomial function​

Answers

Polynomials are expressions whose exponents are non-negative integers and the coefficients are real numbers. The leading term is the term with the highest power. The coefficient of the leading term is the leading coefficient. The power of x in the leading term is called the degree of the polynomial! Here are some examples of polynomials:
Degree Name Example
0 constant 11
1 linear 4x + 7
2 quadratic 3x2 + 4x + 5
3 cubic 4x3 + 3x + 7
4 quartic 3x4 + 2x2 + 4
5 quintic x5 + 3x + 1
Any value of x such that P(x) = 0 is a root of the equation and a zero of the function.
Review of synthetic substitution
To use synthetic substitution, do the following:
1) Write the polynomial in descending order.
2) Make sure any missing terms are replaced with zero!
3) Bring down the leading coefficient.
4) Multiply by the divisor and add to the next term.
5) Repeat the process until the last coefficient is reached.

Example
Use synthetic division to find P(2) for P(x) = 2x3 - 9x2 + 27
2| 2 -9 0 27
4 -10 -20
2 -5 -10 7 The value of P(2) = 7, the last number!!
Sample Problems
1) State whether each is a polynomial function. If yes, find the degree and the zeros.
Problem Polynomial? Degree zeros
a) f(x) = 5 - 4x yes 1 5/4
b) f(x) = 3x2 - 6x yes 2 0, 2
c) f(x) = x - 3/x no
d) f(x) = 18 yes 0 none
e) f(x) = (x-3)/(x+2) no
2) Use synthetic substitution to find P(3) for each function:
a) P(x) = 4x3 - 5x2 + 3
3| 4 -5 0 3
12 21 63
4 7 21 66
Therefore, P(3) = 66

b) P(x) = 3x4 + 2x3 - 5x - 2

3| 3 2 0 -5 -2
9 33 99 282
3 11 33 94 280
Therefore, P(3) = 280


3) If 4 is a zero of f(x) = 3x3 + kx - 2, find the value of k.
Since 4 is a zero, the value of f(4) = 0. Use synthetic substitution.
4| 3 0 k -2
12 48 192 + 4k
3 12 48 + k 190 + 4k
Now 190 + 4k = 0, solve for k
4k = -190
k = -190/4 = -47.5

USE A PROTRACTOR TO MEASURE THE FOLLOW
1)
2)
Answer:
Answer:
3)
4)

Answers

Answer:

1) 130°

2) 180°

3) 200°

4) 50°

Step-by-step explanation:

Hope it helps!!

:D

What is the rate of return when 10 shares of Stock
A, purchased for 20 $/share, are sold for $310? The
commission on the sale is $6.
rate of return = [?] %
Give your answer as a percent rounded to the
nearest tenth.

Answers

Answer:

Rate of return = 52%

Step-by-step explanation:

Cost of Investment = 10 shares × $20 = $200

Gain on Investment = amount sold - commission on the sale

Gain on Investment = $310 - $6 = $304

Using the formula:

ROR = (Gain on investment - cost of Investment)/cost of Investment × 100

Plug in the values into the formula:

[tex] ROR = \frac{304 - 200}{200} * 100 [/tex]

[tex] = \frac{104}{200} * 100 [/tex]

[tex] = \frac{104*100}{200} [/tex]

[tex] = \frac{104}{2} = 52 [/tex]

Rate of return = 52%

What is the slope of the points (2,5) and (0,-4)?

Answers

To find the slope of two points, we have to first assign our points as x1, y1 and x2, y2.

In our problem,

x1 = 2 and y1 = 5

x2 = 0 and y2 = -4

We know that that slope = y2 - y1 / x2 - x1. Let's plug our numbers into this formula.

Slope = -4 - 5 / 0 - 2 = -9 / -2 = 9 / 2

Please help me if you know it thank you so much

Answers

Answer:

a) 9 beats

b) 9 beats per minute

c) y=9x

d) 180 times

write in standard form -4 + y +2x = 0

Answers

Answer:

the answer is 2x+y=4

Step-by-step explanation:

2x+y=4

Answer:

y = -2x + 4

Step-by-step explanation:

Properties of the normal distribution include?

Answers

Answer:

Properties of a normal distribution

The mean, mode and median are all equal.

The curve is symmetric at the center (i.e. around the mean, μ).

Exactly half of the values are to the left of center and exactly half the values are to the right.

The total area under the curve is 1.

Step-by-step explanation:

The solution is , given below.

What is normal distribution?

A normal distribution is a type of continuous probability distribution in which most data points cluster toward the middle of the range, while the rest taper off symmetrically toward either extreme. The middle of the range is also known as the mean of the distribution.

here, we have,

Properties of a normal distributionThe mean, mode and median are all equal.The curve is symmetric at the center (i.e. around the mean, μ).Exactly half of the values are to the left of center and exactly half the values are to the right.The total area under the curve is 1.

To learn more on normal distribution click:

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Which expression is equivalent to 4(6 + 8)? (1 point)

a.
10 + 12
b.
10 + 8
c.
24 + 32
d.
24 + 8

Answers

C. You have to distribute the 4. 4 times 6 is 24. 4 times 8 is 32. Therefore, it would be 24+32.

Hope this helps

Answer:

c

Step-by-step explanation:

distrubte 4 to 6 and 8

4x6=24

4x8=32

24+32

Determine whether the ordered pair (coordinate) is a solution to the inequality.
2. 2x + 3y > -8,
(3,-6)

Answers

Answer:

The ordered pair is not a solution to the inequality.

Step-by-step explanation:

Given expression;

     Inequality :

         2x + 3y > -8

 

Ordered coordinate pair = (3, -6)

Solution:

If the ordered pair is a solution of the inequality, then it must be true that expression on the left -hand side is greater than -8;

So, the values we get on the right-hand side should be -7, -6 on and on.

  x  = 3 and y = -6

Input the parameters into the inequality;

     2(3) + 3(-6)

  = 6 - 18

   =  -12

   -12 is less than -8 and this is not correct for the expression.

The ordered pair is not a solution to the inequality.

Hey I need help with this question:

6(x-3)^2-26 = 10

Answers

Answer:

x = 3 ±sqrt(6)

Step-by-step explanation:

6(x-3)^2-26 = 10

Add 26 to each side

6(x-3)^2-26+26 = 10+26

6(x-3)^2 = 36

Divide by 6

6/6(x-3)^2 = 36/6

(x-3)^2 = 6

Take the square root of each side

sqrt((x-3)^2) = ±sqrt(6)

x-3 =  ±sqrt(6)

Add 3 to each side

x-3+3 =3 ±sqrt(6)

x = 3 ±sqrt(6)

The listed occupations of stockholders of a national computer company included 9% who were housewives. If six of these stockholders are randomly selected, what is the probability that none are housewives?

Answers

Answer:

no se la respuesta

Step-by-step explanation:

no se la respuesta

The probability that none of the six selected stockholders are housewives is,

⇒ 56.8%

The term probability refers to the likelihood of an event occurring. Probability means possibility.

The probability of an event occurring can be calculated by subtracting the probability of the event not occurring from 1.

Given that,

The listed occupations of stockholders of a national computer company included 9% who were housewives.

Since 9% of the stockholders are housewives.

Hence, the probability that a randomly selected stockholder is not a housewife is,

= [tex]1 - 9%[/tex]%

= [tex]1 - 0.09[/tex]

= [tex]0.91[/tex]

So, The probability that none of the six selected stockholders are housewives is,

⇒ [tex](0.91)^6[/tex]

⇒ [tex]0.5678[/tex]

Learn more about the probability visit:

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is 600 : 450 and 4 : 3 equivalent

Answers

Answer:

Yes

Step-by-step explanation:

600/150=4

450/150=3

What is the value of name and tell the value of the underline digit. The number is 25,678 the underline digit is 5.

Answers

It’s the thousands place and the value is 5,000

A random sample of 17 hotels in Boston had an average nightly room rate of $165.40 with a sample standard deviation of $21.70. The critical value for a 98% confidence interval around this sample mean is ________.

Answers

Answer:

153.158 ; 177.642

Step-by-step explanation:

Given the following:

Sample mean (m) = 165.40

Sample standard deviation (s) = 21.70

Sample size (n) = 17

α = 98%

Confidence interval = m ± z(SE)

z at 98% = 2.326

SE = s/√n

SE = 21.70/√17 = 5.2630230

Hence,

Confidence interval = 165.40 ± 2.326(5.2630230)

165.40 - 12.241791498 OR 165.40 + 12.241791498

153.158 ; 177.642

find the value of x. PLEASE HELP.
The answer is 25. Teacher gave us the answer, but I need to show my work.

Answers

Answer:

Step-by-step explanation:

2+5x+53=180

55+5x=180

5x=125

x=25

hope this helps :)

explanation:
2+5x and 53 are supplementary angles (they add up to 180), so you need to set an equation by adding them to equal 180:
2 + 5x + 53 = 180
combine like terms
55 + 5x = 180
we want the x by itself, so subtract both sides by 55
5x = 125
divide both sides by 5 to get:
x = 25°

what value of x will make the equation f(x)=6 true ?

Answers

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]f(x) = 6[/tex]

Required

Solve for x

The question is incomplete as the function f(x) is not given.

However, the following explanation will guide you

As a point of reference, we assume that f(x) is:

[tex]f(x) = 2x + 4[/tex]

To solve further, we substitute 6 for f(x)

[tex]6 = 2x + 4[/tex]

Then, we solve for x

[tex]2x = 6 - 4[/tex]

[tex]2x = 2[/tex]

Divide through by 2

[tex]x = 1[/tex]

So, in your case.

All you need to do is substitute 6 for f(x) then solve for x

In two hours, Christopher can read 150 pages. At this rate, how many pages can Christopher read in three hours?

WILL RECIEVE BRAINLIST AND EXTRA POINTS

Answers

I guess the answer would be 225 if you do 150 divided by 2 it would be 75 and 75 x 3 would equal 225 so I think that’s your answer.

If a histogram of a sample of​ men's ages is​ skewed, what do you expect to see in the normal quantile​ plot?

Answers

Answer: Points are not following a straight-line pattern

Step-by-step explanation:

Histograms are used to show the distribution of a dataset.

If the histogram is skewed, then it means that the points do not follow a straight-line pattern, on the normal quantile plot.

From the question, we understand that:

The histogram is skewed

This means that:

The data points of the histogram are either concentrated on the right or on the left-hand side of the histogram.

The above highlight mean that:

The points on the histogram are unequal.

Hence, you would see that the points do not follow a straight line pattern on the normal quantile plot.

Read more about normal quantile plot at:

https://brainly.com/question/5678453

A spherical balloon is inflated with gas at a rate of 500 cubic centimeters per minute. Find the rates of change of the radius when r = 70 centimeters and r = 95 centimeters.

Answers

Answer:

for r= 70 cm

the rate is 0.008cm/s

for r=95cm

the rate= 0.0044cm/s

Step-by-step explanation:

kindly find attached a rough sketch of the circle and a detailed solution of the problem.

Given data

rate dv/dt=500cm^3

r=70cm

r=95cm

What is the ratio of 20 praise and 2000 rupees

Answers

1:100 because 20 divide by 20=1 and 2000 divide by 20 =100

Answer:

1 rupee=100 paisa

so, 20 paisa:2000 rupees

=>20 paisa:2000×100

=>1:10000.

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