Consider the function.
f(x) = -2/3x-24
Which conclusions can be drawn about f^-1(x)? Select two options.

Consider The Function.f(x) = -2/3x-24Which Conclusions Can Be Drawn About F^-1(x)? Select Two Options.

Answers

Answer 1

Answer:

Statement 3

Step-by-step explanation:

y = -2/3x-24

Make x the subject

y + 24 = -(⅔)x

x = -(3/2)(y + 24)

Intersection variables

f^-1(x) = -(3/2)(x + 24)

Slope: -3/2

No domain restrictions

y-intercept: x = 0

-(3/2)(0+24)

-36

(0,-36)

x-intercepts: y = 0

0 = -(3/2)(x + 24)

x = -24

(-24,0)

Linear function, range is all real values of y

Answer 2

Answer:

[tex]f^{-1}(x)\: \textsf{ has a y-intercept of }\:(0,-36)[/tex]

[tex]f^{-1}(x)\: \textsf{ has a range of all real numbers.}[/tex]

Step-by-step explanation:

Given function

[tex]f(x)=-\dfrac{2}{3}x-24[/tex]

The given function has an unrestricted domain and range.

Domain:  (-∞, ∞)  →  all real numbersRange:  (-∞, ∞)  →  all real numbers

Inverse of a function

[tex]f^{-1}(x)[/tex] is the notation for the inverse of the function.  The inverse of a function is a reflection in the line y = x

Finding the inverse of the given function

Swap f(x) for y:

[tex]\implies y=-\dfrac{2}{3}x-24[/tex]

Rearrange the equation to make x the subject:

[tex]\implies -\dfrac{2}{3}x=y+24[/tex]

[tex]\implies -2x=3y+72[/tex]

[tex]\implies x=-\dfrac{3}{2}y-36[/tex]

Swap the x for [tex]f^{-1}(x)[/tex] and the y for x:

[tex]\implies f^{-1}(x)=-\dfrac{3}{2}x-36[/tex]

The inverse function has a slope of -3/2

The domain of the inverse function is the range of the function.

The range of the inverse function is the domain of the function.

Therefore, the domain and the range are unrestricted.

Domain:  (-∞, ∞)  →  all real numbersRange:  (-∞, ∞)  →  all real numbers

The y-intercept of the inverse function is when x = 0:

[tex]\implies f^{-1}(x)\: \textsf{ has a y-intercept of }\:(0,-36)[/tex]

The x-intercept of the inverse function is when y = 0:

[tex]\implies -\dfrac{3}{2}x-36=0[/tex]

[tex]\implies -\dfrac{3}{2}x=36[/tex]

[tex]\implies x=-24[/tex]

[tex]\implies f^{-1}(x)\: \textsf{ has a x-intercept of }\:(-24,0)[/tex]

Conclusion

[tex]f^{-1}(x)\: \textsf{ has a y-intercept of }\:(0,-36)[/tex]

[tex]f^{-1}(x)\: \textsf{ has a range of all real numbers.}[/tex]

Consider The Function.f(x) = -2/3x-24Which Conclusions Can Be Drawn About F^-1(x)? Select Two Options.

Related Questions

Identify the greatest rommon factor:
3x²y - 6xy2

Answers

The answer is : 3xy(x-2y)

Answer:

If you're looking to simplify, the greatest common factor should be 3xy.

5.006 as a fraction in simplest form

Answers

Answer:

5 3/500

Step-by-step explanation:

Answer:

2503/500

Step-by-step explanation:

You have to turn it into a fraction like 5.006/1 then you multiply by 10 until the numerator is a whole number.

1)  5.006/1

2)  50.06/10

3)  500.6/100

4)  5006/1000

5)  Simplify:    2503/500

What is the difference between joint, marginal, and conditional relative frequencies?

Answers

Answer:

The middle cells are the joint frequency numbers. When analyzing data in a two-way frequency table, you will be looking for joint relative frequency, which is the ratio of the frequency in a particular category and the total number of data values. The purple cells on this table are all joint frequency numbers.

The numbers in the column on the very right and on the row on the very bottom are the marginal frequency numbers. When analyzing data in a two-way frequency table, you will be looking for marginal relative frequency, which is the ratio of the sum of the joint relative frequency in a row or column and the total number of data values.

Conditional relative frequency numbers are the ratio of a joint relative frequency and related marginal relative frequency.

Step-by-step explanation:

Eloise scored a total of 268 points during the basketball season. Of her total points, l points came from left-handed shots. She scored 225 points with right-handed shots.
Write an equation to describe this situation.
How many points did Eloise score with left-handed shots?

Answers

Answer:

43

Step-by-step explanation:

268-225=43

Answer:268 = L + 225 and the points of left - handed shots are 43 .

Step-by-step explanation:

15x+3(10−6x)
HELP HELP

Answers

Answer:

-3x+30

Step-by-step explanation:

Answer:

15x+3(10-6x)=15x+30-18x=15x-18x+30=-3x+30

Answer: 15x+3(10-6x)=  -3x-30

Step-by-step explanati+n:

Hi, I need some help with this question about the circumference of a circle. Help would be greatly appreciated :)

Answers

Answer:

C = 18.84 ft

Step-by-step explanation:

C = 2 * pi *r

The radius is 3 ft

C = 2 * 3.14 * 3

C = 18.84

Multiply the equation (-6)(-5).

Answers

Answer:

30

Step-by-step explanation:

Whrn two negative numbers multiplied or divided the result will be positive

(-6)×(-5) = +30

30. Because 6 x 5 is 30 and 2 negatives cross each other out

can a triangle have to acute angles and one obtuse angle

Answers

Answer:

  yes

Step-by-step explanation:

Any obtuse triangle will also have two acute angles.

__

The sum of angles in a triangle is 180°. If one of the angles is 90° or more (a right or obtuse angle), the other two (non-zero) angles must be less than 90°.

An obtuse triangle is one that has an obtuse angle, so both of the remaining angles must be less than 90°, that is, they must be acute angles.

Answer:

Yes

Step-by-step explanation:

Example:

A triangle with angles: 100°, 50°, 30°

Given ΔSTU and ΔDEF, what is m∠U ?

Answers

Answer:

In this context:

[tex]\boxed{m\angle U=40^{\circ}}[/tex]

Explanation:

Hello! Remember you have to write complete questions in order to get good and exact answers. Here you haven't provided any diagram, so I'll assume ΔSTU and ΔDEF are similar. Two triangles are similar if and only if their corresponding angles are congruent and their corresponding sides are in proportion.

So:

[tex]\angle S=\angle D \ldots eq1 \\ \\ \angle T=\angle E \ldots eq2 \\ \\ \angle U=\angle F \ldots eq3[/tex]

We also know:

[tex]\angle S+\angle T+\angle U=180^{\circ} \ldots eq4 \\ \\ \angle D+\angle E+\angle F=180^{\circ} \ldots eq5[/tex]

Suppose we know:

[tex]\angle S=30^{\circ} \\ \\ \angle E=110^{\circ}[/tex]

Then, by eq2:

[tex]\angle T=\angle E =110^{\circ}[/tex]

By substituting ∠S and ∠T into eq4:

[tex]\angle S+\angle T+\angle U=180^{\circ} \\ \\ 30^{\circ}+110^{\circ}+\angle U=180^{\circ} \\ \\ \\ Isolating \ \angle U: \\ \\ \angle U=180^{\circ}-(30^{\circ}+110^{\circ}) \\ \\ \angle U=180^{\circ}-140^{\circ} \\ \\ \angle U=40^{\circ}[/tex]

Finally:

[tex]\boxed{m\angle U=40^{\circ}}[/tex]

Which expression is the result of factoring the expression below by taking out its greatest common
factor?
4x2 + 16x – 4 =?

Answers

If you take out the greatest common factor which is 2 you get 2(2x1+8-2)

Answer:

According to khan academy the answer is 4(x2+4x-1)

Step-by-step explanation:

khan academy

Consider the expression 10 to the 3rd power time 0.006.

What is the exponent in the power of 10?

Answers

10^3 x 0.006

Answer: 3

sarah can fit 115 books in 2 bookcases at that rate how many bookcases does she need to hold 360 books?

Answers

Answer:115books= 2bookcases

360books=xbookcases

115x=2×360

115x=720

x=720/115

x=6.3 ~ 6bookcases

Step-by-step explanation:

Answer:

7 book cases

Step-by-step explanation:

Add 115 to itself until you reach past 360 (there is a remainder). 115 added 3 times is 345. 115 books=2 bookcases. So you multiply: 2×3=6. Since there is not enough room for all 360 books in 6 bookcases, you need 1 more, which makes it 7 bookcases.

a angle measures 72 degrees more than its supplementary what is the measurement of each angle

Answers

One is 54 degrees the other is 126

Answer:

The angles are 126 and 54

Need help with this question.

Answers

Answer:

the answer is g

Step-by-step explanation:

I just divided 15 and 6 by 3 and simplified that down to 5 and 2

Answer:

G

Step-by-step explanation:

They need to be equivalent. To show this you can use ratios or fractions. 15/5=3, 6/2=3

What is the largest perfect square that can be divided out of 64?*

Answers

Answer:

64 is a perfect square, because the square root of 64 is 8. If you mean divided by 64, it would be 16 because 16x4=64.







The table contains the data of two variables, X and Y. Which regression line shows the best fit to the random sample observations of Xi and Yi in the table?

A) A

B) B

C) C

D) D






edit (will give branliest) but it doesnt tell me if its right or not so yep......

Answers

I believe the answer is b!!


- hope this helped!!

The data in the table shows a sinusoidal relationship between the number of seconds an object has been moving and its velocity v(x), measured in centimeters per second. What is true of the cosine function that models the data in the table?

Drag a value into each box to correctly complete the statements. PLEASE HELP!

Answers

Answer:

40

y = 30.85

10.85

Step-by-step explanation:

One complete cycle is between:

x = 4 and x = 44

Period: 44-4 = 40 cm

Range: 41.7 - 20 = 21.7

Amplitude: 21.7/2 = 10.85

Mean line:

y = 20 + 10.85

y = 30.85

The period of the cosine function is 20, its midline equation is y = 32, and its amplitude is [tex]$\boxed{12}$[/tex].

To analyze the given data, we can notice the sinusoidal nature of the relationship between the number of seconds an object has been moving (x) and its velocity (v(x)$. This indicates that a cosine function can model the data.

Now, let's find the period, midline, and amplitude of the cosine function that models this data.

The period of a cosine function is the distance it takes for the function to complete one full cycle. Looking at the data, we can see that the interval between consecutive peaks or troughs (e.g., between 4 and 24, or 24 and 44) is 20 seconds.

Hence, the period of the cosine function is 20.

The midline of a cosine function is the horizontal line that divides the maximum and minimum values of the function. In this case, since the data oscillates around a central value, it suggests that the midline is not at y = 0.

Instead, it's the average of the maximum and minimum values of the data. The maximum value is 44 and the minimum value is 20, so the midline would be the average of these, which is (44 + 20)/2 = 32.

The amplitude of a cosine function is half the difference between the maximum and minimum values.

In this case, the maximum value is 44 and the minimum value is 20, so the amplitude is (44 - 20)/2 = 12.

So, completing the statements:

- The period of the cosine function is 20.

- The equation of the midline of the cosine function is y = 32.

- The amplitude of the cosine function is [tex]$\boxed{12}$[/tex].

PLEASE HELP WITH MY KHAN HOMEWORK BECAUSE IT’S DUE MONDAY!

Answers

Answer:

7/12 + 2/3q

Step-by-step explanation:

combining like terms

11/12 - 1/3 =

7/12

-1/6q + 5/6q = 4/6q which is also 2/3q

On a coordinate plane, a line goes through (negative 2, negative 4) and (2, 2). A point is at (negative 3, 1).
What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1)?

y – 1=Negative three-halves(x + 3)
y – 1=Negative two-thirds(x + 3)
y – 1= Two-thirds(x + 3)
y – 1= Three-halves(x + 3)

Answers

Answer:

y – 1= Three-halves(x + 3)

Step-by-step explanation:

line goes through  (-2, -4) and (2, 2)

goes through (-3, 1)

slope =  (-4 - 2) / (-2 -2)  = -6/-4 = 3/2

1 =  (3/2)*-3 + b

1 = -9/2 + b

b = 1 + 9/2 = 11/2 = 5.5

y = (3/2)*x + 11/2

(y - 1) = (3/2)(x + 3)

The line goes through  (-2, -4) and (2, 2)

goes through (-3, 1)

If slope = (-4 - 2) / (-2 -2)  = -6/-4 = 3/

1 =  (3/2)*-3 + b

1 = -9/2 + b

b = 1 + 9/2 = 11/2 = 5.5

y = (3/2)*x + 11/2

(y - 1) = (3/2)(x + 3)

So the correct answer is option d. y – 1= Three-halves(x + 3).

What are coordinates planes?

A coordinate plane is a graphing and description system for points and lines. A vertical (y) axis and a horizontal (x) axis make up the coordinate plane. There are four quadrants in the coordinate plane. The point where these lines connect is called the origin (0, 0).

What are the 4 coordinate planes?

Quadrant I: positive x and positive y.Quadrant II: negative x and positive y.Quadrant III: negative x and negative y.Quadrant IV: positive x and negative y.

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awner both and get brainliest

Answers

Answer:

For the first one the answer is 2

For the second one the answer is 72

Step-by-step explanation:

Answer:

The first one is 2.

The second one is 72.

Step-by-step explanation:

First you find the slope of the chart. The formula for finding the slope on a chart is y2-y1 divided by x2-x1. Then you find the y-intercept. The formula for finding the y-intercept is y=mx+b!

What is the area of the base in the figure below?
O 9 square units
O 97 square units
O 72 square units
O 72square units​

Answers

And answer is 72 square units

the price of a price of machinery is 27,000 the table shows the value of the machinery during the first three years after it was purchased based on the table which equation can be used to determine v the value in thousands of dollars of the machinery t years after it was purchased

Answers

Answer:

B  v=27(0.8)

Step-by-step explanation:

if you multipy 27,000 by 0.8 you get 21,600 if you do it again you get 17,280 and so on

Answer:

The answer is B

Step-by-step explanation:

I or the question right , just trust me

What is the length of the paintbrush in centimeters?
A.0.101 cm
B.10,100 cm
C.1,010 cm
D.10.1 cm

Answers

Answer:

D

Step-by-step explanation:

The length of the paintbrush in centimeters is D. 10.1 cm.

What is Unit Conversion?

Unit conversion is defined as expressing the same quantity by different measurement units.

For example, a distance of 20 meter can be also expressed as 2000 cm. The distance is same.

Given that,

Length of the paintbrush in millimeters = 101 millimeters

We have to find the length of the same paintbrush in centimeters.

We have the unit conversion,

1 centimeter = 10 millimeters

So,

1 millimeter = 1/10 = 0.1 centimeters

So, we have to multiply the measurement in millimeter with 0.1.

101 millimeters = 101 × 0.1 = 10.1 centimeters

Hence the length is 10.1 centimeters

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What is the length of the paintbrush in centimeters?

A paintbrush is one hundred one millimeters long.

A. 0.101 cm

B. 10,100 cm

C. 1,010 cm

D. 10.1 cm

Can someone find the area

Answers

Lets split this into two parts; a semi circle and triangle. We can solve fro the area of both individually first.

Area of the Semi Circle:

Formula: A = (πr²)/2

The radius is the diameter divided by two (16 / 2 = 8)

A = (π*8²)/2

A = (π64)/2

A = 200.96/2

A = 100.48 meters

The area of the semi circle is 100.48 meters

Area of the Triangle:

Formula: A = bh/2

A = 16*12/2

A = 192/2

A = 96 meters

The area of the triangle is 96 meters.

To find the total area of the shape, we can add.

100.48 + 96 = 196.48 meters.

Best of Luck!

Trey is putting up fence around a 750 foot by 540 foot lot. How many feet of fence does he need?

Answers

Answer:

2580 feet

Step-by-step explanation:

The question is essentially asking for the perimeter.

Considering the lot is  a parallelogram at the least, it would be (750+540)*2, or 1290*2, or 2580

Write an equation that models this situation. A copier that makes 34 copies per minute runs for 12 minutes. How many copies (x) are made during that time?

Answers

Answer:

x = 34t

408

Step-by-step explanation:

x = 34t

x: no. of copies

t: minutes

x = 34(12)

x = 408

Answer:

x

34

= 12

x = total number of copies

total number of copies

copies per minute

= number of minutes copier runs

B )  x / 34 = 12  is correct

6 if x < −5
f(x) = −x + 1 if |x| ≤ 5
−7 if x > 5

Answers

Use desmos:

This is the piece wise graph

Why must Kyle's and Tynessa's pattern rules be the same, even though their algebraic expressions look different?

Kyles algebraic expression based on his coloring
f(n)=2+2(n+1)

Tynessa's algebraic expression based on his coloring
4+2n

Not question a) tho

Answers

Answer:

they equally colored in the same amount of squares although the colores were different meaning their expressions were the same although they looked different, both kyle and Tynessa got the same expression but they were written in a different way

Step-by-step explanation:

Find x. Round the answer to the nearest tenth. A. 1.7 B. 1.9 C. 2.1 D. 2.2

Answers

A would be 2 solid B would also be 2 and so will the other ones so they all will be 2

Answer:

B: 1.9

Step-by-step explanation:

Simplify the expression:
(2x2 + 3x - 7) + (5x2 - x +9)

Answers

Answer:

[tex]7x^2 + 2x + 2[/tex]

Step-by-step explanation:

Step 1:  Combine

[tex]2x^2 + 3x - 7 + 5x^2 - x + 9[/tex]

[tex](2x^2 + 5x^2) + (3x - x) + (-7 + 9)[/tex]

[tex]7x^2 + 2x + 2[/tex]

Answer:  [tex]7x^2 + 2x + 2[/tex]

7x^2+2x+2 is the best answer
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