Using Equations to Compare Linear Functions
Consider the function and its inverse:
f(x) =
) = x -2
-(x) = (x + 2)
The slope, a, of the inverse function is
and the x-intercept of the inverse function is at x =
Intro

Using Equations To Compare Linear FunctionsConsider The Function And Its Inverse:f(x) =) = X -2-(x) =

Answers

Answer 1

Answer:

[tex]a=3[/tex] and the x-intercept of the inverse function is [tex]x=-2[/tex]

Step-by-step explanation:

Given:

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

[tex]f^{-1}(x)=a(x+2)[/tex]

To find: slope, a, of the inverse function and the x-intercept of the inverse function

Solution:

Let [tex]y=f(x)=\frac{x}{3}-2[/tex]

[tex]y=\frac{x}{3} -2\\\frac{x}{3}=y+2\\x=3(y+2)\\[/tex]

So, [tex]f^{-1}(x)=3(x+2)[/tex]

On comparing [tex]f^{-1}(x)=a(x+2)[/tex] with [tex]f^{-1}(x)=3(x+2)[/tex], [tex]a=3[/tex]

To find the x-intercept of the inverse function, put [tex]f^{-1}(x)=0\Rightarrow 3(x+2)=0\Rightarrow x=-2[/tex]

Answer 2

The slope, a, of the inverse function is  3 , and the x-intercept of the inverse function is at x =  -2 .


Related Questions

I need help quick lot of points easy question marked brainliest the best.
How do you find out a histograms least frequency interval

Answers

Answer:

Histograms are graphs of a distribution of data designed to show centering, dispersion (spread), and shape (relative frequency) of the data. Histograms can provide a visual display of large amounts of data that are difficult to understand in a tabular, or spreadsheet form.

They are used to understand how the output of a process relates to customer expectations (targets and specifications), and help answer the question: "Is the process capable of meeting customer requirements?"

To construct a histogram, the first step is to "bin" (or "bucket") the range of values—that is, divide the entire range of values into a series of intervals—and then count how many values fall into each interval. The bins are usually specified as consecutive, non-overlapping intervals of a variable.

Hope this Helps, good luck on our assignment!

Answer:

Hey! I think this video will help you!

Step-by-step explanation:

It won't let me send the video for some reason so I'll try and spell it out. Hint: there are no actual spaces so look this up without the spaces.

h t t p s : / / w w w . y o u t u b e . c o m / w a t c h ? v = v h c i k R s r d J o

What is the slope of a line perpendicular to y = –5x + 6? answers: A) –1∕5 B) 5 C) 1∕5 D) –5

Answers

Answer:

C) 1/5

Step-by-step explanation

When one line has a slope of m, a perpendicular line has a slope of  −1/m

subtract (-3y2 − 8) − (-5y2 + 1)

Answers

Answer:

2 y^2 - 9

Step-by-step explanation:

(-3y^2 − 8) − (-5y^2 + 1)

Distribute the negative sign

(-3y^2 − 8) + 5y^2 - 1

Combine like terms

-3y^2 + 5y^2 - 1 − 8

2 y^2 - 9

Answer:

The answer to (-3y² - 8) - (-5y² + 1) is 2y² - 9

Step-by-step explanation:

[tex](-3y^2-8)-(-5y^2+1)[/tex]

Since there is a minus sign in front of the second parentheses, then the terms within that parentheses will be changed to their opposite signs.

[tex]-3y^2-8+5y^2-1[/tex]

Combine like terms.

[tex]2y^2-9[/tex]

What is the radius of a circle with a circumference of 23.55 feet

Answers

Answer:

Thanks for question. I am working my way up to more brainliest and Master Answerer. Every question/point helps

The equation for circumference is x = pi*2*r

First divide by 2 then divide by pi to get r. Use algebra to get this explanation. so 23/2/pi = 3.66. Thats the radius.

four men working together can create a trench in 42 days. they begin the job but one man works only half days. How long will it take to complete the trench?

Answers

Answer:

48 days

Step-by-step explanation:

Four men working together can create a trench in 42 days.

Find the number of man-days to complete the job

4*42 = 168 man-days

They begin, but one man works only half-days.

How long will it take to complete the job?

Let d = no. days to complete the trench

d(3 + 0.5) = 168

d(3.5)=168

3.5d = 168

d = 168/3.5

d = 48 days

Please help with this

Answers

Answer:

D) reflection across the origin

Step-by-step explanation:

The answer is D. Reflection across the origin.
Point A is at (3, 1). Point A’ is at (-3, -1). The formula for reflection across the origin is (-x, -y). In the problem, the x and y coordinates changed from positive to negative. I hope this helps :)

Jordan invested $8,500 in an account paying an interest rate of 4.1% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $13,070?

Answers

Answer:

52 days

Step-by-step explanation:

if compounding daily we can see what 1 year accumulates using the function

360 / interest rate = 360/4.1 = 87.8048780488 = 87.80 per day

We can use inverse of the balance profit to use the exact amount difference to then divide into the date of withdrawal

$13070- 8500 = 4570

4570/ 87.8048780488 = 52.04 = 52 days.

please, someone, answer this asap; mean median mode and range:
1)Use the data to calculate the mean. 24, 31, 12, 38, 12, 15 *
22
12
26

2) Use the data to calculate the median. 24, 31, 12, 38, 12, 15 *
19
19.5
20

3) Use the data to calculate the range. 24, 31, 12, 38, 12, 15 *
24
38
26

4) Use the data to calculate the mode. 24, 31, 12, 38, 12, 15 *
12
24
38

5) the mode represents the number that appears the least *
True
False

6) To calculate the range we use the highest and lowest number ? *
True
False

7) Average is another word for *
mode
range
mean
median

8) the range indicates the middle number ? *
True
False

9) which statement best describes the mean. *
add all the numbers and divide by the total number of numbers
highest minus lowest
number that appears the most

10) A data set with two modes is known as *
no modes
bimodal
multimodal



Answers

Answer:

1) 22

2) 19.5

3) 26

4) 12

5) False

6) True

7) Mean

8) False

9) Add all the numbers and divide by the total number of numbers

10) Bimodal

Step-by-step explanation:

1)Use the data to calculate the mean. 24, 31, 12, 38, 12, 15 *

To calculate mean you add all the numbers up and divide by the total number of numbers.

[tex]\frac{24 + 31+12+38+12+15}{6} = 22[/tex]

2) Use the data to calculate the median. 24, 31, 12, 38, 12, 15 *

For median, arrange the numbers from lowest to largest

12, 12, 15, 24, 31, 38

use (n+1) / 2 to figure out which value is the median

(6+1) / 2 = 3.5 (median is in between the 3rd and 4th value)

(15+24) / 2 = 19.5

3) Use the data to calculate the range. 24, 31, 12, 38, 12, 15 *

Range is max value - min value

38 is max and 12 is min

38 - 12 = 26

4) Use the data to calculate the mode. 24, 31, 12, 38, 12, 15 *

Mode is the value that appears most frequently

In this case 12 appears 2 times, therefore it is the mode

5) the mode represents the number that appears the least *

False, mode is the number that appears the most

6) To calculate the range we use the highest and lowest number ? *

True

7) Average is another word for *

mean

8) the range indicates the middle number ? *

False, range is the max value - min value

9) which statement best describes the mean. *

add all the numbers and divide by the total number of numbers

10) A data set with two modes is known as *

bimodal

___________________________________

hey!!

Given data=24,31,12,38,12,15

summation fX=132

N(total no.of items)=6

Now,

Mean=summation FX/N

=132/6

=22

2. Arranging the data in ascending order

= 12,12,15,24,31,38

N=6

Median=(N+1/2)th item

= (6+1/2) th item

=(7/2)th item

=3.5 th item

Again,

median=3 rd item + 4th item/2

=15+24/2

= 39/2

=19.5

3.Range= highest score- lowest score

=38- 12

=26

4. Mode= 12 because it has more frequency.

______________________________________

Answers:2219.5 26 12FalseTrueMeanFalseadd the numbers and divide by the total number of numbers bimodalHope it helps...

Good luck on your assignment

________________________________

470 centimeters = _____ meters

Answers

Answer:

4.7 meters

Step-by-step explanation:

Hope this helps!  : )

Answer:

4.7 meter

Step-by-step explanation:

Pleeaassee heeellllllppppp

Answers

Answer:

Nn

Step-by-step explanation:

The answer would be Nn

Find the surface area and volume of a cube with sides that are 6 inches.

Answers

Answer:

Step-by-step explanation:

Surface Area S=6s²

S=6(36)

S=216 in²

Volume V=s³

V=6³

V=216 in³

8.) Mrs. Ruiz bought six 2-liter bottles of juice. How many dekaliters of juice
did she buy?
a.) 0,012 dekaliter
b.) 0.12 dekaliter
c.) 1,2 dekaliters
d.) 120 dekaliters​

Answers

(B) because 1 litter is equal to .1 dekaliter

A taxi driver charges a flat rate of $3.50 plus an additional $1.65 per mile. If Mohammad wants to spend, at most, $60, how far can he travel in the taxi cab? Round your answer to the nearest mile.

Answers

Answer:

11.6 should be your answer!

Step-by-step explanation:

Im so sorry if its wrong!

Hope this helps!!

( > .< )

Answer:

34 miles

Step-by-step explanation:

3.50 + 1.65m <60

1.65m< 60-3.50

1.65m<56.5

1.65m/1.65< 56.5/1.65

m<34.24242424

m<34

How do I solve this equation:
-5(n-1)=7(n+3)

Answers

-5(n-1) = 7(n+3)

First, distribute the 5 in the first parentheses.

-5n+ 5 = 7(n+3)

Next, distribute the 7 in the second set of parentheses.

-5n + 5 = 7n + 21

Subtract 7n from both sides.

-5n + 5 -7n = 21

Subtract 5 from both sides.

-5n - 7n = 21 + 5

Collect like terms.

-12n = 16

Divide both sides by -12

Answer -3/4

Answer:

-3/4

Step-by-step explanation:

The First step is to distribute the 7 in the second part of parentheses.

-5+5-7n=21

-5-7n=21+5

Then collect the terms

-12n=16

Lastly distribute both sides by -12

And the answer is -3/4

What option is the same as 1/5^-3? A. -1/125 B. -1/15 C. 15 D. 125

Answers

Answer:

D. 125

Step-by-step explanation:

Given

[tex](\frac{1}{5})^{-3}[/tex]

Required

Find Equivalent

From law of indices

[tex](\frac{1}{a})^{-x} = \frac{1}{(\frac{1}{a})^{x}}[/tex]

So,

[tex](\frac{1}{5})^{-3} = \frac{1}{(\frac{1}{5})^{3}}[/tex]

Expand denominator

[tex](\frac{1}{5})^{-3} = \frac{1}{(\frac{1}{5})*(\frac{1}{5})*(\frac{1}{5})}}[/tex]

[tex](\frac{1}{5})^{-3} = \frac{1}{(\frac{1}{125})}}[/tex]

Split expression on the right and side

[tex](\frac{1}{5})^{-3} = 1/{(\frac{1}{125})}}[/tex]

Convert divide (/) to multiplication (*)

[tex](\frac{1}{5})^{-3} = 1*{(\frac{125}{1})}}[/tex]

[tex](\frac{1}{5})^{-3} = 1*125[/tex]

[tex](\frac{1}{5})^{-3} = 125[/tex]

Hence, [tex](\frac{1}{5})^{-3}[/tex] is equivalent to 125

solve for v: 3/5 v= 1/5

Answers

Answer:

Step-by-step explanation:

solve for v:  simplifying both sides of the equation, then the variable.

Exact Form:

v= 1/3

Decimal Form:

v=0.3

A jar of marbles has 23 red marbles, 12 white marbles, 18 yellow marbles and 28 black marbles. What are the chances of the following:
1) Picking a black marble?
2) Picking a purple marble?
3) Picking a red or white marble?
4) Picking a marble whose color has 5 letters in it?

Answers

Answer:

1.) Chances of picking a black marble: 28/81 or 34.6%

2). 0/81 chances of picking a purple marble or 0%

3.) Chances of picking a red or white marble: 35/81 or 43.2%

4.) Chances of picking a marble whose color has 5 letter in it: 40/81 or 49.4%

25 pints= gallons? pints?

Answers

Answer:

3.125 gallons

Step-by-step explanation:

25 pints could be converted to about roughly 3.125 gallons.

Given that 6 > –2, which statements are true? Check all that apply.
(2)(6) > (–2)(2)
StartFraction 6 over 2 EndFraction less-than StartFraction negative 2 over 2 EndFraction
(–2)(6) > (–2)(–2)
StartFraction 6 over negative 2 EndFraction less-than StartFraction negative 2 over negative 2 EndFraction
(2)(6) < (–2)(2)
StartFraction 6 over 2 EndFraction less-than StartFraction negative 2 over 2 EndFraction

Answers

Answer:

1,4,6,  are the answers

Step-by-step explanation:

Answer:

the first, the fourth and the sixth

Step-by-step explanation:

i just did it

Which exponential function has a growth factor of One-half?

f(x) = 2(0.5x)
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It goes through (negative 1, 2) and crosses the y-axis at (0, 0.5).
f(x) = 0.5(2x)
A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries one-eighth, one-fourth, one-half, 1, 2.

Answers

Answer:

C     f(x) = 0.5(2x)

Step-by-step explanation: I got a 96 on the the test so you can trust, unlessssss this is the one question I got wrong!!! .... It's not though so don't worry.

f(x) = 2(0.5)ˣ is the exponential function which has a growth factor of One-half.

What is a function?

A relation is a function if it has only One y-value for each x-value.

An exponential function with a growth factor of 1/2 would have 1.5^x as part of it

y=a(1+0.5)ˣ is the general term of the exponential function.

In the given functions

f(x) = 2(0.5)ˣ On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0.

It goes through (negative 1, 2) and crosses the y-axis at (0, 0.5).

Hence, f(x) = 2(0.5)ˣ is the exponential function which has a growth factor of One-half.

To learn more on Functions click:

https://brainly.com/question/21145944

#SPJ6

Identify the graph of xy=-8 for theta=pi/4 and write and equation of the translated or rotated graph in general form.

Answers

Answer:THE ANSWER IS A

Step-by-step explanation:

CORRECT ON EDGE

Answer:

A

Step-by-step explanation:

edge

Help me please show your work please

Answers

Answer:

27

Step-by-step explanation:

(9)to the 2 power is 81

81/3=27

Answer:  27

(n)^2/3      if n=9

Step-by-step explanation:

first, you do 9*9=81

secound, you put 81/3

third, then you divide 81/3=27

the answer is 27

Find the function that represents the relationship in the table

a)

y = 14x + 14


b)

y = 8x + 14


c)

y = 8x


d)

y = 14x + 8

Answers

Answer:

option B

Step-by-step explanation:

when the x value is multiplied by 8 and the result is added to 14 you will get the corresponding y value

What is the value of X?

Answers

Answer:

45

Step-by-step explanation:

The two angles with measures are a linear pair and supplementary, so their measures add to 180 deg.

3x + x = 180

4x = 180

x = 45

____________________________________

Solution,

+3x°=180°( sum of angle in straight line)

or,4x°=180°

or,X=180/4

X=45

The right answer is 45

hope it helps

Good luck on your assignment

___________________________________

Find two numbers that differ by 8 and whose square roots differ by 1. Those two numbers are ___ and ____

Answers

Answer: 12.25 and 20.25

Step-by-step explanation:

20.25 - 12.25 = 8

Square root of 20.25 is 4.5

Square root of 12.25 is 3.5

4.5 - 3.5 = 1

Hope this helped

how many integers between 17 and 2678 are multiples of 11

Answers

Answer:

242 integers

Step-by-step explanation:

We have to find the number of integers between 17 and 2678 which are the multiple of 11.

Divide 17 by 11 = [tex]\frac{17}{11}=1.55[/tex]

Smallest multiple of 11 which is greater than 11 = 2nd multiple = 22

Divide the largest number 2678 by 11 = [tex]\frac{2678}{11}=243.45[/tex]

Largest multiple of 11 which is less than 2678 = 443rd multiple

                                                                            = 243 × 11

                                                                            = 2673

Therefore, number of integers between 17 and 2678 multiple of 11

= 243 - 2 + 1

= 242 integers

Help pleasseee •-•
1. The dot plot below shows the vertical jump of some NBA players. A vertical jump
is how high a player can jump from a standstill. Draw a box plot of the heights for the
vertical jumps of the NBA players above the dot plot.

Answers

The picture below shows the box plot.

One angle is
angle is 65 degrees, the other is
90 degrees, what is my missing angle?
What is my first and last name?

Answers

Answer:

your missing angle is

90+65 = 155

180-155 = 25

so your missing angle is 25 degrees

Maya is building a wooden box with a rectangular base that is 20 in and by 14 in tall. If she wants an open box without a top how much wood will Maya use?

Answers

Area of one face = 280 inches squared
Area of 5 faces = 280 x 5

= 1400 inches squared worth of wood

Janice is traveling to Canada and will change $250 US dollars into Canadian dollars. At the current exchange rate, $1 US dollars is equal to $1.28 Canadian dollars. How many Canadian dollars will she get for her trip?

Answers

Answer:

She will get $320 in Canada

Step-by-step explanation:

multiply $350*1.28 witch is the Canadian dollar currency

that gets you $320

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