Find the inverse. Check your answer algebraically and graphically.
f(x) = 4x/x − 9, x ≠ 9
f^-1(x)=
Answers
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
[tex]\stackrel{f(x)}{y}~~ = ~~\cfrac{4x}{x-9}\implies \stackrel{\textit{quick switcheroo}}{x~~ = ~~\cfrac{4y}{y-9}}\implies xy-9x=4y\implies -9x=4y-xy \\\\\\ -9x=y(4-x)\implies \cfrac{-9x}{4-x}=y\implies \cfrac{9x}{x-4}=\stackrel{f^{-1}(x)}{y}[/tex]
how to test algebraically? well, for any (a,b) pair in f(x), its inverse will have another pair but (b,a), hmmm let's plug hmmm say
f(10) = 40, and f⁻¹(40) = 10.
we could plug more values in each, same pair will come up.
as far as testing them graphically, Check the picture below.
Related Questions
HELP PLEASE math isn’t really my thing at it’s due an hour
Answers
Carly jogged 1/2 mile in 1/10 of an hour. At this rate, how long does she jog in one mile?
Answers
Answer:
2/10 of an hour for 1 mile
Step-by-step explanation:
1/2 for 1/10 since its half all you have to do is multiply by 2 then you got 2/2 and 2/10
Hope this helped!
Steve is paid overtime for all time worked past 40 hours in a week. His regular-time pay rate is $12 an hour, and his overtime pay rate is $18 an hour. Last week Steve worked 47.3 hours. 1. How many regular-time hours did Steve work? 2. How many overtime hours did he work last week? 3. What was Steve's regular-time pay last week? 4. What was Steve's gross or total pay last week?
Answers
Answer:1. 40 hours 2).7.3 hours, 3).$480 4).$611.4
Step-by-step explanation:
STEP 1
stating all requirements
regular hour = 40 hours at $12 an hour
overtime = beyond 40 hours at $18 an hour
Step 2--- Solving out
1. Steve worked 40 regular time hours
2. Over time hours =Total 47.3 hours - 40 regular time hours = 7.3 hours
3. Regular time pay = Regular tmes hours x regular time pay rate
= 40 x $12 =$480
4) Steve gross pay = Regular time pay + overtime pay
= $480 + ( 7.3 hours x $18)
=$480+$131.4
=$611.4
What is 1 3/4 divided by 3?
Answers
Answer:
7/12 is the answer
find the greastest common factor of 10,30,and 45.
Answers
10/5 = 2
30/5 = 6
45/5 = 9
===================================================
Explanation:
Find the prime factorization of each value. A factor tree may help.
10 = 2*5
30 = 2*3*5
45 = 3*3*5
We see that '5' is found in each of the factorizations. This is the only factor that shows up in all three values, and it only shows up one time. So that's why 5 is the GCF.
An engineer is designing a runway for an airport. Several planes will use the runway and the engineer must design it so that it is long enough for the largest planes to become airborne before the runway ends. If the largest place accelerates at 3.30 m/s^2 and has a takeoff speed of 88.0 m/s then what is the minimum allowed length for the runway?
Answers
Answer:
d=117.33 m
Step-by-step explanation:
Initial velocity of planes, u = 0 (because they are at rest)
Acceleration, a = 3.3 m/s²
Final take off speed, v = 88 m/s
We need to find the minimum allowed length for the runway. Let it is d. d will be the distance. It can be calculated using third equation of motion as follows :
[tex]v^2-u^2=2ad\\\\d=\dfrac{v^2-u^2}{2a}[/tex]
Putting all the values, we get :
[tex]d=\dfrac{88^2-0^2}{2\times 33}\\\\d=117.34\ m[/tex]
Hence, the minimum allowed length for the runway is 117.33 m.
How many times greater
is 1.837 X 10^9 than
3.6x10^5
Answers
Answer:
1.837 X 10^9 is 5103 times greater than 3.6x10^5
Step-by-step explanation:
1.837 X 10^9 =
Calculate the value
Solution
1,837,000,000
3.6x10^5
Evaluate the power
3.6 x 100,000
Multiply the numbers
360,000
Solution
360,000
Divide
1,837,000,000 / 360,000
Solution
5102.77778
Round
5103
1,837,000,000 > 360,000
Which point results when the point (−100, −100) is rotated 180° around the point (100, 100)? A) (200, 200) B) (300, 300) C) (−200, −200) D) (−300, −300) E) None of these.
Answers
Answer:
answer: A
Step-by-step explanation:
-100 -100, rotated by 180 would be the opposite, 100 100
Answer:
A
Step-by-step explanation:
Which relation is a function?
Answers
Answer:
b
Step-by-step explanation:
complete the multiplication problem to find the answer 36.1 times 1.1
Answers
Answer:
39.71
Step-by-step explanation
1 x 36.1 = 36.1, 3.61 + 36.1 = 39.71.
36.1 times 1.1 = 39.71
hope this helps!! <3
A taxi ride cost a flat fee of of $5.00 plus an additional $1.75 per mile. How many miles would a person
travel if they paid $15.50?
Answers
Answer:
6 miles
Step-by-step explanation:
15.50-5 is 10.50 and 10.50/1.75 is 6
hope this helped also could i get brainliest?
Give an example of a balance that has a greater integer value than a balance of -$12, but represents a debt of less than $5.
Answers
Answer:
An example of a balance that has a greater integer value than a balance of -$12, but represents a debt of less than $5 is any integer belongs to [-6,-11]
Step-by-step explanation:
Let x be the balance that has a greater integer value than a balance of -$12, but represents a debt of less than $5.
We are given that a balance that has a greater integer value than a balance of -$12
So, x>-12
We are given that balance represents a debt of less than $5.
Debt = -5
So, x< -5
So, -5>x>-12
So, x∈[-6,-11]
Hence an example of a balance that has a greater integer value than a balance of -$12, but represents a debt of less than $5 is any integer belongs to [-6,-11]
The solution to 9(x + 2) = 5 - 2(x - 1) is
Answers
Answer:
x = -1
Step-by-step explanation:
9(x + 2) = 5 - 2(x - 1)
9x + 18 = 5 -2x + 2
9x + 18 = -2x + 7
Add 2x and 9x. Subtract 18 from 7.
11x = -11
x = -1
Please mark me the brainliest!?!
What is the range of the given function?
{(-2, 0), 6-4, -3), (2, -9), (0, 5), (-5, 7)}
Answers
The table shows what time the sunrise and
sunset occurred on dates in October. Based
on the data, what is the total number of
minutes of daylight recorded across these
dates?
Answers
Answer:
There are 2,802 minutes of daylight recorded across these dates.
Step-by-step explanation:
Elapsed Time
Elapsed time is the amount of time that passes from the start of an event to its finish.
We have to recall 1 hour has 60 minutes. Another useful fact is that from a specific time AM to the same time PM there are 12 hours or 720 minutes.
Let's find the minutes of daylight recorded day by day.
Oct, 4th:
From 7:26 am to 7:26 pm there are 720 minutes. Since the sunset time is 13 minutes less, the minutes of daylight are 720 - 13 = 707 minutes.
Oct, 6th:
From 7:27 am to 7:27 pm there are 720 minutes. Since the sunset time is 18 minutes less, the minutes of daylight are 720 - 18 = 702 minutes.
Oct, 8th:
From 7:28 am to 7:28 pm there are 720 minutes. Since the sunset time is 21 minutes less, the minutes of daylight are 720 - 21 = 699 minutes.
Oct, 10th:
From 7:30 am to 7:30 pm there are 720 minutes. Since the sunset time is 26 minutes less, the minutes of daylight are 720 - 26 = 694 minutes.
The total minutes of daylight is 707 + 702 + 699 + 694 = 2,802 minutes
There are 2,802 minutes of daylight recorded across these dates.
Write a sequence with five terms with a third term is six
Answers
Answer:
2, 4, 6, 8, 10
Step-by-step explanation:
This is a sequence that answers the question. Hope it helped
; the boy to girl ratio is 10 to 8. If there are 16 girls in the class, how many boys are there?
Answers
Answer:
There are 20 boys
Step-by-step explanation:
A summer camp wants to buy some new boats. It costs $381 to buy a new canoe and $354 to buy a new rowboat. How much more does it cost to buy a canoe than a rowboat?
Answers
Answer:
28$ more
Step-by-step explanation:
To answer this you'll need to subtract $354 out of $381.
You should get 27 (or $27).
That means that the canoe costs $27 more then the rowboat.
________________________________________________
Sorry if this is unhelpful.
Which equation could be represented by the number line?
A. -5 + 6 = 1
B. -6 + 5 = -1
O c. 1 +(-7) = -6
D. 1 + (-6) = -5
Help!!!
Answers
Answer:
I think it’s C
Step-by-step explanation:
Ming works at a travel agency. Her base monthly salary is $1,750 plus 8% commission on her total sales for the year. Last year Ming sold $478,500 of travel. How much did ming earn, including commission, last year?
Answers
Answer:
59,280
Step-by-step explanation:
$1750x12months=$21,000 base sal.
478,500x.08=38,280 commiss.
21,000+38,280=59280
The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.
Ming earn, including commission, last year exists 59280.
What is meant by mathematical operation?Calculating a value using operands and a math operator is referred to as performing a mathematical "operation." The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers. In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.
Calculations in mathematics are done using arithmetic operators. A property or variable can be given a value using assignment operators. Text, dates, systems, times, and numeric assignment operators are all possible.
Given: Her annual sales commission is 8% of her base monthly salary, which is $1,750. Ming made $478,500 in travel sales last year.
From the given information, we get
$21,000 base salary = $1750 × 12 months.
478,500 × 0.08 = 38,280 commissions.
simplifying the above equation, we get
21,000 + 38,280 = 59280
Therefore, Ming earn, including commission, last year exists 59280.
To learn more about commission refer to:
brainly.com/question/957886
#SPJ2
3.
Ms. Bringas went to staples to buy hand sanitizer. They were $1 each. She
purchased 24 bottles. She got a teacher discount of 10% what was her final price?
Original Cost:
Discount:
New Price:
Answers
discount: 2.4
og cost: 24$
Please help I’ll mark brainliest
Answers
y-intercept is -3
Slope is -1
The equation is y= -1x - 3
Please help me out with this..
Answers
Answer:
y=-3x+3
Step-by-step explanation:
The equation you want to use is y=mx+b. First you want to find m, the slope, but since the slope of 3 is given in all of the answers, you just want to determine if the line is negative or positive. This line is going negative because it approaches the x axis, and crosses it in the negative direction. Now we know the slope is -3x all that's left to do is to find the y intercept represented in the equation y=mx+b as +b. The point where the line crosses the y axis is positive 3, so the final equation is y=-3x+3.
Pleaseee helpppppp
————————————————-
Answers
Answer:
i'm pretty sure s the second one. that answer just makes the most sense to me
Step-by-step explanation:
Which of the following happens when 21.63 is multiplied by 10^3?
A. The digit in the tens place moves to the hundredths place.
B. The digit in the tens place moves to the thousandths place.
C. The digit in the hundredths place moves to the tens place.
D. The digit in the hundredths place moves to the hundreds place
Answers
Answer: C. The digit in the hundredths place moves to the tens place.
Step-by-step explanation:
In 21.63,
place value of 2 = tens
Place value of 1 = ones
Place value of 6 = tenths
Place value of 3 = hundredths
21.63 × 10^3 = 21.63 × 1000 = 21630
From here , we can see that the digit in the hundredths place which is 3 has moved to the tens place.
Therefore, C is the answer.
factor: a^2+b^2–c^2+2ab
Answers
Rearrange the polynomial:
a^2–2ab+b^2 - c^2
((a-b)(a-b))-c^2
(a-b)^2-c^2
Set x =a-b and y=c. The formula becomes
x^2-y^2
factoring this polynomial, we get
(x+y)(x-y)
Substituting back, we get:
(a+b+c)(a+b-c)
Let’s multiply it out to check:
A^2 -ab ac
- ab B^2 -bc
-ac bc -c^2
Answer:
(a + b + c)(a + b - c)Step-by-step explanation:
Use of formula:
(a+b)^2 = a^2 + 2ab + b^2a^2 - b^2 = (a + b)(a - b)Factoring the expression
a^2 + b^2 – c^2 + 2ab =(a^2 + 2ab + b^2) - c^2 = (a + b)^2 - c^2 =(a + b + c)(a + b - c)F(x) = x^2 and g(x) = 2x-3 What is the value of g(4) + f(-3)?
Answers
Answer: 66
Step-by-step explanation:see attachment.
If this helps you please rate brainest
What type of graph is best to use to compare two sets of data over time?
Answers
Answer:
Line graphs.
Step-by-step explanation:
If you have two sets of data, the easiest graph to use would be a line graph. You can insert information and tell which line represents each category. Line graphs are also specifically used to compare data that changes over time.
I hope this helped you out!! Have a nice day :3
Answer:
line graphs
Step-by-step explanation:
i got 100
x³+y³+z³
if you can answer this ill give you Brainliest
Answers
Answer:
This expression reminds me a lot of Fermat's last theorem x^n+y^n=z^n where n is three(odd). Which is one of many famous diophantine equations such as the well known pythagorean theorem a^2+b^2 = c^2. Where one of the variables should be even, and all are coprime. The parity is odd since it has a remainder and is not evenly divisible. It has been proven that Fermat's last theorem does not have any real solutions because you would need a complex number to cancel out the cubes. You will also see that x^n+y^n=z^n does not have any solutions if n>=3. This cannot be factored either since the numbers are rational.
what the answer and how you got it
-2x/7=3x-46
Answers
Answer:
x=14
Step-by-step explanation:
-2x/7=3x-46
7(-2x/7)=7(3x-46)
-2x=21x-322
-23x=-322
x=14