Anyone please solve and explain part b
Answer:
f(2) = -6
f inverse of 1/2 is 17/2
Step-by-step explanation:
We are given a function [tex]\displaystyle \large{f(x) = \frac{6}{2x-5}}[/tex]
To solve for part (a), we have to substitute x = 2 in f(x).
[tex]\displaystyle \large{f(2)=\frac{6}{2(2)-5} \\\displaystyle \large{f(2)=\frac{6}{4-5}=\frac{6}{-1}=-6[/tex]
Therefore, f(2) is -6.
Now we solve for part (b), we see the notation which is a minor different similar to f(x). We see that there is exponent of -1 between f and 1/2. The part (b) indicates that the function is an inverse of f(x).
[tex]\displaystyle \large{y=f^{-1}(x) \longrightarrow x=f(y)}[/tex]
To solve for part (b), first we solve for x in the function. Let f(x) = y.
[tex]\displaystyle \large{y=\frac{6}{2x-5}}[/tex]
Multiply both sides by 2x-5.
[tex]\displaystyle \large{y(2x-5)=\frac{6}{2x-5}(2x-5)}\\\displaystyle \large{y(2x-5)=6}[/tex]
Divide both sides by y-term.
[tex]\displaystyle \large{\frac{y(2x-5)}{y}=\frac{6}{y}}\\\displaystyle \large{2x-5=\frac{6}{y}}\\\displaystyle \large{2x=\frac{6}{y}+5}\\\displaystyle \large{x=\frac{6}{2y}+\frac{5}{2}}\\\displaystyle \large{x=\frac{3}{y}+\frac{5}{2}}[/tex]
Then swap x and y which we receive [tex]\displaystyle \large{y=\frac{3}{x}+\frac{5}{2}}[/tex]
Therefore, [tex]\displaystyle \large{f(x)=\frac{6}{2x-5} \longrightarrow f^{-1}(x)=\frac{3}{x}+\frac{5}{2}}[/tex]
Thus, [tex]\displaystyle \large{f^{-1}(\frac{1}{2})=\frac{3}{\frac{1}{2}}+\frac{5}{2}}\\\displaystyle \large{f^{-1}(\frac{1}{2})=6+\frac{5}{2}}\\\displaystyle \large{f^{-1}(\frac{1}{2})=\frac{17}{2}}[/tex]
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Is 1 a real or an imaginary number?
someone.. please help me asap...............................................
Answer :
4x + 9y = 27
Explanation :
Multiply the equation with 9
9( y = -4x/9 + 3 )
9y = -4x + 27
4x + 9y = 27
A group of students are working on a project. They complete 30%percent of the project in 12 hours. If they continue to work at the same speed, how many hours will it take the group to finish the project
Answer: 40 HOURS
Step-by-step explanation:
If the students complete 30% of the project in 12 hours,
that means:
12 h................................30%
? h...................................100%
(12*100)/30= 40H
THE STUDENTS NEED 40H TO COMPLETE THE PROJECT
It will take 40 hours for the group to finish the project.
How many hours will it take the group to finish the project?
If the students complete 30% of the project in 12 hours,
that means:
⇒ 12 h = 30%
⇒ ? h = 100%
By using percentage theory:
Percentage formula = (Value/Total value) × 100.
⇒ (12*100)/30= 40H
The answer is 40 hours.
What are a percentage and its formula?
To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100. Percentage formula = (Value/Total value) × 100.
Learn more about percentage here: brainly.com/question/843074
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The sum of the digits of a two-digit number is 12. If the number is multiplied by 3, the result is 144. Write
and solve a system of equations. Find the number.
Answer 48
Step-by-step explanation:
The two-digit number that satisfies the given condition will be 48.
What are digits?In a positional numeral system, a numerical digit is a single sign that can be used singly or in combination to represent numbers.
For example 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are digits.
Suppose the two-digit number is xy.
Sum x + y = 12
By multiplying by 3,
3(10x + y) = 144
10x + y = 48
Put y = 12 - x
10x + 12 - x = 48
9x = 36
x = 4
And, y = 12 - 4 = 8 so the number will be 48.
Hence "The two-digit number that satisfies the given condition will be 48".
To learn more about digits,
https://brainly.com/question/10913044
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Is this relation a function? {(3, 2), (5, 9), (11, 25)}
Answer:
Yes
Step-by-step explanation:
None of the X values are the same number.
Please helppp!!
I have to find the slope of the blue line that is in the graph!!
What are the coordinates of the image Triangle ABC reflection over the line y=x ( please help!!)
Answer:
A (2,-1)
B (-3,-2)
C (-2,1)
Step-by-step explanation:
A (-2,-1), B (3, - 2), and C (2,1)
Image of triangle ABC reflexión over the y: opposite of the x-coordinates. The y coordinates stay the same.
A’ (2,-1), B’ (-3, -2), and C’ (-2,1)
I'm really bad at mathematics. It would be nice if anyone could help me out :) thanks
Pleaseeee help meee with this!!!!!!!!!!!!
Answer:
x=19
Step-by-step explanation:
The 2 angles are same side interior angles, so together they add to 180 degrees. So you can make this equation:
6x + 4 + 4x - 14 = 180
10x - 10 = 180 (Combine like terms)
10x = 190 (add 10 to each side)
x = 19 (divide both sides by 10)
On a line, if XY=6, YZ=8 and XZ=2, which point is between the other two?
A. X
B. Y
C. Z
D. Cannot tell
25 points! :)
Pretty simple question, just not sure how to do it.
ANSWER
-3 -2, 0, .5, 1, 100 for domain
0, 1.8, 10, 19, 77, 100 For Range
Step-by-step explanation:
Domain is all the x values from least to greatest, and range is all the y vlues from least to greatet
How long does it take him to make $375.25
In Damien's classroom, the ratio
of boys to girls is 4:5. If there
are 12 boys, how many students
are there in all in Damien's
classroom
Answer:
The answer would be 27 students
Step-by-step explanation:
4=boys
5=girls
4 x 3 = 12
5 x 13 = 15
12+ 15 = 27
Concrete tiles are made using buckets of cement, sand and gravel mixed in the ratio 1:4:6. If 20 buckets of sand are used, how many buckets of EACH of the following will be
needed?
a)
Cement:
T
b) Gravel:
CAN SOMEONE HELP ME PLEASE ASAP!?
A certain stock sold for $24.89 per share on Thursday. On Friday it sold for $21.36. Find the decrease in the price of the stock from Thursday to Friday.
Pick the corrrect one form the dropdown
Answer:
easy
Step-by-step explanation:
Its very easy for any human to be able to see and compare data as when they are right next to eachother, so you can easily prove a good strong point
can someone help me for this?
Answer:
500000N=2m
x. =6m
cross multiply, it'll be
6×50000÷2
=150,000N
What is the HCF of 62 and 24 ?
Answer: As you can see when you list out the factors of each number, 2 is the greatest number that 24 and 62 divides into.
Step-by-step explanation:
What is the equation of a line with a slope of 4 that passes
through point (-2,5)? A y = -1/4x - 3 B y = -4x + 5 C y = 4x + 5 D y = 4x + 13
Answer:
Solution given:
slope(m)=4
passes through (x',y')=(-2,5)
we have
equation of a line is:
y-y'=m(x-x')
substituting value we get
y-5=4(x-(-2))
y-5=4(x+2)
y-5=4x+8
y=4x+8+5
y=4x+13 is a required equation of a line.
Please someone help solve:
2/2t√3≡4-2√3
Answer:
i'm assuming you want to solve for t?
t=(2√3+3)/6
Kasey had to make a down payment of 17% of the selling price of her house. She was approved for a $255,000 mortgage. What range of costs might she expect to pay at the closing?
Answer:
aq lang to Yung d na binalikan Yung iniwan na parang basura
HELPPPPP!!!!!!!!!!!!!!!!!!!!!!!
[tex]\left(-\dfrac 16 \right)^2 +\dfrac 58 \left(-\dfrac 19} \right)\\\\\\=\dfrac 1{36} -\dfrac{5}{72}\\\\\\=\dfrac 2{72} - \dfrac{5}{72}\\\\\\=-\dfrac 3{72}\\\\\\=-\dfrac 1{24}[/tex]
Answer:
Step-by-step explanation:
(-1/6)^2 + 5/8(-1/9)= -0.0416
Thus the answer is -1/24
Can someone please help me with this one? Tysm!!
Answer:
-26
Step-by-step explanation:
well add the negative numbers first so you get
-17-18=(-35)
then you add 9 so its (-35)+9=26
Answer:
Step-by-step explanation:
-17 + 9 +(-18) = -8 -18 = -26 final answer
Luke is going to reflect point R(6, 10) over the y-axis what are the coordinates for R
Answer:
R - (-6,10)
Flip the x-value when reflecting over y axis, and flip y-value when reflecting over x-axis
Which of the following gives and example of an equation that is non-linear?
A y=2x+1
B y=15/x
C y=10x
D y=x/5
The answer is A. y=2x+1
A is the only equation in which the numbers are not naturally written,but there is another numbering being either taken or added to the situation (+1). B and D both are divided which is linear, and C is multiplying which is also linear. This only leaves us with A.
Hope this helps. & don't forget to drink water <3
what is 2 2/3 - (-3 2/6)
Answer:
6
Step-by-step explanation:
‼️‼️‼️PLS HELP I WILL MARK U BRAINLIEST‼️‼️‼️
Which translation can be used to prove that figures two and three are congruent?
A) (x, y) —> (x, y - 4)
B) (x, y) —> (x - 3, y + 1)
C) (x, y) —> (x + 2, y)
D) (x, y) —> (x + 1, y - 3)
Answer: a I think
Step-by-step explanation:
- The price of an item increases from $90 to $100. Find the increase per cent.
Answer:
The increase as a percentage was 11.1%.
Step-by-step explanation:
The increase is $10. The ratio of this increase to the original $90 is
$10
------- = 1/9
$90
Multiplying this by 100%, we get 11.1%.
The increase as a percentage was 11.1%.