Answers
Answer:
f^(-1)(x) = 1/5x
Step-by-step explanation:
[tex] \large{f(x) = mx + b \longrightarrow f^{ - 1} (x) = \frac{x - b}{m} }[/tex]
Inverse Function is when we swap the x-term and y-term. Here is an explanation to the inverse of linear function above.
[tex] \large{f(x) = mx + b}[/tex]
Here we define f(x) = y. It is better to use y instead of f(x)
[tex] \large{y = mx + b}[/tex]
Swap x-term and y-term.
[tex] \large{x = my + b}[/tex]
Arrange/Simplify in the y-isolated equation.
[tex] \large{x - b = my} \\ \large {\frac{x - b}{ m} = y} \\ \large{ y = \frac{x - b}{m} }[/tex]
Since the function is in inverse form. It's recommended to use f^(-1) to point out that the function is an inverse of the original function.
[tex] \large \boxed{ {f}^{ - 1} (x) = \frac{x - b}{m} }[/tex]
Hence, y = (x-b)/m is an inverse of y = mx+b. A one-to-one function can have an inverse form. Back to the question!
We are given the linear function:
[tex] \large{f(x) = 5x}[/tex]
We will be using substitution method by substituting the original function in inverse form.
Since we know that the slope is 5 and doesn't have y-intercept which is b-value. Hence
[tex] \large{ {f}^{ - 1} (x) = \frac{x - 0}{5} } \\ \large{ {f}^{ - 1} (x) = \frac{x }{5} } \\ \large{ {f}^{ - 1} (x) = \frac{1}{5} x}[/tex]
Or we swap x-term and y-term.
[tex] \large{f(x) = 5x} \\ \large{y = 5x} \\ \large{x = 5y} \\ \large{ \frac{x}{5} = y} \\ \large{y = \frac{x}{5} = \frac{1}{5} x} \\ \large{ {f}^{ - 1} (x) = \frac{1}{5} x}[/tex]
Related Questions
A bag contains 6 green marbles and 4 red marbles. Two marbles are drawn at random as follows; one marble is drawn and not replaced. then the second marble is drawn. What is the probability that the first marble is red and the second one is green
Answers
Answer:
4/15
Step-by-step explanation:
4/10*6/9
2/5*2/3
4/15
Mel received notice that his monthly health care rate will increase 20% next year. If Mel currently pays $150 per month for health care, by what amount will his rate increase next year?
Answers
We need to convert the percentage to a decimal by dividing by 100. Then we multiply by the $150.
150 x 0.20 = 30
AHH ILALAGAY KO PO YUNG TANONG YUNG IBA PO NA KAILANG NG PICT NASA PIC SA TAAS masagot po sna plsssssssssssssssssssssssssss
A.draw the following lines in the boxes
1.line AB and line CD-parallel lines
2.line FH and line XY - intersecting line
3.line MN and line QP-perpendicular line
performance 2
A.classify the triangles by their sides and angle
Answers
Step-by-step explanation:
seriously another one its ok i can do it
hey! i’ll give brainliest help thanks
Answers
Answer:
B
Step-by-step explanation:
A story about someone's life, written by that person.
Good luck with the rest!
Answer:
Option B, A story about a person's life, written by that person
Step-by-step explanation:
We can take Autobiography, the term auto refers to by one's self, therefore autobiography would mean a story written by a person about them selves.
Hope this helps!
NEED ANSWERS ASAP THREE POINTERS
Scatter plot project
Below are the average three-point field goals per NBA game over seasons between 1979 and 2019. (The year refers to the
year each season began. For example, 2019 refers to the 2019-2020 season.) Create a scatter plot of the data. Then, write
a detailed analysis of what your scatter plot shows about the relationship of the variables. Include details about
correlation, whether or not the data is linear, any outliers, and how your scatter plot might be used to make predictions
3 Point Field
3 Point Field
3 Point Field
3 Point Field
Year Goals per Year Goals per Year Goals per
Year Goals per
Game
2019
12.1
2008 6.6
1998 4.5
1988 2.1
Game
Game
Game
2018
11.4
2007
6.6
1997
4.4
1987
1.6
2017
10.5
2006
6.1
1996
6
1986
1.4
2016
9.7
2005
5.7
1995
5.9
1985
0.9
2015
8.5
2004
5.6
1994
5.5
1984
0.9
2014
7.8
2003
5.2
1993
3.3
1983
0.6
2013
7.7
2002
5.1
1992
3
1982
0.5
2012
7.2
2001
5.2
1991
2.5
1981
0.6
2011
6.4
2000
4.8
1990
2.3
1980
0.5
2010
6.5
1999
4.8
1989
2.2
1979
0.8
2009
6.4
Answers
You’re welcome stranger
find nth term of -15,-18,-21.....
Answers
Answer:
I think the question is from Sequence.
on the basis that I have studied I think this is the way. if I am wrong sorry
Find the derivative of f(x) = 6 divided by x at x = -2
Answers
Answer: x=-3
Step-by-step explanation:
i don't really know if this is what I was supposed to do, but i did 6 divided by x=-2 and got x=-3
What is the area of a triangle with a base of 9 feet and a height of 10 feet?
38 ft 2
90 ft 2
19 ft 2
45 ft 2
Answers
Answer:
45 [tex]ft^2[/tex]
Step-by-step explanation:
Multiply 9 · 10 = 90 then divided by 2 = 45
Answer:
45
Step-by-step explanation:
Did the test
Find the area of the triangles with
congruent sides of 25 ft, a height
of 20 ft and a base of 30 ft.
Answers
how many lakhs are there in 2 millions?
Answers
Answer:
2,000,000 - 2 million
20,00,000 - 20 lakhs
Answer:
10 lakh = 1,000,000
So 20 lakh is = 2 million
Hope it helps!
Work out the size of the angle marked X.
Give your answer correct to 1 decimal place.
Answers
Answer:5
Step-by-step explanation:
Answer:
Step-by-step explanation:
take x degree as reference angle
using sin rule
sin x=opposite/hypotenuse
sin x=10/15
sin x=0.66
x=sin 42
therefore x=42 degree
Select all expressions that equal −7−(−12) .
A
7+(−12)
B
−7+(−12)
C
−7+12
D
7+12
Answers
Answer:
C, -7+12
Step-by-step explanation:
-7--12= 5
-7--12 can also be -7+12
Answer:
The answer is c
Step-by-step explanation:
-7-(-12) = 5
Find perimeter of polygon :
Pls explain answer
Answers
Answer:
270
------
6 x 9 = 54
54 x 5 = 270
=270
Step-by-step explanation:
270
Step by step:
Ezzzzzzzz
write an equation in SLOPE- INTERCEPT FORM of the line that has the slope of -6 and a y- intercept of 2.
ANSWER THIS ASAP PLEASE!
Answers
Answer:
y=-6x=2
Step-by-step explanation:
y= mx+b
m=slope
b=y-intercept
SOMEONE PLEASE HELP ME! I promise i will mark brainlest, but i need the right answer for this. help is much appreciated <3
Answers
Answer:
I say A or B but in favor A
Step-by-step explanation:
What value of x solves the equation 56/x = 8 (Trigonometry)
(In image)
Answers
Answer:
b. 7
[tex] \frac{56}{x} = 8 \\ 8x = 56 \\ x = 7[/tex]
please help will mark brainlyist and 10 points if right
Answers
Answer:
can u copy the text and send it to help u
I'LL GIVE BRAINLIEST IF CORRECT
The illustration below shows the graph of y as a function of x.
Complete the following sentences based on the graph.
- The slope of the graph of the function is equal to ___ for x between x = -3 and x = -2.
- The slope of the graph is equal to ___ for x between x = 3 and x =4.
- The greatest value of y is y = ___.
- The smallest value of y is y = ___.
Answers
Answer:
Did you mean to attach something?
Step-by-step explanation:
I don't see the illustration... without it I cannot answer the question.
Answer:
0, 0, 4, -3
Step-by-step explanation:
Help me with Math please
Answers
Answer:
18 in²
Step-by-step explanation:
Given 2 similar figures with ratio of sides = a : b , then
ratio of areas = a² : b²
Here ratio of sides = 9 : 12 = 3 : 4
ratio of areas = 3² : 4² = 9 : 16
let x be the area of the smaller figure then by proportion
[tex]\frac{x}{9}[/tex] = [tex]\frac{32}{16}[/tex] = 2 ( multiply both sides by 9 )
x = 18
That is area of smaller figure = 18 in²
4. Mrs. Hernandez drew a quadrilateral on the board.
What type of quadrilateral did Mrs. Hernandez
draw?
A. Rectangle
B. Trapezoid
C. Rhombus
D. Square
Answers
Which matrix represents the system of equations shown below?
y = 5
4x = 3
Answers
Answer:
[tex]\left[\begin{array}{ccc}1&0\\0&4\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}5\\3\end{array}\right][/tex]
Step-by-step explanation:
A matrix is an algorithm that has many applications. It is composed of a series of numbers (typically coefficients of variables) organized in a pattern. When dealing with a matrix, one must always remember the rule (rows by columns). One such application is that a matrix can facilitate the process by which one solves a system of equations.
When given the following system:
y = 5
4x = 3
One can see that not all of the equations have all variables in them. Yet, bear in mind that any number times zero is zero, therefore, one can rewrite the equation such that it has all of the variables if one ensures that the coefficient of the missing variable is (0).
y + 0x = 5
0y + 4x = 3
Now organize this in the form of a matrix, the coefficients of the variable go in a (4 x 4) since there are now (4) elements. The variables are vertically arranged in a (2 x 1), and the equation results are also vertically arranged in a (2 x 1).
[tex]\left[\begin{array}{ccc}1&0\\0&4\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}5\\3\end{array}\right][/tex]
Classify the triangle by sides and angles.
Answers
Answer:
c) right isosceles triangle
Step-by-step explanation:
two equal sides and a 90 degree angle make a right isosceles triangle
Between 02 30 and 05 15, the same day ,the volume of water in a reservoir increased from 1500 L to 14 700 L. What was the average rate of increased in volume of water, giving your answer in L/h?
Answers
Answer:
4,800
Step-by-step explanation:
(14,700- 1,500) / 2 h 45 m
= 13,200 / 2.75
= 4,800 L/h
Time in minutes between 2 30 and 5 15 = 165 minutes= 2.75 hrs
raise in water level = 14700-1500= 13200
the average rate of increased in volume of water, giving your answer in L/h = 13200/2.75 = 4800 L/h
A team from the high school went on a science-and-math quiz show. The science questions were worth 10 points and the math questions were worth 3 points. The team answered a total of 10 questions and earned 65 points. How many questions did the team answer in each category?
Answers
Answer:
The answered 5 math questions, and 5 science questions.
5 * 3 = 15
5 * 10 = 50
15 + 50 = 65
Step-by-step explanation:
A drawbridge rises at a constant rate. It takes 1 1/2 minutes for the drawbridge to rise 3/10 of its total height. How much time, in minutes, does it take for the drawbridge to reach its total height?
Group of answer choices
1/5
9/20
20/9
5
Answers
helppppppppppp no links or you'll get reported
Answers
Answer:
1.95
Step-by-step explanation:
area = (1/2 ×1 ×1 )×3 = 1.5 ( for sides)
area = ( 1/2 ×1 ×0.9) = 0.45 for base
area =1.5+0.45 = 1.95
Find the total volume of the composite figure below. Round to the nearest thousandth.
Use the π key.
Answers
Answer:
The volume of the composite figure is approximately 3567.198 cubic feet.
Step-by-step explanation:
The composite figure consists in the combination of a right cone and a cuboid. The volume of the composite ([tex]V[/tex]), in cubic feet, figure can be determined by this expression:
[tex]V = \frac{1}{3}\cdot \pi \cdot r^{2}\cdot h + w\cdot H \cdot l[/tex] (1)
Where:
[tex]r[/tex] - Radius of the circle of the right cone, in feet.
[tex]h[/tex] - Height of the cone, in feet.
[tex]w[/tex] - Width of the cuboid, in feet.
[tex]H[/tex] - Height of the cuboid, in feet.
[tex]l[/tex] - Length of the cuboid, in feet.
If we know that [tex]r = 10\,ft[/tex], [tex]h = 10\,ft[/tex], [tex]w = 20\,ft[/tex], [tex]H = 7\,ft[/tex] and [tex]l = 18\,ft[/tex], then the volume of the composite figure is:
[tex]V = \frac{1}{3}\cdot \pi \cdot (10\,ft)^{2}\cdot (10\,ft) + (20\,ft)\cdot (7\,ft)\cdot (18\,ft)[/tex]
[tex]V = \left(\frac{1000\pi}{3} + 2520\right)\,ft^{3}[/tex]
[tex]V \approx 3567.198\,ft^{3}[/tex]
The volume of the composite figure is approximately 3567.198 cubic feet.
What's the area of a trapezoid
Answers
Answer:
A=27 square units
Step-by-step explanation:
3x+4y=−2. 2x−4y=−8
Select the statement that correctly describes the solution to this system of equations.
Answers
Answer:
One solution at (-2,1)
Step-by-step explanation:
3x+4y=−2.
2x−4y=−8
Add the two equations together
3x+4y=−2
2x−4y=−8
------------------------
5x +0y = -10
Divide by 5
5x/5 = -10/5
x=-2
Now find y
2x-4y = -8
2*-2 -4y = -8
-4-4y = -8
Add 4 to each side
-4+4 -4y = -8+4
-4y = -4
Divide by -4
y = 1
Help me pls I need this to pass low key stuck
Answers
Answer:
m<F = 44°
length of FH = 15
length of GF = 21
Perimeter of ∆FGH = 50
Step-by-step explanation:
✔️Find m<F using the sum of triangle theorem:
The small box indicates angle 90°. Sum of a triangle is 180°. Therefore,
m<F = 180° - (90° + 46°)
m<F = 180° - 136°
m<F = 44°
✔️Find FH using trigonometric function:
Reference angle = 46°
Length of Opposite side = FH = ?
Length of Adjacent side = GH = 14
Apply TOA because we are concerned with the OPP and ADJ sides:
Tan 46° = Opp/Adj
Tan 46° = FH/14
14*Tan 46° = FH
14.4974243 = FH
FH = 15 (approximated to nearest whole number)
✔️Find GH by applying either a trigonometric function or just simply apply pythagorean theorem:
Pythagorean theorem is given as,
c² = a² + b²
c is the longest side (hypotenuse) = GF = ?
a = GH = 14
b = FH = 15
Thus:
GF² = 14² + 15²
GF² = 421
GF = √421
GF ≈ 21 (nearest while number)
✔️Perimeter of ∆FGH = GH + GF + FH
= 14 + 21 + 15
= 50