Answer:
[tex]P(Brown\ or\ Green) = \frac{13}{25}[/tex]
Step-by-step explanation:
Given
[tex]n(Brown) = 20[/tex]
[tex]n(Green) = 6[/tex]
[tex]n(Blue) = 17[/tex]
[tex]n(Hazel) = 7[/tex]
Required
Determine the probability of Brown or Green eyes
First, the total number of respondents have to be calculated;
[tex]Total = 20 + 6 + 7 + 17[/tex]
[tex]Total = 50[/tex]
The events described above is a mutually exclusive event and as such, the required probability will be calculated by;
[tex]P(Brown\ or\ Green) = P(Brown) + P(Green)[/tex]
Calculating P(Brown)
[tex]P(Brown) = \frac{n(Brown)}{Total}[/tex]
Substitute 20 for n(Brown) and 50 for Total
[tex]P(Brown) = \frac{20}{50}[/tex]
Calculating P(Green)
[tex]P(Green) = \frac{n(Green)}{Total}[/tex]
Substitute 6 for n(Green) and 50 for Total
[tex]P(Green) = \frac{6}{50}[/tex]
So;
[tex]P(Brown\ or\ Green) = P(Brown) + P(Green)[/tex]
[tex]P(Brown\ or\ Green) = \frac{20}{50} + \frac{6}{20}[/tex]
Take LCM
[tex]P(Brown\ or\ Green) = \frac{20+6}{50}[/tex]
[tex]P(Brown\ or\ Green) = \frac{26}{50}[/tex]
Divide the numerator and denominator by 2
[tex]P(Brown\ or\ Green) = \frac{13}{25}[/tex]
Answer:
13/25
Step-by-step explanation:
Total number of people = 50
Probability of choosing a person with brown eyes [P(A)] = 20/50
Probability of choosing a person with green eyes [P(B)] = 6/50
Using the addition rule of mutual exclusive events (since they have specified brown OR blue, we use this formula):
P(A U B) = P(A) + P(B)
=> P(A U B) = 20/50 + 6/50 = 26/50 = 13/25
Therefore the probability of a person choosing a group that has brown or green eyes = 13/25
Also I got it right on edge haha, if you're still worried!!!!!!!!
Hope this helps :))))))))))))))
Need help!!! IF YOU KNOW HOW TO DO THIS GO AHEAD AND DO IT BUT IF YOU DONT THEN DONT BOTHER THANKS
1. Yes a circle is a two-dimensional figure. It lies in the plane, which is basically a flat piece of paper that doesn't bend or curve, and the paper extends infinitely in all directions.
2. A circle is not a polygon. A polygon has finitely many straight line segments that glue together to form an enclosed figure. Think of fencing in an area with straight fence portions.
3. Yes this is what makes a circle. Every point on the circle is the same distance from the center. We say these points on the circle are equidistant from the center.
Answer:
Is a circle a two d figure?
YES. It is a flat figure.
Is a circle a polygon?
NO, because it does not have 4 straight sides.
Is every point in a circle the same distance from the center?
YES. All points in a circle are equidistant from the center (they are all equal)
calculate EG if a=5 and b=15
22. A parallelogram in which one angle 90° is necessarily:
A. Square
B. rhombus C. rectangle
D.trapezium
Answer:
C. Rectangle
Step-by-step explanation:
A parallelogram can not have a single 90° angle. This is because the opposite angles of a parallelogram are equal.
Therefore, the two opposite sides are equal.
In a parallelogram, neighboring angles add up to 180°. This therefore implies that all the angles are 90°.
This describes a rectangle.
-3a(a^2-10a+25)= expand it and it has to be in polynomial form
Answer:
[tex] - 3 {a}^{3} + 30 {a}^{2} - 75a[/tex]Step-by-step explanation:
[tex] - 3a( {a}^{2} - 10a + 25)[/tex]
Multiply each term in the parentheses by -3a
[tex] = - 3a \times {a}^{2} - 3a \times ( - 10a) - 3a \times 25[/tex]
Calculate the product
[tex] = - 3 {a}^{3} - 3a \times ( - 10a) - 3a \times 25[/tex]
Multiplying two negatives equals a positive [tex]( - ) \times ( - ) \ = ( + )[/tex]
[tex] = - 3 {a}^{3} + 3a \times 10a - 3a \times 25[/tex]
Calculate the product
[tex] = - 3 {a}^{2} + 30 {a}^{2} - 75a[/tex]
Hope this helps...
Best regards!!
Bro did you go in the next grade?
Explain how you can determine the number of real number solutions of a system of equations in which one equation is linear and the other is quadratic–without graphing the system of equations.
Answer:
To determine the number of real number solutions of as system of equations in which one equation is linear and the other is quadratic
1) Given that there are two variables, x and y as an example, we make y the subject of the equation of the linear equation and substitute the the expression for y in x into the quadratic equation
We simplify and check the number of real roots with the quadratic formula, [tex]x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex] for quadratic equations the form 0 = a·x² - b·x + c
Where b² > 4·a·c there are two possible solutions and when b² = 4·a·c equation there is only one solution.
Step-by-step explanation:
Answer:
Isolate one variable in the system of equations. Use substitution to create a one-variable equation. Then, set the quadratic equation equal to zero and find the discriminant. If the discriminant is negative, then there are no real number solutions. If the discriminant is zero, then there is one real number solution. If the discriminant is positive, then there are two real number solutions.
Step-by-step explanation:
I just took the test on Edge 2020
Can someone help me solve this :): ?
( brainliest to the correct answer/explanation)
Answer:
1and1/2yrs ago
Step-by-step explanation:
price dis year= 56545
reduction per year= 11309
...number of years ago = 73810-56545=17265
and is about 20% of annual deductions
so if 56545 +20% + 1/2 20% = 1nd1/2 yrs
Convert the following to Slope-Intercept Form: 4x – 3y = 24.
The equation 4x – 3y = 24 can be represented in the slope-intercept form will be y = (4/3)x - 8.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equation is given below.
4x – 3y = 24
Convert the equation from standard form to slope-intercept form. Then we have
4x – 3y = 24
3y = 4x - 24
y = (4/3)x - 24 / 3
y = (4/3)x - 8
The equation 4x – 3y = 24 can be represented in the slope-intercept form will be y = (4/3)x - 8.
More about the linear equation link is given below.
https://brainly.com/question/11897796
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Simplify the expression.
a4b3 + 8a4b3=???
PLEASE HELP??! ASAP!!?
Answer:
9[tex]a^{4}[/tex]b³
Step-by-step explanation:
The 2 terms are like terms and can be combined, that is
[tex]a^{4}[/tex]b³ ( 1 + 8)
= 9[tex]a^{4}[/tex]b³
Answer:
9a^4b^3
Step-by-step explanation:
a^4b^3 + 8a^4b^3
These are like terms so we can add them together
Factor out a^4b^3
a^4b^3( 1+8)
a^4b^3 (9)
9a^4b^3
Express n as the subject of formula
Step-by-step explanation:
Check the attachment... Hope it helps:)
Good luck!!
PLEASE HELP. WILL MARK BRAINIEST!!! 1. What shape should Kylee use to draw the swimming pool on the diagram? 2.If Kylee wanted to put the swimming pool directly between the flower beds, at what point would the center of the swimming pool be? 3.Use the point you identified in Part 1 to write an equation that will draw the swimming pool on the diagram so that it is directly between the flower beds. 4.Can Kylee place the swimming pool directly between the flower beds? Use the equation you wrote in Part 3 prove or disprove that the swimming pool will touch one of the flower beds. (Hint: Plug in points that are on a flower bed to check if they are also on the circle.) 5.Where can Kylee put the pool? Write an equation that will draw the pool on the diagram so that it does not touch anything.
Answer:
1) A rectangular shape
2) Point (30, 50)
3) (x - 30)² + (y - 50)² = 10²
4) Yes, the swimming pool will touch the flower beds
5) Point (45, 25)
Step-by-step explanation:
1) Given the number of shapes that are rectangles (4) and the number of circular shapes (1) to conserve more space Kylee should drw the swimming pool with a rectangular shape
2) So as to avoid touching the flowerbeds which are 20 feet apart, the center of the swimming pool will be moved slightly up to (30, 50)
3) The equation that will draw the swimming pool is the equation of a circle, given as follows
(x - h)² + (y - k)² = r²
Where (h, k) is the coordinate of the center of the circle, and r is the radius of the circle,
Given that the diameter, D, of the circle = 20 feet, the radius, r = D/2 = 20/2 = 10 feet
The equation of the circle is therefore;
(x - 30)² + (y - 50)² = 10²
4) The coordinates of the center of the flower bed is (30, 45) which gives
(x - 30)² + (y - 45)² = 10²
Where the coordinates of the side of the flower pot is (20, 45), we have;
(20 - 30)² + (45 - 45)² = 10²
(-10)² = 10² = r²
Hence, point (20, 45) is on the circle
The other flower bed side has coordinates (40, 45) which gives
(40 - 30)² + (45 - 45)² = 10²
10² = r² = 10²
Point (40, 45) is also on the circle
Therefore, the swimming pool will touch the flower beds
5) At point (45, 25), we have;
(x - 45)² + (y - 25)² = 10²
The closest point is the patio with coordinates (40, 15) which gives;
(40 - 45)² + (15 - 25)² = 10² = 100
(-5)² + (-10)² = 125 > 100
Therefore, point (40, 15), is not on the circle.
what is 3x^3 - 11x^2 - 26x + 30 divided by x-5?
Answer:
Most likely the answer is
3x^2+4x-6
Answer:
3x^2+4x-6 is correct
A current of 2.5 A delivers 3.5 of charge
1 Ampere = 1 Coulomb of charge per second
2.5 A = 2.5 C of charge per second
Time to deliver 3.5 C of charge = (3.5 C) / (2.5 C / sec)
Time = (3.5 / 2.5) (C / C-sec)
Time = 1.4 sec
A current of 2.5 A delivers 3.5 C of charge in 1.4 seconds.
Which is not a property of a parallelogram? a: Diagonals are perpendicular. b: Opposite sides are congruent. c: Opposite angles are congruent. d: Opposite sides are parallel.
Answer:
A
Step-by-step explanation:
Diagonals are perpendicular.
This means that there have to be 90 degree angles in the parallelogram which is not true at all. They can be slanted as well!
Hope this helped :) good luck!
V2=u2+2as v 2 = u 2 + 2 a s Where v v is the final velocity (in m/s), u u is the initial velocity (in m/s), a a is the acceleration (in m/s²) and s s is the distance (in meters). Find v v when u u is 9 m/s, a a is 7 m/s², and s s is 28 meters.
Answer:
Final velocity, v = 21.75 m/s
Step-by-step explanation:
Given that the relation between final velocity, initial velocity, acceleration and distance traveled is expressed as:
[tex]v^2=u^2+2as[/tex]
Also, given that:
Initial velocity, u = 9 m/s
Acceleration, a = 7 m/[tex]s^2[/tex]
Distance, s = 28 m
To find:
Final velocity, v = ?
Solution:
The given relation between v, u, a and s is:
[tex]v^2=u^2+2as[/tex]
We have the values of initial velocity, acceleration and distance traveled in the question statement. We just need to put all these values to find the value of final velocity.
Let us put all the values in the given equation and try to find final velocity, v:
[tex]v^2=9^2+2\times 7 \times 28\\\Rightarrow v^2=81+14 \times 28\\\Rightarrow v^2=81+392\\\Rightarrow v^2=473\\\Rightarrow v=\sqrt{473}\\\Rightarrow v=21.75\ m/s[/tex]
So, the answer is:
final velocity, v = 21.75 m/s
Social Networking Sites
In a survey of 2255 randomly selected US adults (age 18 or older), 1787 of them use the Internet regularly. Of the Internet users, 1054 use a social networking site.7 Find and interpret a 95% confidence interval for each of the following proportions:________
(a) Proportion of US adults who use the Internet regularly.
(b) Proportion of US adult Internet users who use a social networking site.
(c) Proportion of all US adults who use a social networking site. Use the confidence interval to estimate whether it is plausible that 50% of all US adults use a social networking site.
Answer:
(a). ( 0.776 ,0.809).
(b). (0.567 , 0.613).
(c). 0.600.
Step-by-step explanation:
Okay, we are given the following set of values or data or parameters;
=> "A survey of 2255 randomly selected US adults (age 18 or older)"
=> "1787 of them use the Internet regularly. Of the Internet users, 1054 use a social networking site".
=> Also, "95% confidence interval for each of the following proportions"
Therefore, we are going to make use of one (major ) mathematical formula in solving this particular Question and it is given below;
Confidence Interval = p +/- z* × [ √p( 1 - p) / n].
(a).
Where p = 1787/2255 = 0.793.
95% confidence Interval = z* = 1.96.
= 0.793 +/- 1.96 × [√0.793 ( 1 - 0.793)/ 2255] .
= 0.793 +/- 0.0167.
= ( 0.776 ,0.809).
(b). Where p = 1054/ 1787 = 0.5900
95% confidence Interval = z* = 1.96.
= 0.5900 +/- 1.96 × [√0.5900 ( 1 - 0.5900)/ 1787]
= 0.5900 +/- 0.0228.
= (0.567 , 0.613).
(c). 1054/1787 = 0.59 = 0.600.
Answer:
your answer is the third one
Step-by-step explanation:
8. The world's tallest
totem pole is in Alert
Bay, B.C., home of the
Nimpkish First Nation.
Twenty feet from the
base of the totem pole,
the angle of elevation
of the top of the pole
is 83.4º. How tall is
the totem pole to the
nearest foot?
Answer:
The height of the totem tree is approximately 172.8ft
Step-by-step explanation:
Hello,
To find the height of the totem pole, we need to use our date to make a pictorial representation so that we can know if the pole and base makes a right angle triangle with the angle of elevation.
See attached document for better illustration.
Let T represent the height of the pole.
Using trigonometric ratio,
SOHCAHTOA, we can use tangent since we have our adjacent and we're to solve for the opposite.
Tanθ = opposite/ adjacent
Opposite = T
Adjacent = 20ft
θ = 83.4°
Tan83.4 = T / 20
T = 20Tan83.4
T = 20 × 8.64
T = 172.8ft
The height of the totem tree is approximately 172.8ft
Tanisha lives in an apartment and pays the following expenses each month: electric bill, $42.42; TV streaming services, $27.99; and rent, $587.70. Estimate her total expenses for the month by first rounding each value to the nearest tens place.
A) $670
B) $ 650
C) $659
D) $660
Answer:
It is C
Step-by-step explanation:
42.60=43.00
587.70=588.00
27.99=28.00
simplify
[tex](xy) ^{ - 1} [/tex]
Answer:
Below
Step-by-step explanation:
●(xy)^(-1)
● x^(-1) * y^(-1)
● (1/x)*(1/y)
● 1/xy
Rewrite 4 - 5 using the addictive inverse and display the expression on a number line
Answer:
d. (4) + (-5)
Step-by-step explanation:
We know that 4 is the positive value and 5 is the negative value, therefore if to be able to rewrite in it we will almost make a sum of these values without changing the meaning of each one of the values, therefore:
(+4) + (-5)
Which means that the correct option is the last option, that is, d. (4) + (-5). Furthermore, the representation is correct because the resulting arrow is the one corresponding to -1.
The area of a sector of a circle is given by the equation , where r is the radius of the circle and S is the angle measure of the sector. If Mia solved this equation for S, which of the following equations did she write?
This question is incomplete
Complete Question
The area of a sector of a circle is given by the equation A = πr²S/360 where r is the radius of the circle and S is the angle measure of the sector. If Mia solved this equation for S, which of the following equations did she write?
a) 360A+ πr²
b) 360A - πr²
c) 360 + A / πr²
d) 360A/ πr²
Answer:
d) 360A/ πr²
Step-by-step explanation:
In the above question,
Area of the sector (A) = πr²S/360
r = radius
We are also told that Mia solved for S = Angle measure of the sector.
In other to find the equation that Mia used to solve for S,
We would use the Subject of the formula method.
Area of the sector (A) = πr²S/360
We cross Multiply
360 × A = πr²S
Making S the subject of the formula, we divide both sides by πr²
360 × A / πr² = πr²S/ πr²
S = 360 × A/ πr²
S = 360A/ πr²
Therefore, the equation Mia wrote if she solve this equation ( A = πr²S/360) for S is :
S = 360A/ πr²
Option d is the correct option.
Can someone please tell me the answer! THANK YOU
Answer: approximately 24 square units in the shaded areas
Step-by-step explanation:
The area of the entire dark circles will be for each πr², then divided by 2 to get the area of the semicircles created on the sides of the triangles:
16π + 9π = 25π Half that times value for pi
≈ 39.2699 is the area of the dark semicircles. Round to 39.27
Now the fun! Find the area of the parts subtracted by the light semicircle:
The area of the entire circle is 25π or about 78.54. The triangle is half of an inscribed rectangle, 6×8, so 48. Subtracted from the circle leaves about 30.54 in the four slices between the arcs of the circumference and the perimeter of the rectangle. We are concerned with only half of the slices, so we will subtract 15.27
Area of the dark semicircles minus the area of the light slices will leave the area of the shaded crescents:
39.27 - 15.27 = 24 square units . Voila!Jim and Krutika win some money and share it in the ratio 2:3. Jim gets £10. How much did Krutika get?
Answer:
£15
Step-by-step explanation:
The 2 part of the ratio represents the £10 that Jim gets.
Divide the amount by 2 to find the value of one part of the ratio.
£10 ÷ 2 = £5 ← value of 1 part of the ratio, thus
3 parts = 3 × £5 = £15 ← amount Krutika gets
Find the area of this shape.
4 cm
2 cm
4 cm
4 cm
-
1
5.75 cm
1
1
The area of the shape is __
square centimeters.
Answer:
shape AREA= 35cm^2
Step-by-step explanation:
you should know that this shape is a combination of triangle and trapezoid. therefore you have to find the area of each shape and add them.
A=h/2(b1 + b2) for trapezoid
A=2/2((4+4)+4)
A=1*12
A=12cm^2
A=bh/2. for TRIANGLE
A=1/2((4+4)*5.75)
A=1/2(46)
A=23cm^2
shape AREA= triangle AREA + trapezoid AREA
shape AREA=12cm^2 + 23cm^2
shape AREA= 35cm^2
Driving on the highway, you can safely drive 70 miles per hour. “How far can you drive in ‘h’ hours?” What is the domain of the function which defines this situation?
Answer:
70 +60muinte= 13
Step-by-step explanation:
so that the ans
In h hours you will go 70h far from the original position and domain of the function is the amount of hours you drive option (C) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The complete question is:
Driving on the highway, you can safely drive 70 miles per hour. “How far can you drive in ‘h’ hours?” What is the domain of the function which defines this situation?
A.)The amount of gas you use.
B.) 70.
C.) The amount of hours you drive.
D.)The distance you drive
We have:
Driving on the highway, you can safely drive 70 miles per hour.
The speed of the vehicle = 70 miles per hour
As we know,
Distance = speed×time
1 hour → 70 miles
h hour → D miles
D(t) = 70h
The above expression represents the situation.
Thus, in h hours you will go 70h far from the original position and domain of the function is the amount of hours you drive option (C) is correct.
Learn more about the function here:
brainly.com/question/5245372
#SPJ5
In ABC, BC = a = 16, AC = b = 10, and m<C = 22º. Which equation can you use to find the value of c = AB?
Answer:
10 times 16 = C
Step-by-step explanation:
c2 = a2 + b2 − 2ab cos C = 162 + 102 − 2(10)(16) cos 22°
Find the x-intercepts of the graph
Answer:
(1,0) and (3,0)
Step-by-step explanation:
y=x^2-4x+3
To factor we need to know what numbers add up to -4 and multiply will equal to 3.
y=(x-3)(x-1)
The zeroes would be 3 and 1.
x=3 so y=0 for (x-3)
x=1 so y=0 for (x-1)
If right pls give me brainliest thank you.
Answer:
(1, 0) and (3, 0)
Step-by-step explanation:
[tex]y=x^2-4x+3[/tex]
Plug y as 0 to find the x-intercepts.
[tex]0=x^2-4x+3[/tex]
Factor right side.
[tex]0=x^2-1x-3x+3[/tex]
[tex]0=x(x-1)-3(x-1)[/tex]
[tex]0=(x-1)(x-3)[/tex]
Set factors equal to 0.
[tex]x-1=0\\x=1\\x-3=0\\x=3[/tex]
x=1 or x=3 when y=0
The area of a circle is increasing at a rate of 0.4 cm square per second. What is the rate of change of the circumference of the circle when its radius is 5cm?
Answer: 4π cm^2/minute
Step-by-step explanation:
Rate of change :
Change with respect to time (dr/dt)
dr/dt = 0.4cm^2/s
r = 5cm
The rate of change when the Radius is 5cm
Area / Circumference of a circle (A) = πr^2
From chain rule of differentiation:
dA/dt = (dr/dt) * (dA/dr)
If A = πr^2
dA/dr = 2πr
dA/dr = 2π * 5 = 10π
However,
dA/dt = (dr/dt) * (dA/dr)
dA/dt = (0.4) * (10π)
dA/dt = 4π cm^2/minute
pls help me with this question
Answer:
32 cm
Step-by-step explanation:
The volume of the container is:
V= area of the base * the heigth
Since the container has a rectangular base the area of it is:
A = length * width
Let L be the missing length
A = L * 10
V = 10* 25 * L
The container can hold 8 Liters when it's completely full to its brim.
8 liters is 8000 cm^3 ( multiply by 1000)
8000 = 10*25*L
8000 = 250 *L
L = 8000/250
L = 32 cm
v=8litres which is 8 × 1000
l=?
b=10
h=25
since, v=lbh (volume of cuboid)
8000=l × 10 × 25
l=8000/250
l=32
therefore the length is 32cm
A square tile has a piece broken off it with 7cm².If the area of the remaining rule is 137cm²,what were the dimensions of the original tile?
Answer:
12 cm × 12 cm.
Step-by-step explanation:
It is given that a square tile has a piece broken off it with 7 cm². The area of the remaining rule is 137 cm².
Total area of square = 7 + 137 = 144 cm² ...(1)
Area of a square is
[tex]Area=a^2[/tex] ...(2)
where, a is side length of square.
From (1) and (2), we get
[tex]a^2=144[/tex]
Taking square root on both sides.
[tex]a=\sqrt{144}[/tex]
[tex]a=12\ cm[/tex]
Therefore, the dimensions of the original tile are 12 cm × 12 cm.
25 POINTS AND BRAINLIEST FOR THESE!
Answer:
Step-by-step explanation:
Hello,
For any function f which has an inverse function we can write
[tex]x=(f^{-1}of)(x)=(fof^{-1})(x)=f(f^{-1}(x))[/tex]
This is why, in practice, to find the inverse of f we will consider f(x) = y and we will look for x as a function of y, so we switch x and y and solve for y. Let's do it.
Step 1 - The function f(x) can be written as a variable. [tex]\boxed{y}=f(x)[/tex]
f(x) = y = 5x + 2
Step 2 - switch the variables x <-> y
x = 5y + 2
subtract 2 to both parts of the equation
<=> x - 2 = 5y + 2 - 2 = 5y
divide by 5 both parts of the equation
[tex]<=> y=\dfrac{x-2}{5}[/tex]
It means that the inverse of f is as below.
[tex]\boxed{ \ f^{-1}(x)=\dfrac{x-2}{5}\ }[/tex]
Step 3 - Find the inverse of g(x)
We already found that the inverse of f is g, so the inverse of g is f.
Let's do it again.
[tex]g(x)=y=\dfrac{x-2}{5} \ \ \text{ switch x and y } \\ \\ x= \dfrac{y-2}{5} \ \ \text{ solve for y }\\ \\ y-2=5x \ \ \text{ mulitply by 5 both parts of the equation } \\ \\ y = 5x+2 \ \ \text{ add 2 to both parts of the equation }[/tex]
And we found what we already known, meaning f is the inverse of g.
[tex](gof)(x)=(fog)(x)=x[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answers and Step-by-step explanation:
Step 1:
We want to find the variable that ff(x) represents. Well, we know it can't be x because we already have x on the other side of the equation: ff(x) = 5x + 2.
So, ff(x) must equal y.
Since ff(x) = y, we know then that ff(x) = y = 5x + 2. And our equation is:
y = 5x + 2
Step 2:
Let's switch the variables now. This means that what used to be y will be x and what used to be x will be y:
y = 5x + 2 ⇒ x = 5y + 2
Subtract 2 from both sides:
5y = x - 2
Divide by 5 from both sides:
y = (x - 2)/5
Step 3:
Let's find the inverse of g(x) by doing the exact same thing as we did with ff(x):
g(x) = y = (x - 2)/5
Switch the variables:
y = (x - 2)/5 ⇒ x = (y - 2)/5
Multiply by 5 on both sides:
5x = y - 2
Add 2 to both sides:
y = 5x + 2
Notice that this is the exact same as ff(x)! This means that ff(x) and g(x) are inverses.