Given:
The function is:
[tex]f(x)=\dfrac{2x}{3}-4[/tex]
To find:
The inverse of the given function, i.e., [tex]f^{-1}(x)[/tex].
Solution:
We have,
[tex]f(x)=\dfrac{2x}{3}-4[/tex]
Step 1: Substitute [tex]f(x)=y[/tex].
[tex]y=\dfrac{2x}{3}-4[/tex]
Step 2: Interchange x and y.
[tex]x=\dfrac{2y}{3}-4[/tex]
Step 3: Isolate y.
[tex]x+4=\dfrac{2y}{3}[/tex]
[tex]3(x+4)=2y[/tex]
[tex]\dfrac{3x+12}{2}=y[/tex]
[tex]\dfrac{3}{2}x+6=y[/tex]
Step 4: Substitute [tex]y=f^{-1}(x)[/tex].
[tex]f^{-1}(x)=\dfrac{3}{2}x+6[/tex]
Therefore, the inverse of the given function is [tex]f^{-1}(x)=\dfrac{3}{2}x+6[/tex].
Find the missing side. Round to the nearest tenth.
Like what that guy said sorry did not mean to disturb
At age 21, Felipe is 60% of the minimum age he must be to become U.S. President.
What is the minimum age he must be to become U.S. President?
Answer:
35 years
Step-by-step explanation:
[tex]\frac{60}{100} = \frac{21}{y}[/tex]
Cross Multiplying:
[tex]21*100 = 2,100\\2,100/60 = 35[/tex]
find the area of each shaded sector. Round to the nearest hundredths place. Use 3.14 for pi
Answer:
8.48cm²
Step-by-step explanation:
area of a sector = [tex]\frac{0\pi r^2\\\\}{360}[/tex]
where 0 = angle measure of sector
and r = radius
we are given the angle measure ( 23° ) and the radius ( 6.5 cm )
so all we have to do is plug in the values into the formula
(Note that the question asks us to use 3.14 for pi)
[tex]A=\frac{23*3.14* 6.5^2\\\\}{360}\\6.5^2 = 45.25\\23*3.14 =72.22\\72.22*45.25 = 3051.295\\\frac{3051.295}{360} =8.47581944[/tex]
so the area of the sector = 8.47581944 cm^2
finally we want to round to the nearest hundredth and we get that the answer is 8.48cm²
What is the answer :>
um.. it’s just a black picture. :>
6
There are 20 sweets in a bag.
Seven of them are strawberry.
A sweet is taken at random from the bag.
What is the probability that the sweet taken is not strawberry?
Your scores on the first 4 tests in Algebra were 85, 80, 90, and 93. What do you need to make on the 5th test to have a 90 average in the class?
Answer:
you would have to get a 100 on your fifth test
Step-by-step explanation:
because between your first 4 tests, the average is only 87 something but when you add 100 to that, the average turns to 89.6 which when rounded becomes 90.
2a+3b as a column vector
Answer:
Step-by-step explanation:
A submarine descends
300 meters in one hour.
What was it's average
change in depth per
minute?
Answer:
5 meters per minute
Step-by-step explanation:
300/60 = 5 meters per minute
BRAINLIEST FOR CORRECT ANSWER!
What is the transformation rule for a translation 3 units right?
Answer:Translation happens when we move the image without changing anything in it. ...
Rotation is when we rotate the image by a certain degree. ...
Reflection is when we flip the image along a line (the mirror line). ...
Dilation is when the size of an image is increased or decreased without changing its shape.
Please help I give brainliest
Answer:
Questions:
#1) one complex solution
#2) two solutions
#3) one complex solution
#4) one solution
Step-by-step explanation:
1) x² = -100; x = 10i
2) 5x² = 1; x = ±[tex]\sqrt{1/5}[/tex]
3) 6x² + 6 = 0; x = i²
4) 7(x² + 6) - 42 = 0; x = 0
The equation g=3r represents how much Trevin makes per hour at his job. What is the unit rate?
Answer:
Hope It Help
Brainliest please
Answer:
3
Step-by-step explanation:
The unit rate is a rate with 1 in the denominator. The unit rate for this equation would be how much money he makes in one hour. So, to find the unit rate plugin 1 for r and solve for g. One times three (1*3) is equal to 3; therefore, that is the unit rate.
Si por 3 kilogramos de manzana se pagan $20. ¿Cuánto hay que pagar por 15 kilogramos?
Answer:
$100
Step-by-step explanation:
15÷3=5
20•5=100
Hope this helps
What is the perimeter of the rectangle whose vertices are at (6, 3), (−6, 3), (−6, −1), and (6, −1)?
Given:
The vertices of a rectangle are (6, 3), (−6, 3), (−6, −1), and (6, −1).
To find:
The perimeter of the rectangle.
Solution:
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2-(y_2-y_1)^2}[/tex]
Let the vertices of a rectangle are A(6, 3), B(−6, 3), C(−6, −1), and D(6, −1).
Using the distance formula, we get
[tex]AB=\sqrt{(-6-6)^2-(3-3)^2}[/tex]
[tex]AB=\sqrt{(-12)^2-(0)^2}[/tex]
[tex]AB=\sqrt{144}[/tex]
[tex]AB=12[/tex]
Similarly,
[tex]BC=\sqrt{\left(-6-\left(-6\right)\right)^2+\left(-1-3\right)^2}=4[/tex]
[tex]CD=\sqrt{\left(6-\left(-6\right)\right)^2+\left(-1-\left(-1\right)\right)^2}=12[/tex]
[tex]AD\sqrt{\left(6-6\right)^2+\left(-1-3\right)^2}=4[/tex]
Now, the perimeter of the rectangle is:
[tex]Perimeter=AB+BC+CD+AD[/tex]
[tex]Perimeter=12+4+12+4[/tex]
[tex]Perimeter=32[/tex]
Therefore, the perimeter of the rectangle is 32 units.
please help due todayyy://
Answer:
B. product graph
Step-by-step explanation:
Hope it helps
CarryOnLearning
PLEASE HURRY: On Monday, Florencia's hair was h centimeters long. She got a haircut on Tuesday, so her hair was only 75% of
the length it was on Monday.
Which of the following expressions could represent how many centimeters long Florencia's hair was after the
haircut?
Chose 2 answers:
h(1 - 0.75)
(1 - 75/100)h
3/4h
0.75h
1/4h
Answer:
It seems that you are trying to find the length of hair of Florencia on Tuesday.
Given that length of the hair of Florencia on Monday = h centimeters
On Tuesday, she got hair cut.
So new length of the hair of Florencia on Tuesday = 75% of Monday value
= 75% of (h)
= 0.75* (h)
= 0.75h
Hence final answer is the length of the hair of Florencia on Tuesday is ( 0.75h ) centimeters.
Answer:
3/4h and 0.75h
Step-by-step explanation:
khan
Given DE || BC, find the length of BD.
Answer:
BD = 12.5
Step-by-step explanation:
Full answer in the attachment!!
I suck at math
The math problem is below
Answer:
Brooklyn earns four more dollars than Anna does each hour.
Step-by-step explanation:
So basically in order to get the amount ech of them recieve you would have to divide. So for Anna's since her least given number is 10 hours you would divide how much she earns (256) by how many hours she has been working (10) and you get 25.6
Now for Brooke she is given only one piece of evidence so you would use that she has been working for 26 hours and earns 769.6. So divide her earning by the hour and get 29.6
Subtract each of the answers (29.6-25.6) and you would get 4
Sorry if it doesn't make sense I was trynna rush and give you the answer
Answer:
Brooklyn earns four more dollars than Anna does each hour.
Step-by-step explanation:
The area of the rectangle below is 18 square units and the length is 3 3/4 .What is the width of the rectangle?
Answer:4.8
Step-by-step explanation:18/3.75=4.8
Does this graph represent a function?
would -60 be the opposite of 60?
Answer:
yes,please mark me brainlest
Step-by-step explanation:
Answer:
Yes.
Step-by-step explanation:
A negative number is the opposite of it's positive.
What is the perimiter of a quadrilateral with verticles at (5,2), (10,2), (5,5), and (10,5)
Answer:
55
Step-by-step explanation:
help me please!!! no links 10 points
in persectev i think the answer in bound to be 17/10
Answer:
x=3 y=13
Step-by-step explanation:
now you got x... substitute x value with one of the questions then you get y
-3×3+2y=17
-9+2y=17
2y=17+9
y=26/2
y=13
i hope it's clear this is how elimination method works... this is how i learned.... t☺️❤️
An estate valued at $60 000 is divided among
three daughters Annette, Betty and Carol in the
ratio 1:2:3 respectively.
(a) Calculate the amount each received.
Answer:34 13
Step-by-step explanation:
ffrff
Find the volume of the cylinder. Round your answer to the nearest hundredth.
9514 1404 393
Answer:
1763.01 m³
Step-by-step explanation:
The height of the cylinder will be ...
h = (18 m)sin(60°) = 9√3 m
The volume of the cylinder is ...
V = Bh
where B is the area of the end circle.
B = πr² = π(6 m)² = 36π m²
Then ...
V = (36π m²)(9√3 m) ≈ 1763.01 m³
The volume of the cylinder is about 1763.01 m³.
The measures of the exterior angles of a hexagon are x°x°, 2x°2x°, 5x°5x°, 6x°6x°, 7x°7x°, and 9x°9x°. Solve for x.
Answer:
x = 12°
Step-by-step explanation:
The measures of the exterior angles of a hexagon are x°, 2x°, 5x°, 6x°, 7x°, and 9x°. Solve for x.
The sum of the exterior angles of a polygon sums up to 360
An hexagon is a 6 - sided polygon
(x + 2x + 5x + 6x + 7x + 9x) = 360
30x = 360
Divide both sides by 30
x = 360 / 30
x = 12
Hence, x = 12°
Help me with these questions
Answer:
A is the correct Answer
Step-by-step explanation:
hope that helps
Answer:
igual es lo mismo
Step-by-step explanation:
hope that help
Help! Plz thank you!!!!
Answer:
i do not see a picture or an image of what you need.
Step-by-step explanation:
hiii please help i’ll give brainliest:)
Somebody please help. this is quadratics
Solve each equation by taking square roots.
[tex]1.)6x^2=-90\\2.)b^2-4=-2\\3.)16x^2-7=-6\\4.)10p^2+9=239[/tex]
Answer:
1)
[tex]6x^2=-90\\x^2=-15\\\sqrt{x^2} =\sqrt{-15} \\x=i\sqrt{15} ,-i\sqrt{15}[/tex]
2)
[tex]b^2-4=-2\\b^2=2\\\sqrt{b^2} =\sqrt{2} \\b=\sqrt{2} ,-\sqrt{2}[/tex]
3)
[tex]16x^2-7=-6\\16x^2=1\\x^2=\frac{1}{16} \\\sqrt{x^2} =\sqrt{\frac{1}{16}} \\x=\frac{1}{4} ,-\frac{1}{4}[/tex]
4)
[tex]10p^2+9=239\\10p^2=230\\p^2=23\\\sqrt{p^2} =\sqrt{23} \\p=\sqrt{23},-\sqrt{23}[/tex]
BRAINLISRST AND EXTRA POINTS I NEEDS I HELP
A study found that a car
depreciates 12% per year. If the
car was purchased for $15,000, how
much is it worth after 4 years?
Answer:
7800
Step-by-step explanation: :)