If the function f(2x + 3) = 3x- 8, find f -¹(x)​

Answers

Answer 1

Answer:

(2x + 35)/3

Step-by-step explanation:

f(2x + 3) = 3x - 8

= 3(2x)/2 - 8

= 3(2x + 3 - 3)/2 - 8

= 3(2x + 3)/2 - 3(3)/2 - 8

= ( 3(2x + 3) - 25)/2

Therefore, f(x) = (3x - 25)/2

Let f(x) = (3x - 25)/2 = y

Therefore,

x = (2y + 35)/3 = f(y)

Hence,

f-¹(x) = f(y) = (2y + 35)/3

Just by merely replacing y,

f-¹(x) = (2x + 35)/3

Answer 2

Answer:

Step-by-step explanation:

[tex]let~g(x)=2x+3,~ then~f\circ g(x)=f(g(x)=3x-8\\\\[/tex]

lets assume that f(x) is a line, so f(x)=mx+b

[tex]f(g(x))=m(2x+3)+b=2mx+3m+b=3x-8[/tex]

the follow equation system results:

[tex]2m=3 \\ 3m+b=-8[/tex]

[tex]m=\frac{3}{2}\\\\b=-\frac{25}{2}[/tex]

finally:

[tex]y=f(x)=\frac{3}{2}x-\frac{25}{2}[/tex]

now is time to calculate the inverse function:

[tex]y=\frac{3}{2}x-\frac{25}{2}=>2y+25=3x=>x=\frac{2}{3}y+\frac{25}{3}[/tex]

so

[tex]f^{-1}(x)=\frac{2}{3}x+\frac{25}{3}[/tex]


Related Questions

a net ball team won 24 out of 40 matches. what percentage of the match did the team win​

Answers

Answer:

60%

Step-by-step explanation:

[tex]percentage = \frac{24}{40} \times 100\% \\ = 60\%[/tex]

[tex]\Huge{\textbf{\textsf{{\purple{Ans}}{\pink{wer}}{\color{pink}{:}}}}} \\ [/tex]

[tex]percentage = \frac{24}{40} \times 100\% \\ = 60\%[/tex]

so answer is 60%

find the value of x. round your answer to the nearest tenth.

Answers

9514 1404 393

Answer:

  x ≈ 13.7

Step-by-step explanation:

The relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(58°) = 22/x

  x = 22/tan(58°) ≈ 13.747

The value of x is about 13.7 units.

For f(x) = 3x +1 and g(x) = x - 6, find (f- g)(x).
A. K - 3x-7
B. 3x - 17
c. -x + 3x + 7
D. -x + 3x - 5
SUBND

Answers

Answer:

c. -x + 3x + 7  = 2x+7

Step-by-step explanation:

f(x) = 3x +1 and g(x) = x - 6

f-g = 3x +1 - ( x - 6)

Distribute the minus sign

     = 3x+1 - x+6

     = 2x +7

how to find the area of a circle with the diameter 21​

Answers

Answer:

A ≈ 346.36

Step-by-step explanation:

To find the answer, you must use the formula, A=πr²

Since only the diameter was provided, you need to divide it by 2 to find the radius. 21 divided by 2 equals 10.5, so that will be your radius.

Another formula that can be used while using only the diameter would be A= 1/4 π d²

Which table represents a linear function?

Answers

Answer:

Option 3 (C)

Step-by-step explanation:

It is the only one that changes the same amount every time ( times 2 )

Suppose that for a certain company ​C(x)=35x+300,000 represents the total cost​ function, and ​R(x)=75x represents the total revenue function. Find the​ total-profit function and​ break-even point.
Which of the following functions represents the​ total-profit function?
A) 40x-300,000
B) 40x+300,000
C) 110x+300,000

Answers

Answer:

40x - 300,000

7,500

Step-by-step explanation:

profit  = revenue - cost

p(x) = 75x - (35x + 300,000)

p(x) = 40x - 300,000

Break even is when profit is zero

40x - 300,000 = 0

40x = 300,000

x = 7,500

The functions that represents the​ total-profit function would be p(x) = 40x - 300,000. so the correct option is A.

What is a function?

Function is a type of relation, or rule, that maps one input to specific single output.

Given that for a certain company ​C(x) =35x+300,000 represents; the total cost​ function, and ​R(x)=75x represents the total revenue function.

WE can calculate the profit by the following formula;

Profit  = revenue - cost

p(x) = 75x - (35x + 300,000)

p(x) = 40x - 300,000

Now Break even is when profit is zero,

40x - 300,000 = 0

40x = 300,000

x = 7,500

Hence, the break-even point is 7500.

Therefore,  the functions that represents the​ total-profit function would be p(x) = 40x - 300,000. so the correct option is A.

Learn more about function here:

https://brainly.com/question/2253924

#SPJ2

Sylvia is twice as old as her brother. Find their ages now if in seven years her brother will be what her age was last year.

Answers

Answer:

Sylvia=16

brother=8

Step-by-step explanation:

8+7=15

16-1=15

D(p) is the​ price, in dollars per​ unit, that consumers are willing to pay for p units of an​ item, and​ S(p) is the​ price, in dollars per​ unit, that producers are willing to accept for p units. Find the equilibrium point. ​D(p)=3500−20p​, ​S(p)=2500+5p
What are the coordinates of the equilibrium​ point?

Answers

Answer:

(40,2700)

Step-by-step explanation:

Given

[tex]D(p)=3500-20p[/tex]

[tex]S(p)=2500+5p[/tex]

Required

The equilibrium point

To do this, we have:

[tex]D(p) = S(p)[/tex]

So, we have:

[tex]2500+5p = 3500-20p[/tex]

Collect like terms

[tex]20p+5p = 3500-2500[/tex]

[tex]25p = 1000[/tex]

Divide both sides by 25

[tex]p = 40[/tex]

Substitute [tex]p = 40[/tex] in [tex]D(p)=3500-20p[/tex]

[tex]D(40) = 3500 - 20 * 40[/tex]

[tex]D(40) = 2700[/tex]

Hence, the coordinates of the equilibrium is: (40,2700)

What is 2/6 in simplest form? Find the greatest common factor of 2 and 6 and divide by that number. *

Answers

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

2 = 2 × 1

6 = 2 × 3

GCF = 2

[tex]\frac{2 /2 }{6/2} =\frac{1}{3}[/tex]

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]\boxed{\frac{1}{3}}[/tex]

»»————- ★ ————-««  

Here’s why:  

We would take the GCF of the two numbers in order to simplify.

⸻⸻⸻⸻

[tex]\boxed{\text{Simplify:}}\\\\\frac{2}{6}\\\\\boxed{\text{Finding the Factors:}}\\\\2: 2\\6 : 2,3\\\\\boxed{\text{The GCF would be 2.}}\\\\\frac{2}{6} =\frac{2/2}{6/2}=\boxed{\frac{1}{3}}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

A right cone has a radius of 5 cm and an altitude of 12 cm. Find its volume.


A)

300 cm3

B)

64.1 cm3

C)

942.5 cm3

D)

314.2 cm3

Answers

Answer:

D. V=314.2cm³

Step-by-step explanation:

The volume of the cone is:

V=pi×r²×h/3=pi×5²×12/3=100×pi=314.2cm³

Answer: D) 314.2 [tex]cm^3[/tex]

Step-by-step explanation:

The formula for finding the volume of a right cone is [tex]V=\pi r^2\frac{h}{3}[/tex]

r is the radius and h is the height/altitude.

We can sub these values in and solve

[tex]V=\pi (5^2)(\frac{12}{3} )\\V=\pi (25)(4)\\V=100\pi[/tex]

Let's sub in 3.14 for [tex]\pi[/tex] since that is a close estimate

[tex]V=(100)(3.14)\\V=314[/tex]

The volume is about 314.

Our closest answer to that is D so that is the correct choice.


I was wondering if anyone could answer this :)

Answers

Step-by-step explanation:

The sides with the variables are the same length, so make them equal.

x+2=2x-3

Get x alone on one side.

5=3x

Simplify.

5/3 = x

Answer:

5

Step-by-step explanation:

x+2 = 2x-3

+3 +3

x+5 = 2x

-x -x

x=5

Hope this helps! :)

Hurry which one ITS NOT 270

A.84
C.128
D.540

Answers

Answer:

84 cm^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh where b is the length of the base and h is the height

A = 1/2 ( 5+9) * 12

A = 1/2 (14) * 12

A =84

A laptop company claims up to 8.1 hours of wireless web usage for its newest laptop battery life. However, reviews on this laptop shows many complaints about low battery life. A survey on battery life reported by customers shows that it follows a normal distribution with mean 7.5 hours and standard deviation 27 minutes. (a) What is the probability that the battery life is at least 8.1 hours

Answers

Answer:

0.0918 = 9.18% probability that the battery life is at least 8.1 hours.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean 7.5 hours

This means that [tex]\mu = 7.5[/tex]

Standard deviation 27 minutes.

An hour has 60 minutes, which means that [tex]\sigma = \frac{27}{60} = 0.45[/tex]

What is the probability that the battery life is at least 8.1 hours?

This is 1 subtracted by the p-value of Z when X = 8.1. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{8.1 - 7.5}{0.45}[/tex]

[tex]Z = 1.33[/tex]

[tex]Z = 1.33[/tex] has a p-value of 0.9082.

1 - 0.9082 = 0.0918

0.0918 = 9.18% probability that the battery life is at least 8.1 hours.

Find the Value of x from the angles

Answers

[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]

The value of [tex]x°[/tex].

[tex]\sf \bf {\boxed {\mathbb {SOLUTION :}}}[/tex]

[tex]\longrightarrow{\blue{ x°\:=\:35° }}[/tex] 

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]

We know that,

[tex]\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}[/tex]

➪ [tex]x°[/tex] + 125° + 20° = 180°

➪ [tex]x°[/tex] + 145° = 180°

➪ [tex]x°[/tex] = 180° - 145°

➪ [tex]x°[/tex] = 35°

Therefore, the value of [tex]x°[/tex] is 35°.

Now, the three angles of the triangle are 35°, 125° and 20°.

[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY:}}}[/tex]

✒ 35° + 125° + 20° = 180°

✒ 180° = 180°

✒ L. H. S. = R. H. S.

Hence verified.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]

Double a number and subtract nine. algebraic expression

Answers

Answer:

2y - 9

Step-by-step explanation:

number = y

2 × y - 9

2 × y can be simplified to 2y.

2y - 9

. Seja (G, ·) um grupo tal que para todo x ∈ G temos x
2 = eG. Mostre
que G ´e abeliano.

Answers

13 25 76 yah yeet averse a

The symbols for elements with accepted names Group of answer choices consist of a single capital letter consist of a capital letter and a small letter consist of either a single capital letter or a capital letter and a small letter no answer is correct

Answers

Answer:

consist of either a single capital letter or a capital letter and a small letter.

Step-by-step explanation:

A chemical reaction can be defined as a reaction in which two or more atoms of a chemical element react to form a chemical compound.

In Chemistry, a chemical element can be defined as any pure substance that is typically made up of only atoms and cannot be broken down into simpler substances through chemical processes. Thus, the atomic number (the number of protons in the nuclei of an atom) of a particular chemical element distinguishes from other chemical elements.

Generally, all chemical elements are denoted or represented by a symbol, which may either be single capital letter or a capital letter and a small letter.

This ultimately implies that, the symbols for elements with accepted names consist of either a single capital letter or a capital letter and a small letter. For example, the symbol for sodium is Na, copper is Cu, carbon is C, oxygen is O, iron is Fe, nitrogen is N, magnesium is Mg, potassium is K, argon is Ag, hydrogen is H, helium is He, phosphorus is P, etc.

4x-2 3x+14 how do I find x?

Answers

Answer:

x = 16

Step-by-step explanation:

4x - 2 = 3x + 14

4x - 2 + 2 = 3x + 14 + 2

4x = 3x + 16

4x - 3x = 3x - 3x + 16

x = 16

show how to solve 1/4 (4 + x) = 4/3



pls solve for 2 brainliest

Answers

Simplify
1
4
(
4
+
x
)
4
1

(4+x) to
4
+
x
4
4
4+x

.
4
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4
=
4
3
4
4+x

=
3
4



2 Simplify
4
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4
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4+x

to
1
+
x
4
1+
4
x

.
1
+
x
4
=
4
3
1+
4
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=
3
4



3 Subtract
1
1 from both sides.
x
4
=
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3

1
4
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=
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4

−1

4 Simplify
4
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1
3
4

−1 to
1
3
3
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.
x
4
=
1
3
4
x

=
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5 Multiply both sides by
4
4.
x
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3
×
4
x=
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×4

6 Simplify
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3
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x
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4
3
x=
3
4

One of the legs of a right triangle measures 15 cm and the other leg measures 6 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.

Answers

Answer:

16.2 cm

Step-by-step explanation:

use the pythagoran theorem

a² + b² = c²

15² + 6² = c²

225 + 36 = c²

261 = c²

Take the square root of both sides

16.1554944214 = c

Rounded

16.2 cm

Really struggling and stressing out. Anyone mind helping?

Answers

Answer:

it should be 314.16, so I would choose 314

In a political science class, the teacher gives a midterm exam and a final. The association between midterm and final scores is linear. The summary statistics are shown below. Midterm Mean=75, Midterm Standard Deviation=10 Final Mean=75, Final Standard Deviation=10 r=0.8 According to the regression equation, for a student who gets 85 on the midterm (one standard deviation above average) what is the predicted final exam grade?

Answers

Answer:

The predicted final exam grade is 83

Step-by-step explanation:

Given

[tex]\bar x = 75[/tex] -- midterm mean

[tex]\sigma_x = 10[/tex] --- midterm standard deviation

[tex]\mu =75[/tex] --- final mean

[tex]\sigma = 10[/tex] --- final standard deviation

[tex]r = 0.8[/tex]

Required

The predicted final grade of student who score 85 in midterm

The prediction is represented as:

[tex]y = \alpha + \beta x[/tex]

Where:

[tex]\beta = r * \frac{\sigma}{\sigma_x}[/tex]

[tex]\beta = 0.8 * \frac{10}{10}[/tex]

[tex]\beta = 0.8 * 1[/tex]

[tex]\beta = 0.8[/tex]

and

[tex]\alpha = \mu - r * \bar x[/tex]

[tex]\alpha = 75- 0.8 * 75[/tex]

[tex]\alpha = 75- 60[/tex]

[tex]\alpha = 15[/tex]

So:

[tex]y = \alpha + \beta x[/tex]

[tex]y = 15 + 0.8x[/tex]

For a student who gets 85, the prediction is:

[tex]y = 15 + 0.8*85[/tex]

[tex]y = 15 + 68[/tex]

[tex]y = 83[/tex]

Let XX be a random variable that is equal to the number of heads in two flips of a fair coin. What is \text E[X^2]E[X 2 ]

Answers

Answer:

Step-by-step explanation:

From the given information, it is likely that the random variable(X) have the values below:

Let head be H

Let tail be T

So;

X(HH) = 2;

X(HT) = 1;

X(TH) = 1;

X(TT) = 0

The distribution can now be computed as:

[tex]p(X= TT) = \dfrac{1}{4}[/tex]

[tex]p(X=TH) = \dfrac{1}{4}[/tex]

[tex]p(X=HT) = \dfrac{1}{4}[/tex]

[tex]p(X=HH)= \dfrac{1}{4}[/tex]

Now, the expected value that is equivalent to the number of heads when the coin is flipped twice is:

[tex]E(X) = p(TT)*X(TT)+p(TH)*X(TH)+p(HT)*X(HT)+p(HH)*X(HH)[/tex]

[tex]E(X) = \dfrac{1}{4}\times 0 + \dfrac{1}{4}\times 1 + \dfrac{1}{4}\times 1 + \dfrac{1}{4}\times 2[/tex]

[tex]E(X) = 0 + \dfrac{1}{4}+ \dfrac{1}{4} + \dfrac{1}{2}[/tex]

[tex]E(X) =\dfrac{1+1+2}{4}[/tex]

[tex]E(X) =\dfrac{4}{4}[/tex]

E(X) = 1

[tex]E(X^2) = p(TT)*X(TT)^2+p(TH)*X(TH)^2+p(HT)*X(HT)^2+p(HH)*X(HH)^2[/tex]

[tex]E(X^2) = \dfrac{1}{4}\times 0^2+ \dfrac{1}{4}\times 1^2 + \dfrac{1}{4}\times 1^2 + \dfrac{1}{4}\times 2^2[/tex]

[tex]E(X^2) = 0 + \dfrac{1}{4}+ \dfrac{1}{4} + \dfrac{4}{4}[/tex]

[tex]E(X^2) =\dfrac{1+1+4}{4}[/tex]

[tex]E(X^2) =\dfrac{6}{4}[/tex]

[tex]E(X^2) =1.5[/tex]

Finally; To compute E²[X]

E²[X] = E[X]²

E²[X] = 1²

E²[X] = 1

Find the surface area of the square pyramid 8mm 6mm

Answers

Answer:

136 mm²

Step-by-step explanation:

[tex]A=a^{2} +2a\sqrt{\frac{a^{2} }{4} } +h^{2}[/tex]

[tex]A=6^{2} +2(6)\sqrt{\frac{6^{2} }{4} } +8^{2}[/tex]

[tex]A=36 +12\sqrt{\frac{36 }{4} } +64[/tex]

[tex]A=36 +12\sqrt{9 } +64[/tex]

[tex]A=36 +12(3)+64[/tex]

[tex]A=36 +36+64[/tex]

A = 136

Complete the remainder of the table for the given function rule:
Y=3x-5
[X] -6 -3 0 3 6
[Y] -23 ? ? ? ?

Answers

answer is

(Y)=-23,-14, -5,4,13

hope this will help you

given sin x =-4/5 and x is in quadrent 3, what is the value of tan x/2

Answers

Answer:

We can write sin x in terms of tan x/2 using the formula:

⇒ sin x = (2 tan (x/2)) / (1 + tan2(x/2))

Therefore, using the above formula, we can find the values of tan x/2 by putting the value of sin x.

⇒ -4/5 = (2 tan (x/2)) / (1 + tan2(x/2))

Now, if we replace tan (x/2) by y, we get a quadratic equation:

⇒ 0.8y2 + 2y + 0.8 = 0

⇒ 2y2 + 5y + 2 = 0

By using the quadratic formula, we get y = -0.5, -2

Hence, the value of tan (x/2) = -0.5, -2

Now, we have two solutions of tan (x/2).

Now, let's check for the ideal solution using the formula tan x = (2 tan (x/2)) / (1 - tan2(x/2)).

For tan (x/2) = -0.5:

⇒ tan x = 2(-0.5) / 1 - (-0.5)2 = -4/3

It is also given that x lies in the third quadrant. We know that tan is positive in the third quadrant, and here we get tan x = -4/3 which is negative.

Hence, we can say that tan (x/2) = -0.5 is not a correct solution. Hence it is rejected.

Now let's check for tan (x/2) = -2.

⇒ tan x = 2(-2) / 1 - (-2)2 = 4/3

Here, we get tan x = 4/3 which is positive.

Hence, we can say that tan (x/2) = -2 is a correct solution.

Find the amount of money in an account after 9 years if $2,600 is deposited at 8% annual interest compounded monthly

Answers

Answer:

5328.78

Step-by-step explanation:

formula:

[tex]P(1+\frac{i}{n})^{n*t}\\2600(1+\frac{.08}{12})^{12*9}\\\\2600(1.006667)^{108}=5328.77861305[/tex]

this rounds to 5328.78

Draw a model to represent each expression.

Answers

Answer:

OK

Step-by-step explanation:

The first screenshot is for #7 and the second screenshot is for #8

There are 20 rows of seats on a concert hall: 25 seats are in the 1st row, 28 seats on the 2nd row, 31 seats on the third row, and so on. How many seats are in the last row?

Answers

Answer:

It is a sequence topic.

The general term of the sequence is 25+3(n-1) where n is the number of the term (here it is the row no.)

So the 20th term is the term with n=20. Substitute n=20 into the above general term, we will get 25+3(20-1) .

Please go on by yourself to work out the answer.

If the value of a in the quadratic function f(x) = ax^2 + bx + c is -2, the function will_______.
a open down and have a minimum
b open down and have a maximum
c open up and have a maximum
d open up and have a minimum

Answers

Answer:

b open down and have a maximum

Step-by-step explanation:

A negative value for a will make the quadratic function open down

A downward facing parabola will have a maximum

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