F (x) = x+1
——
x+8

F-1(-7) =

F (x) = X+1 X+8F-1(-7) =

Answers

Answer 1

The value of  [tex]f^{-1}(-7)[/tex] is given by -57/8.

Given that:-

f(x) = (x + 1)/(x + 8)

We have to find the value of [tex]f^{-1}(-7)[/tex].

Let f(x) = y

Hence,

[tex]f^{-1}(y) = x[/tex]

Now, we will find the inverse of the given function.

Hence, we can write,

y = (x + 1)/(x + 8)

We can rewrite it as:-

y = (x + 8 - 7)/(x + 8) = (x + 8)/(x + 8) - 7/(x + 8) = 1 - 7/(x + 8).

1 - y = 7/(x + 8)

x + 8 = 7/(1 - y)

x = 7/(1 - y) - 8

x = 7/(1 - y) - 8(1 - y)/(1 - y)

x = (7 - 8(1 - y))/(1 - y)

x = (7 - 8 + 8y)/(1 - y)

[tex]f^{-1}(y) = \frac{(8y - 1)}{( 1 - y)}[/tex]

Replacing y with x in the above equation, we can write,

[tex]f^{-1}(x) = \frac{(8x - 1)}{( 1 - x)}[/tex]

The above equation is the inverse of the function.

Putting x = -7 in the above equation, we get,

[tex]f^{-1}(-7) = \frac{(8(-7) - 1)}{( 1 - (-7))}[/tex]

= (-56 - 1)/ (1 + 7) = - 57/8

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Related Questions

Divide: (u² - 3u - 5) ÷ (u+3).

Answers

Answer:

u - 6 + 13/u+3

Step-by-step explanation:

Have a good day :)

Please answer question 5 and 6.
5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).
6.Graph the function.

Answers

By graphing both equations and finding where the graphs intercept, we can see that the solution for the system is x = 3.

For which value of x both functions give the same output?

Here we have the functions:

f(x) = -2x +4

g(x) = 2x - 8

We want to find the value of x such that:

f(x) = g(x).

If we graph the two functions, we just need to identify the x-value of the point where the functions intercept.

The graph can be seen in the image below.

There we can see that the graphs intercept at (3, -2), meaning that the solution of:

f(x) = g(x) is x = 3.

Which is the same thing that if we write:

f(x) = g(x)

-2x + 4 = 2x - 8

4x = 12

x = 12/4 = 3

x = 3

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What are some similarities between sales tax and hotel tax? Select all that apply. Multiple select question. cross out A) Both are an additional amount one must pay. cross out B) Both must be paid in advance when you make a hotel reservation. cross out C) Both are based on a percentage of the original cost. cross out D) Both the sales tax and the hotel tax are equal when you stay in a hotel. cross out E) Both represent a guest fee that hotels charge their customers.

Answers

Some of the similarities between sales tax and hotel tax include the following:

B) Both must be paid in advance when you make a hotel reservation.

C) Both are based on a percentage of the original cost.

What is taxation?

Taxation can be defined as the involuntary fees that are levied on individuals or business firms by the government of a particular country, so as to generate revenues that can be used to fund public projects, institutions and activities.

The types of tax.

In Economics, there are different types of tax that are levied on individuals or business firms by the government and these include the following:

Hotel taxSales taxProperty taxIncome tax

In conclusion, we can reasonably infer and logically deduce that both sales tax and hotel tax must be paid in advance when making a hotel reservation in the United States of America.

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the graph of g(x) = (x + 2)2 is a translation of the graph of f(x) ___ by ___ units

Answers

The provided translated function, f(x), shifts left by two units on the horizontal axis.

Describe translation.

One type of transformation is translation. Both the scaling calculation and the compression calculation are performed using it. This approach wouldn't change the object's form or shape.

The given graph equation for the translation, as per the query, is g(x) = (x + 2)²

The translation of the given quadratic function is: y = g(x) = (x + 2)²

Consequently, the parent function is written as y = g(x) = x2.

Additionally, the vertex should be known when graphing the translated function:

a(x - h)2 + k = y = g(x);

where the parent function is (0, 0) and the vertex values are (h, k).

(h, k) = is the vertex for the function that is provided (-2, 0)

This information causes the translation function to move the graph two units to the left.

Horizontal translation is the name given to the translation.

As a result, the given function, f(x), shifts horizontally, or left, by 2 units.

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The water pressure on a submerged object is given by P = 64d, where P is the pressure in pounds per square foot, and d is the depth of the object in feet.
a. solve the formula for d.


b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.

Answers

a. Solving for 'd' as the subject of formula gives d = P/64

b. The depth of a submerged object if the pressure is 672 pounds per square foot is 10. 5 feet

What is a function?

A function can be defined as an expression, law or rule that shows the relationship between two variables.

These variables are namely;

Independent variableDependent variable

Given the function as;

P = 64d

Where;

P is the pressure in pounds per square foot d is the depth of the object in feet

Now, let's make the variable 'd' the subject of formula

Divide both sides of the equation with the coefficient of the variable 'd' which is 64. This is done so that the variable stands alone.

We have;

P/64 = 64d/64

d = P/ 64

If the pressure, P equals  672 pounds per square foot

Substitute the value of the variable into the formula, we have;

d = P/64

Then,

d = 672/64

Find the quotient

d = 10. 5 feet.

Thus, the value is 10. 5 feet

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For
f(x) = 3x and g(x) = x4 + 2, find the following.

(b)(g ∘ f)(x)

Answers

I think the answer is b(f(x))=10+16x

Jackie deposited $500 in an account for 10 years at 6% interest.How much money did she earn?

Answers

After 10 years, the money dis she earn is $800 with the interest of 6%.

Interest:

Interest is the amount for a particular principal amount of money at some rate of interest.

Given,

Jackie deposited $500 in an account for 10 years at 6% interest.

Here we need to find the money did she earned.

We know that, the interest for the amount is 6%.

So, the amount after 10 years is,

=> 500 x (6/100) x 10

=> 30 x 10

=> 300

Therefore, the interest amount is 300.

So, the total amount she will receive after 10 years is,

=> 500 + 300

=> 800

Therefore, she will earn $800 after 10 years.

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3+2x1/10+4x1/1000 in standard form

Answers

Answer:

3.204

Step-by-step explanation:

3 + 0.2 +  0.004

Help giving 100 points!!

Answers

find 2 points. for me i would choose (0,4) and (2,-2). the formula for gradient is (y1-y2)/(x1-x2). so it would be (4--2)/(0-2)=-3.
slope is -3!!

Given the coordinates of two points on the line, use the slope formula to determine the slope of the line. The slope formula is the quotient of the difference in y-values and the difference in x-values.

4) A done relevant a bomb witha velocity of 20m/s horizotally from a hieght of 50m the ground clculate time

Answers

The time taken for the bomb to fall to the ground is 2.5 sec.

What is a projectile motion?In this case, the bomb is moving like a projectile and has projectile motion.A body can only move in a projectile motion when it is affected by gravity. A body moving as a projectile is a projectile motion.We model a particle as having zero acceleration (and thus constant velocity) when it is projected horizontally.The particle in this instance has a zero initial velocity and a constant downward vertical acceleration of g.

Given:

Height (h) = 50 m

Horizontal velocity(u) = 20 m/s

Time (t) =?

We use, h = ut to determine the time

50 = 20 × t

Divide both sides by 20,

t = 50 / 20

t = 5/2 s ≅ 2.5 sec

Thus, the bomb will take 2.5 sec to land on the ground.

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The complete question is: "A bomb is projected horizontally downward from a height of 50m with a velocity of 20m/s. Calculate the time taken for the bomb to fall to the ground."

The ages of the signers of the Declaration of Independence are shown. (Age is approximate since only the birth year appeared in the source, and one has been omitted since his birth year is unknown.) Construct a grouped frequency distribution and a cumulative frequency distribution for the data, using 7 classes.

Answers

Answer:

Step-by-step explanation:

The ages of the signers of the Declaration of Independence are shown. (Age is approximate since only the birth year appeared in the source, and one has been omitted since his birth year is unknown.) Construct a grouped frequency distribution and a cumulative frequency distribution for the data using 7 classes. Limits Boundaries 27-33 26.5-33.5 7 41 54 47 40 39 35 50 37 49 42 70 32 44 52 39 50 40 30 34 69 39 45 33 42 44 63 60 27 42 34 50 42 52 38 36 45 35 43 48 46 31 27 55 63 46 33 60 62 35 46 45 34 53 50 50 34-40 33.5-40.5 14 41-47 40.5-47.5 15 48-54 11 47.5-54.5 54.5-61.5 55-61 3 62-68 61.5-68.5 3 69-75 68.5-75.5 55

Peter enrolled $80,000 worth of debt with National Debt Relief. Peter’s fee for the service is 20% of the enrolled debt. How much is Peter’s fee?*

Answers

Answer:

16000

Step-by-step explanation:

slove using elimination10x + 8 y = 20 10 x + 2 y = -10

Answers

we have

10x + 8 y = 20 ------> equation A

10 x + 2 y = -10 ​------> equation B

Multiply equation A by -1 both sides

so

-10x-8y=-20 -----> new equation A

Adds new equation A and equation B

\

--------------------

-8y+2y=-20-10

-6y=-30

y=5

Find the value of x

substitute the value of y in equation A or equation B or new equation A

10x + 8(5) = 20

10x+40=20

10x=20-40

10x=-20

x=-2

therefore

the solution is the ordered pair (-2,5)

are y=5x-4 and y=-5x+5 parallel or perpendicular

Answers

Answer:

Perpendicular

Step-by-step explanation:

It js seems right. i did one very similar and the awnser was Perpendicular

2(4x-3)-8-2x=4


someone please help me with this, fast

Answers

....................... .x=3

thank u plssssssss do it

Answers

Answer:

63

Step-by-step explanation:

23 + 94  = 117

180 degrees ( sum of all angles in a triangle)

180 - 117 = 63

You need 600 mL of a 20% alcohol solution. On hand, you have a 60% alcohol mixture. How much of the 60% alcohol mixture and pure water will you need to obtain the desired solution?

Answers

Answer:  there 3,000 total milliliters accourding to my calculation

there for your looking for 60% so your answer should be 1800 since 60% of 3,000 is 1800

1800 ML = 60%

Step-by-step explanation:

the math is above

Missed the class now lost

Answers

substitute the given values in the formula of (BAC) we have

[tex]48\cdot3.2\colon160-3\cdot0.015[/tex]

Remember

Applying PEMDAS

P ----> Parentheses first

E -----> Exponents (Powers and Square Roots, etc.)

MD ----> Multiplication and Division (left-to-right)

AS ----> Addition and Subtraction (left-to-right)

so

step 1

solve the multiplication

48*3.2=153.6

substitute

[tex]153.6\colon160-3\cdot0.015[/tex]

step 2

Solve the division

153.6/160=0.96

substitute

[tex]0.96-3\cdot0.015[/tex]

step 3

solve the multiplication

3*0.015=0.045

substitute

[tex]0.96-0.045[/tex]

step 4

solve the subtraction

0.96-0.045=0.915

At a speed of 7.2 km per 2 hours how far can you drive for 7 hours

A. 357
B.358.50
C.359

Answers

Answer:

Step-by-step explanation:

divide 7.2 by 2 so you have an hourly rate. Then you have 3.6, multiply that by 7 to get 25.2. Assuming its not in km cause that wouldn't make sense you would just have to convert it into whichever unit it would take

what is the slope of the line?

Answers

Answer:

slope :

[tex] \dfrac{y2 -y1}{x2 - x1} [/tex]

[tex] \dfrac{3 - 1}{0 - 1} [/tex]

[tex] \dfrac{2}{ - 1} [/tex]

[tex] - 2[/tex]

Correct option - F

a ferry charges $40 for each car and $8.50 for each person in the car. Does this situation represent a function?

Answers

Yes, This situation represent a function.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The cost of each car = $40

The cost of each person = $8.50

Let the number of car = x

The number of persons in a car = z

Then, Total cost of car = $40x

Total cost of persons in car = $8.50z

So, Total cost (y) = $40x + $8.50z

Thus, The function for this situation is;

y = $40x $8.50z

Clearly, This is a linear function with three variable.

Thus, This situation represent a function.

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Find the median 6, 13, 15, 9, 6, 11, 14

Answers

The median of a set of numbers is the number that appears in the middle after arranging the set of numbers in ascending or descending order

Step 1:Arrange the given values in ascending order.

Step 2. Find the number of observations in the given set of data. It is denoted by n.

Step 3. If n is odd, the median equals the [(n+1)/2]th observation.

The set of numbers given in the question are

[tex]6,13,15,9,6,11,14[/tex]

By rearranging the numbers in ascending order, we will have

[tex]6,6,9,11,13,14,15[/tex]

The numbers are 7 in number that is

[tex]N=7[/tex]

Since the value of N is an odd number, then the median will be calculated using the formula below

[tex]\begin{gathered} \text{Median}=\frac{(n+1)}{2}th \\ \text{Median}=\frac{7+1}{2}th\text{ number} \\ \text{Median}=\frac{8}{2}th\text{ number} \\ \operatorname{median}=4th\text{ number} \end{gathered}[/tex]

The 4th number after arranging the set of numbers is

[tex]=11[/tex]

Hence,

The median of the set of numbers in the question = 11

Check all the angles that are congruent to angle 5.

Answers

The angles congruent to ∠5 are as follows:

∠8∠1∠4∠9∠12

How to find angles in parallel lines?

According to the diagram, line l, m and n are parallel lines.

Therefore, when parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertical opposite angle etc.

Hence, the angles that are congruent to ∠5 can be solved as follows:

∠5 ≅ ∠8 (vertically opposite angles)

Vertically opposite angles are congruent.

∠5 ≅ ∠1 (corresponding angles)

Corresponding angles are congruent.

∠5 ≅ ∠4 (alternate angles)

Alternate angles are congruent.

∠5 ≅ ∠9 (corresponding angles)

∠5 ≅ ∠12 (alternate exterior angles)

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Write an equation for the quadratic graphed below:
x-intercepts: (-3,0) and (-1,0); y-intercept: (0,-2)

Answers

The equation for the quadratic graphed as x-intercepts: (-3,0) and (-1,0); y-intercept: (0,-2) can be written as y = -1/2 (x+3)(x+1)

Which of these equations is quadratic?

An equation of the second degree, or one with at least one squared term, is a quadratic equation. The equation in standard form is written as ax2 + bx + c = 0, where a, b, and c are numerical coefficients that are constants, and x is an unknown variable.

The initial constant, “a,” cannot be 0, and this is an unbreakable rule.

How do you translate a graph into some equation?

In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change.

Thereafter draw a sloping triangle connecting the two spots you find on the line.

If the x intercepts are -3 and -1, then the factored form is y = a(x + 3)(x + 1). In order to find "a", we plug in the data point (x, y) of (0, -2) so:

-2 = a(0+3)(0+1)

-2 = 4a

a = -1/2

So the equation can be written as y = -1/2 (x+3)(x+1)

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Can someone please help with this



Answers

Answer:

x = 8

y = 8

Step-by-step explanation:

The two equations are:

x + y = 16    (1)

x = y           (2)

Since x = y substitute for y in terms of x in (1):
x + x = 16

2x = 16

2x/2 = 16/2

x = 8

y = 8

What system of linear inequalities is shown in the graph?

Answers

The system of inequalities is:

y < -4*x + 1

y ≥ (1/2)*x + 1

Which system of linear equations is graphed here?

Here we can see two lines, one dashed that passes through (0, 1) and (-1, 5), then the slope is:

s = (5 - 1)/(-1 - 0) = -4

And the y-intercept is 1, then the inequality is:

y < -4*x + 1

The other line is solid, and the shaded region is above the line.

This line passes through (0, -1) and (2, 0), then the slope is:

s = (0  + 1)/(2 - 0) = 1/2

So the inequality is:

y ≥ (1/2)*x + 1

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The numerator of a rational number is 4 less than its denominator. If I is added to both its numerator and denominator, it becomes 2/3 Find the rational number.​

Answers

The required rational number is 7/11.

let the denominator be x.      

and since we are given that the numerator of a rational number is 4 less than its denominator, the numerator will be x-4.

working on the given condition, i.e. If I is added to both its numerator and denominator, it becomes 2/3

(x-4+1)/(x+1) = 2/3

further solving it by cross multiplication we get,

3(x-4+1)=2(x+1)

=> 3(x-3)=2x+2

=> 3x-9=2x+2

=> 3x-2x=9+2

=> x=11

=> x= 11 (denominator)

we know the numerator is 4 less than the denominator i.e.

11-4=7

thus the required fraction will be 7/11.

What are rational numbers?

A rational number is-" one that can be stated mathematically as the ratio or fraction p/q of two integers, p and q, which must both be non-zero".

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One Serving of pancakes takes 2/3 cups of milk how many cups of milk with 24 servings for pancakes required

Answers

Answer:

Step-by-step explanation:

Given that:-

Since, Serving of 1 pancakes takes 2/3 cups of milk

Hence, serving of 24 pancakes takes (2/3)*24

                                                    =48/3

                                                   =16

So that; 16 cups of milk are required for serving of 24 pancakes.

Answer:

16 cups of milk

Step-by-step explanation:

Make a proportion

[tex]\frac{serrvings}{cups of milk}[/tex] = [tex]\frac{servings }{cups of milk}[/tex]

[tex]\frac{1}{\frac{2}{3} }[/tex] = [tex]\frac{24}{x}[/tex]  cross multiply and solve

1x = [tex]\frac{2}{3}[/tex][tex](\frac{24}{1})[/tex]       1x is the same a x.  24 is the same as [tex]\frac{24}{1}[/tex]

x = [tex]\frac{48}{3}[/tex]

x = 16

i need help with question 17

Answers

Answer:

[tex]42[/tex]

Step-by-step explanation:

To find the median of a stem and leaf plot, use the equation:

[tex]\begin{gathered} median=\frac{n+1}{2} \\ where, \\ n=\text{ number of data} \end{gathered}[/tex]

Therefore, for the given plot, there are 16 elements.

[tex]\begin{gathered} \text{ median=}\frac{16+1}{2} \\ \text{ median=8.5} \end{gathered}[/tex]

When there are two middle values, the median is the mean of these two values:

[tex]\begin{gathered} \frac{3+1}{2}=2 \\ \text{ Hence, the median is 42.} \end{gathered}[/tex]

need asap TIA bonus brownie points if you edit the graph <3

Answers

From the following figures, we have that:

a) The sequence of transformations that maps triangle ABC to triangle A''B''C'' is given by:

Reflection over the x-axis.Translation of 11 units right and 1 unit up.

b) The rules are given as follows:

Reflection: (x,y) -> (x, -y).Translation: (x,y) -> (x + 11, y + 1).

What are transformations on the graph of a function?

The transformations used in this problem are as follows:

Translation: Can be in the direction left/right or down/up, changing just the position of the figure.Reflections: Can be a reflection over one of the axes or over a line, changing the orientation of the figure.

For this problem, the orientation of the triangle changed, with the C at the bottom of the triangle being transformed into C'' at the top of the transformed triangle, hence the figure was reflected over the x-axis, and the rule is:

(x,y) -> (x, -y).

After the reflection, the coordinates of C' are given as follows:

C' (-4, -1).

The final coordinates of C'' are given as follows:

C'' (7, 0).

Meaning that it was translated 11 units right and 1 unit up, and the rule is given by:

(x,y) -> (x + 11, y + 1).

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