If f(x)=5x-12, find a value for $x$ so that f^{-1}(x)=f(x+1).

Answers

Answer 1

Answer:

[tex]\boxed{\sf \ \ \ x=\dfrac{47}{24} \ \ \ }[/tex]

Step-by-step explanation:

Hello,

f(x)=5x-12

we need to find x so that

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

so first of all we can write

[tex]x = (fof^{-1})(x)=f(f^{-1}(x))=5f^{-1}(x)-12\\\\<=>5f^{-1}(x)=x+12\\\\<=>f^{-1}(x)=\dfrac{x+12}{5}[/tex]

and f(x+1) = 5(x+1) - 12 = 5x + 5 -12 = 5x - 7

then solving

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

is equivalent to

[tex]\dfrac{x+12}{5}=5x-7 \ multiply \ by \ 5 \\\\<=> x+12 = 5(5x-7)=25x-35\\<=> 25x-x=12+35\\\\<=>24x=47\\\\<=>x=\dfrac{47}{24}[/tex]

Hope this helps

Answer 2

Answer:

Step-by-step explanation:

let f(x)=y

y=5x-12

flip x and y

x=5y-12

5y=x+12

[tex]y=\frac{x+12}{5} \\or \\f^{-1}(x)=\frac{x+12}{5} \\f(x+1)=5(x+1)-12=5x-7\\\frac{x+12}{5} =5x-7\\x+12=25x-35\\25~x-x=12+35\\24 x=47\\x=\frac{47}{24}[/tex]


Related Questions

What is the simplified expression for 5 to the power of negative 3 multiplied by 2 to the power of 2 multiplied by 5 to the power of 6 whole over 2 to the power of 3 multiplied by 5 to the power of 2?

Answers

Answer

the third(5/2)

Step-by-step explanation:

[(5^(-3))*(2^2)*(5^6)]/[(2^3)*(5^2)]

=[(5^3)*(2^2)]/[(2^3)*(5^2)]

=[5^(3-2)]*[2^(2-3)]

=5*(1/2)

=5/2 or 2.5

Answer:

5/2

Step-by-step explanation:

Hope it helps!!

Btw it was right on the test!!

The outside of this set of four cubic blocks with no space between blocks is painted. What is the number of painted square faces?

Answers

Answer:

18

Step-by-step explanation:

There would be four faces on the top, left, bottom, and right.  That equals 16.  (4x4)

There would also 1 on each end, so you have to add 2.  That equal 18.

This is assuming you paint the faces on the bottom.  If you didn’t, the answer would be 14.  (But it doesn’t say not to paint them.)

Complete the synthetic division problem below.
-32 4
What is the quotient in polynomial form?
O A. 2x2 + 2x-6
B. 2x2 + 2x-2
C. 2x2 - 2x + 6
D. 2x2 - 2x+ 2​

Answers

Answer:

D. 2x^2-2x+2

Step-by-step explanation:

Step 1: -3 | 2 4 -4 6

Step 2: -3 | 2 4 -4 6

                    -6  6 -6            

                | 2 -2  2 0

Bring 2 down to the answer then multiply it with 3 and add it with the next coefficient. Repeat the process until you get to the last number and you're done. Sorry its kind of hard to explain the steps for synthetic division. Hope this helps!

The synthetic division problem that is given has the quotient in polynomial form is 2x2 - 2x+ 2​. The correct option is D.

What is the polynomial form?

A polynomial is made up of terms, each of which has a coefficient, whereas an expression is a statement that has at least two integers and one mathematical expression.

Polynomials can be discovered by observing which formulas contain just addition, subtraction, multiplication, and non-negative integer exponents. Non-polynomial expressions will be those that contain other operations.

-3 | 2 4 -4 6

-3 | 2 4 -4 6

-6  6 -6            

2 -2  2 0

Bring 2 down to the solution, multiply it by 3, and then add it to the next coefficient. Repeat the process until you reach the last number, then stop.

Therefore, the correct option is D. 2x2 - 2x+ 2​.

To learn more about polynomial form, refer to the link:

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Mike packed three granola bars, measuring 8 cm by 3 cm by 1cm. What volume a box needs
to hold twelve bars?​

Answers

Helloyo!


Answer: 288 cm^3

Explanation:

Volume of on bar = 8*3*1 = 24 cm^3

Volume of 12 bars = 8*3*1*12 = 24*12 = 288 cm^3


Hope it helps ya

Answer:

288 cm^3

Step-by-step explanation:

First, you have to calculate the volume of your individual bar. To do this, you multiply the three given values, so it would look like 8*3*1=24. This means that your individual bar has a volume of 24 cm^3.

To hold 12 granola bars, this would mean that your volume of the individual granola bar would be multiplied by 12, because that is how many you want to fit inside the box. So your operation would looked like 24*12=288 cm^3

how do i measure the bounce height of a tennis ball released from a height of 150 cm?​

Answers

Answer:

You can use a slow motion camera and see clearly. You should probably put a meter ruler in the background so you can check the height

Step-by-step explanation:

I WILL GIVE BRAINLIEST FOR THE CORRECT ANSWER!!! Which equation does the graph below represent? y = −2x y = x y = 2x y = x (click the picture below)

Answers

Answer:

y = -2x

Step-by-step explanation:

Some points are (1,-2) , (2, -4), and (3,-6).

From these three points, we can try each of the equations to see what is correct.

If y = -2x

-2 = (-2)1

-4 = (-2)2

-6 = (-2)3

If y = x

-2 ≠ 1

-4 ≠ 2

-6 ≠ 3

If y = 2x

-2 ≠ 2(1)

-4 ≠ 2(2)

-6 ≠ 2(3)

9. Find P(rolling 1 or 5) with one number cube.

Answers

Answer:

1/3

Step-by-step explanation:

There are 6 possible outcomes when rolling 1 die

1,2,3,4,5,6

P ( 1 or 5) = number of times 1 or 5 happens / total outcomes

               = 2/ 6

               = 1/3

What is the volume of the cylinder below?
1
1
4
5
A. 4577 units 3
B. 90 units
C. 367 units 3
D. 727 units 3

Answers

Answer:

36pi Units^3

Step-by-step explanation:

Slanted (oblique) cylinders have the same volume as standard (right) cylinders.  

V=pi r-squared h

V=pix3x3x4

V=36 pi Units cubed

Answer:

The correct answer is 36 pi units^3

Step-by-step explanation:

Please hurry!

Which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm is a right triangle?

Answers

Answer: the first one I’m pretty sure! Due to the hypotenuse being the longest length (13) and you would use the Pythagorean theorem

Step-by-step explanation:

The first one is the best

is this right? i’ll give brainliest :)

Answers

It is.

[tex]x-10 \geq 0\\\\x \geq 10\\\\\\-5 +n< -6\\\\n < 5-6\\\\n< -1[/tex]

Answer:

Correctomundo!

Step-by-step explanation:

For x-10 > 0:

1. Add 10 to both sides. x- 10 + 10 > 0 + 10

x > 10

For -5 + n < -6:

1. Simplify both sides of the inequality.  n - 5 < -6

2. Add 5 to both sides. n - 5 + 5 < -6 + 5

n < -1

:)

Which inequality is represented by the graph

Answers

Answer:

(-2, 5) < x

Step-by-step explanation:

Answer:

2/5x-1.5 > 0

Step-by-step explanation:

PLEASE HURRY!⚠️

Which is a perfect square?

Answers

6^2 is the correct answer

Answer:

Step-by-step explanation:

A number squared is a perfect square, thus

6² ← is a perfect square

Answer pls I can answer ur question maybe

Answers

Answer:

[tex]C=5\pi \approx15.71[/tex]

Step-by-step explanation:

The arc length of the semicircle is basically the circumference of it. Therefore, we can use the circumference formula.

The circumference of a full circle is:

[tex]C=2\pi r[/tex]

Therefore, the circumference of a semicircle is half of that (ignoring the diameter):

[tex]C=\pi r[/tex]

The radius is 5.

[tex]C=\pi (5)=5\pi \approx15.71[/tex]

The arc length is around 15.71 units.

Answer:

39.25

Step-by-step explanation:

5^2=25

25x3.14=78.5

78.5/2=39.25

Phil received a prize of xxx dollars from a poker tournament. The tournament cost him 100100100 dollars to enter.
What were Phil's net winnings from the tournament?
Write your answer as an expression.

Answers

Answer:

The answer would be 999 because 100 has 3 digits Hope You get a Good Grade And have a wonderful day!!

please answer need help with equation

Answers

Answer:

12

Step-by-step explanation:

We can use PEMDAS. First, we need to calculate the stuff in the parentheses, then the exponent, then the multiplication and finally, the addition.

1/3(4 · 3) + 2³

= 1/3 · 12 + 2³  -- Parentheses

= 1/3 · 12 + 8 -- Exponents

= 4 + 8 -- Multiplication

= 12 -- Addition

let f(x)= 8x³ + 16x² -15 and g(x) = 2x+1. f(x)/g(x).

4x²+6x-3+12/2x+1. 4x²+6x+3+12/2x+1. 4x²+6x-3-12/2x+1. 4x²+6x+3-12/2x+1​

Answers

Answer:

f(x)/g(x) = 4x^2+6x-3  remainder -12

or

f(x)/g(x) = (4x^2+6x-3)/(2x+1) + (-12)/(2x+1)

or

((4x²+6x-3)-12)/(2x+1)

Step-by-step explanation:

f(x)= 8x³ + 16x² -15

g(x) = 2x+1.

Using long division,

f(x)/g(x) = 4x^2+6x-3  remainder -12

Solve the inequality $2x - 5 \le -x +12$. Give your answer as an interval.

Answers

Answer:

[tex]$\left(-\infty, \frac{17}{3} \right]$[/tex]

Step-by-step explanation:

[tex]2x - 5 \le -x +12[/tex]

[tex]2x - 5 +5\le -x +12+5[/tex]

[tex]2x\le -x+17[/tex]

[tex]3x \le17[/tex]

[tex]$x \le \frac{17}{3} $[/tex]

We have

[tex]$\{x \in \mathbb{R}:x \le \frac{17}{3} \}$[/tex]

Interval notation:

[tex]$\left(-\infty, \frac{17}{3} \right]$[/tex]

In the figure below which term best describes point 7?​

Answers

The three lines drawn are at 90 degree angles, so are drawn perpendicular to the vertex.

This means point T is the orthocenter.

The answer is A

A taxi driver charges a flat rate of $3.50 plus an additional $1.65 per mile. If Mohammad wants to spend, at most, $60, how far can he travel in the taxi cab?
Round your answer to the nearest mile.
O A. 34 miles
OB. 17 miles
C. 35 miles
D. 16 miles

Answers

Answer:

A. 34 miles

Step-by-step explanation:

First, you want to subtract $3.50 from $60. Now you have $56.50. Now you want to divide that by $1.65, to see how many miles you can achieve with your price limit. So, now you have a grand total of 34.24. You round that, and you finally have your answer.

The answer to this problem is A. 34 miles

The number of miles that he can travel in the taxi cab will be 17 miles. Then the correct option is B.

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.

A cab driver charges a level pace of $3.50 in addition to an extra $1.65 per mile.

Let 'y' be the total amount and 'x' be the number of miles. Then we have

y = 3.50x + 1.65

If Mohammad wants to spend, at most $60. Then the number of miles is given as,

60 = 3.50x + 1.65

3.50x = 58.35

x = 16.67

x ≈ 17 miles

The number of miles that he can travel in the taxi cab will be 17 miles. Then the correct option is B.

More about the linear equation link is given below.

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The operation symbol and the exponent are missing in the equation shown below.
7,320
10
0.07320
Which operation symbol and exponent should go in the boxes to make the
equation true?

Answers

Answer:

The operating symbol is divide (/) and the exponent is 5

[tex]7,320 / \ 10^5 = 0.07320[/tex]

Step-by-step explanation:

Given

[tex]7,320 \ \_\ 10^{\_} = 0.07320[/tex]

Required

Fill in the gap

[tex]7,320 \ \_\ 10^{\_} = 0.07320[/tex]

Multiply the right hand side by 1

[tex]7,320 \ \_\ 10^{\_} = 0.07320 * 1[/tex]

Express 1 as 100000/100000 because 100000/100000 = 1

[tex]7,320 \ \_\ 10^{\_} = 0.07320 * \frac{100000}{100000}[/tex]

Split the fraction

[tex]7,320 \ \_\ 10^{\_} = 0.07320 * 100000 * \frac{1}{100000}[/tex]

Multiply 0.7320 and 10000

[tex]7,320 \ \_\ 10^{\_} = 7,320 * \frac{1}{100000}[/tex]

Express [tex]\frac{1}{100000}[/tex] as an exponent

[tex]7,320 \ \_\ 10^{\_} = 7,320 * \frac{1}{10^5}[/tex]

Change the * sign to /

[tex]7,320 \ \_\ 10^{\_} = 7,320 / \frac{10^5}{1}[/tex]

[tex]7,320 \ \_\ 10^{\_} = 7,320 / \ 10^5[/tex]

Compare the expression on the right hand side with the left hand side base on the order of appearance;

[tex]7,320 = 7,320[/tex]

[tex]The first\ \ _ = \ /[/tex]

[tex]10 = 10[/tex]

[tex]The second\ \_ = 5[/tex]

Hence, the operating symbol is / and the exponent is 5

There were some people on a train. 19 people got off the train at the first stop. 17 people get on the train. Now there is 63 people on the train. How many people were on the train to begin with?

Answers

Answer:

65 people.

Step-by-step explanation:

We have to work backwards.

We end with 63 people, and at the stop we lost 19 people and gained 17.

[tex]x - 19 + 17 = 63\\[/tex]; if x = # people at the beginning

[tex]x - 19 + 17 = 63\\x - 2 = 63\\x = 65[/tex]

There were 65 people on the train to begin with.

Answer:

65 people

Step-by-step explanation:

Well, we need to work backward,

63 on the train and 17 got on so we do 63 - 17 = 46

Then 19 got off so 46 + 19 = 65

Hence, 65 people were on the train on the first stop.

Based on the tables, what is the solution to the equation 2(3)X = 3x + 3? (4 points)
x = -1
x = 0
x = 1
X = 6

Answers

Answer: x=1

Step-by-step explanation:

When solving for x you must isolate the terms. In order to isolate the terms divide both sides by 3 in order to break up the 3x. that way you should have 2x=x+1 from there i will subtract the x from both sides, so i receive x=1.

X=1

Explanation:

2(3)x = 3x+3
6x=3x+3
3x=3
X=1

alice drank 18 ounces of gatorade after her gymnastic meet. there were 14 ounces left.How many ounces of gatorade was origanally in the container.​

Answers

Answer:

32 ounces

Step-by-step explanation:

18+14=32

32 is the total

Answer:

32 ounces

Step-by-step explanation:

She already drank 18 ounces and 14 ounces was left which means that If she didn't drink anything it would have been 32 ounces as 18 + 14 = 32

Hope this helps and pls mark as brainliest : )

Solve the system using elimination 20x+3y=20 -20x+5y=60

Answers

8y=80
y=10
Substitute this y into one of the equations and solve for x. For example:
20x+30=20
x=-1/2.

(-1/2,10) is the solution.

Answer:

x=2, y=20

Step-by-step explanation:

20x+3y=20-20x+5y=60

Combine like terms, so you would do plus 20x both sides and minus 3y both sides.

After that you can also do minus 20 both sides.

So you are left with 40x=2y=40

Which of the following theorems verifies that WXY=PME?

A. HA
B. HL
C. LA
D. AA

Answers

Answer: B.  HL

HL = hypotenuse leg

We see that WX = PM are the congruent legs (they are the same length due to the similar single tickmark). Also, XY = ME is the congruent pair of hypotenuses. The HL rule only works for right triangles, as the term "hypotenuse" would not apply for a non-right triangle.

The theorem used is HL.

What is theorem?

A theorem is a statement which has been proved true by a special kind of logical argument called a rigorous proof.

Given:

In both triangles

XW = MP  (given)

XY = ME (given)

As, hypotenuse of both triangle is equal and leg of one right triangle are congruent to the hypotenuse.

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Select all that apply. To decide if 12.5 centimeters is greater than 140 millimeters, the first step is to set up a proportion. Which of the following proportions are correct? Please help! D:

Answers

Answer:

Hey there!

We can't compare two measurements without converting them to  the same units. Thus, we use proportions to make all the values into the same unit.

[tex]12.5 cm(\frac{10 milimeters}{1 centimeter})[/tex], which converts to centimetres to millimetres.

12.5 cm=125 mm.

Now, we can compare the values of 125 mm and 140 mm.

Clearly, we see that 140 mm is greater than 125 mm.

Let me know if this helps :)

Answer:

If this is your question:

Select all that apply.

To decide if 12.5 centimeters is greater than 140 millimeters, the first step is to set up a proportion. Which of the following proportions are correct?

[tex]\frac{10 mm}{1 cm} = \frac{140 mm}{x} \\\\\frac{10 mm}{1 cm} = \frac{x}{140 mm} \\\\\frac{1 cm}{10 mm} = \frac{12.5 cm}{x} \\\\\frac{12.5 cm}{1 cm} = \frac{140 mm}{x} \\\\[/tex]

Then your answer is:

[tex]\frac{10 mm}{1 cm} = \frac{140 mm}{x} \\\\\frac{1 cm}{10 mm} = \frac{12.5 cm}{x}[/tex]    

I saw a lot of one answers, but the question is Select ALL that Apply

not just c or b

I hope this helped :))))) (●'◡'●)

PS: brainliest would be great but i'm not askin for it

The linear combination method gives a solution of (–4, 2) for which of these systems of linear equations?

Answers

Answer:

[tex]3x + 13y = 14[/tex]

[tex]6x + 11y = -2[/tex]

Step-by-step explanation:

See Attachment for complete question

To determine which of the options has (-4,2) as its solution; we have to test each linear combination until we arrive at an answer;

Given that

[tex](x,y) = (-4,2)[/tex]

Testing Option A

[tex]3x + 13y = 14[/tex]

[tex]6x + 11y = -2[/tex]

Substitute [tex]x = -4[/tex] and [tex]y = 2[/tex] in [tex]3x + 13y = 14[/tex]

[tex]3(-4) + 13(2) = 14[/tex]

Open Brackets

[tex]-12 + 26 = 14[/tex]

[tex]14 = 14[/tex]

Substitute [tex]x = -4[/tex] and [tex]y = 2[/tex] in [tex]6x + 11y = -2[/tex]

[tex]6(-4) + 11(2) = -2[/tex]

Open Brackets

[tex]-24 + 22 = 2[/tex]

[tex]2 = 2[/tex]

In both cases, the expression on the right hand side equates to that on the left hand side;

Hence, there's no need to check for other options.

On the graph of an exponential function representing growth what happens to the slope of the graph as X increases

Answers

Answer:

The slope of the graph will increase and get steeper.

Step-by-step explanation:

As x increases in an exponential growth graph, f(x) will have a larger value because the exponent value increases.

So, the graph will become steeper due to a larger slope.

The slope of the graph will increase and get steeper.

What is Slope?

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,m = Δy/Δx where, m is the slope

Given:

As we know that, all points on an exponential curve are always at a constant distance from one another because the slope of an exponential curve equals the constant rate of expansion.

The graph is not exponential if the slope is not constant.

So, In an exponential growth graph, f(x) will have a greater value as x grows as the exponent grows.

Consequently, a larger slope will cause the graph to grow steeper.

Learn more about Slope here:

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The interior ages of a triangle have measure
55,25", and x find the value of
these 3 problems ty

Answers

Answer:

See below in bold.

Step-by-step explanation:

1. The 3 angles in a triangle add up to 180 degrees.

So x = 180 - (55 + 25)

= 180 - 80

= 100 degrees.

2.  The 4 angles in a quadrilateral add up to 360 degrees,, so

3x + 127 + 54 + 119 = 360

3x + 300 = 360

3x = 360 - 300

3x = 60

x = 20 degrees.

3. Exterior angle

= 94 + 42

= 136 degrees.

Answer:
100 degrees just think about how all the angles in a triangle add up to 180 degrees

Isabella filled her pool with water at a constant rate. The table compares the remaining volume of water left to fill the pool (in liters) and the time since Isabella started filling the pool (in minutes).

Time (m) Remaining Volume (L)
4 148
6 112
8 76

What is the size of her pool?

Answers

Answer:

It was kinda hard to really understand your question but as of all the information that I received the answer is 220 liters

Step-by-step explanation:

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