Find the inverse of the linear function

Answer: (4m+n)(4m-n)

Step-by-step explanation:

16m² -n²=

(4m)²-n²=

(4m)²+4mn-4mn-n²=

4m(4m+n)-n(4m+n)=(4m+n)(4m-n)

Answer:

[tex] = { \tt{16m {}^{2} - {n}^{2} }} \\ { \tt{ = {4}^{2} {m}^{2} - {n}^{2} }} \\ { \tt{ = (4m - n)(4m + n)}}[/tex]

Answer: Our carpet calculator will help you determine your approximate floor area in square metres. Simply measure the length and width of each room to the nearest 10cm, i.e. 5.4m x 3.7m, then enter your totals into the calculator and hit the 'calculate' button at the bottom.  

For awkwardly shaped rooms (such as an L shape) divide the room into blocks, measure them separately and add them in as individual rooms.

Step-by-step explanation:

The value of x is 3 and  -3 respectively.

Given that;

From equation (1)

4x+60 < 72  

First, collect like terms

4x < 72 - 60

subtract like terms

4x < 12

Make 'x' the subject

x < 12/ 4

x < 3

For equation (2)

14x +11 <-31

collect like terms

14x < -31 - 11

14x < -42

Make 'x' the subject

x < -42/ 14

x < -3

Thus. the value of x is 3 and  -3 respectively.

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Answer:

(-1, 0) and (8, 9)

Step-by-step explanation:

x² - 6x-7 = x + 1

x² - 7x - 8 = 0

(x - 8)(x + 1) = 0

x = -1, 8.

When x = - 1, y = 0

and x = 8, y = 9

The length of BE is 15 cm.

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Answer:

602.88 cubic inches

Step-by-step explanation:

Volume of cylinder = pi ×r^2×height

=3.14×4^2×12

=3.14×16×12

=602.88

Answer:

What do you need help with?

Step-by-step explanation:

The miles for which  Austin drove the truck  is 141 miles

It is given that Austin rents a truck for one day

The daily rental base fee of the truck is $17.99

It is also given that additional charge of 73 cents per mile is charged.

It is also to be noted that 1$ =100 cents

Therefore, 73 cents in the form of dollar is 0.73$

Now it is given that total bill that is paid is $120.92

Now the total number of miles travelled by Austin is total bill minus the base fee and 73 cents multiplied by miles

Let the miles travelled by Austin be 'x'

Therefore, Miles travelled by Austin = 120.92$-17.99$

                                     0.73 x =(120.92 -17.99)  $                      

                                     x= 102.93 / 0.73

                                     x=141

Hence, the miles for which Austin drove the truck is 141 miles

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Step-by-step explanation:

3n just means 3 × n

To actually solve the equation, the value of n would have to be given.

In some equations, you would have to solve for n and then answer the equation, but that's not possible with this one.

The nth term of the given sequence is 4n - 1.

So,

Therefore, the nth term of the given sequence is 4n - 1.

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The price of the jacket is $23.75

Let m be the price of a jacket and n be the price of pair of pants.

The total cost of a jacket and a pair of pants was $52.37

So, we get an equation,

m + n = 52.37              ................(1)

Also, the price of the jacket was $4.87 less than the pair of pants

So, we get an equation,

m = n - 4.87               .............(2)

Substitute above value of m in equation (1)

⇒ (n - 4.87) + n = 52.37

⇒ 2n - 4.87 = 52.37

⇒ 2n = 52.37 + 4.87

⇒ 2n = 57.24

⇒ n = 28.62

This means, the cost of a pair of pants is $28.62

Substitute above value of n in equation (2)

⇒ m = n - 4.87

⇒ m = 28.62 - 4.87

⇒ m = 23.75

This means, the cost of a jacket is $23.75

Therefore, the price of the jacket is $23.75

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[tex]scale \: from \: b \: to \: a = \frac{3}{2} \\ x = \frac{2}{3} \times 10.5 = 7[/tex]

Answer:

$70

Step-by-step explanation:

$70 was collected on the second day of the month.

Answer:

1st one

Step-by-step explanation:

My mom is a teacher lol

The probability that no Tails is achieved on flipping a fair coin for three consecutive times is [tex](\frac{1}{8})[/tex].

As per the question statement, we are to flip or toss a fair coin thrice consecutively.

We are required to calculate the probability that no Tails is achieved during the above mentioned event.

To solve this question, first let us calculate all the possible outcomes of flipping a fair coin thrice consecutively. [We will denote a Heads outcome as "H" and a Tails outcome as "T"]

The total number of outcomes can be given by the formula [tex](2^{n})[/tex], where "n" is the number of times, the coin is tossed.

Here, (n = 3), therefore, total number of outcomes in our case [tex]=(2^{3})=8[/tex].

These 8 outcomes can be listed as [tex][{(H, H, H), (H, H, T), (H, T, H), (H, T, T), (T, H, H), (T, H, T), (T, T, H), (T, T, T)}][/tex]

And among the above listed 8, our favorable outcome is (H, H, H), i.e., 1 favorable outcome of 8.

Hence, probability that no Tails is achieved on flipping a fair coin thrice consecutively = [tex]\frac{1}{8}[/tex].

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Answer:

I think Dessicant

Step-by-step explanation:

i hope it helped you if I'm right :D

Answer:

Quadrant 1

Step-by-step explanation:

Answer:

X = 9287.5

Step-by-step explanation:

Solving steps

7.5+ 9287=x+7

Calculate

9294.5=x+7

Move the terms

-x=7-9294.5

Calculate

-x=-9287.5

Change the signs

Solution

X = 9287.5

The maximum distance Jameel can travel is 11.5 miles

The equation that determines the distance is given as

2 + 0.4(4m - 1) = 20

Subtract 2 from both sides of the equation

So, we have

0.4(4m - 1) = 20 -2

Evaluate the like terms

So, we have

0.4(4m - 1) = 18

Divide both sides by 0.4

So, we have

(4m - 1) = 18/0.4

Evaluate the quotients

So, we have

(4m - 1) = 45

Remove the bracket

So, we have

4m - 1 = 45

Add 1 to both sides of the equation

4m = 46

Divide both sides of the equation by 4

So, we have

x = 11.5

Hence, the maximum distance Jameel can travel is 11.5miles

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There are 5 possible arrangements to make seat all 22 children.

The smallest number of tables Ms. Francis is 10 tables.

Total number of children at the party = 22

When we picturize the scenario, each child need to get a side of the table.

So at least 22 sides should be there after arranging it into rectangles. Also the square card tables are arranged side to side to get rectangle rows.

It is also said that there can be multiple rows. So combining all these points, we can consider a row of 10 tables. Then the the squares on the ends contribute a total of 6 sides and the remaining 16 seats can be arranged by 8 square tables in between the end square tables. So a total of 10 square table is required to make a rectangle in one row.

For making 22 seats in 2 rows, the 4 square tables on the ends contribute 8 seats. For the remaining 12 seats add 7 square tables in each row, that is a total of 14 square tables. That is, for 2 rows, the square tables required is 14 + 4 = 18.

Similarly, for 3 rows, a total of 24 square tables are required.

For 4 rows, a total of 28 tables and for 5 rows, a total of 30 tables are needed.

We cannot make a 6 row because it will be same as a 5 row.

So 5 different arrangements can be made to seat all 22 children.

They are:

1 row → 1 x 10 = 10 tables

2 rows → 2 x 9 = 18 tables

3 rows → 3 x 8 = 24 tables

4 rows → 4 x 7 = 28 tables

5 rows → 5 x 6 = 30 tables

The smallest number of tables that Ms. Francis needs to rent is, therefore, 10 tables.

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Answer:

A

Step-by-step explanation:

43987-32650= 11337

And it’s more

The area of a square is the square of the length of a side is a^2.

The quantity of space occupied within the square can be used to calculate the size of a square using mathematics. We'll go over the equation for calculating the square's area below. It is mainly known for its geometric quadrilaterals. The simplest definition of a square is a regular polygon with four equal sides. A square has all the same facts and characteristics as regular polygons.

The number of square units that are anticipated to fill a square is used to describe the area of a square. The area is typically defined as the area included by the confines of a level article or 2D figure.

Mathematical Area of Square Formula = a×a=a^2.

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Figure B is not a scale copy of figure A. The answer is NO. The corresponding lengths of both figures have different ratios.

If a figure is the scale copy of another figure, the corresponding side lengths of both figures would be proportional to each other, which means their ratios would be the same.

From the figure given, the ratios of their side lengths are:

18/9 = 2

12/12 = 1

30/15 = 2

This shows that their ratios are not the same.

Therefore, we can conclude that figure B is not a scale copy of figure A. The answer is NO. The corresponding lengths of both figures have different ratios.

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Answer:

13.68

Step-by-step explanation:

72 * 0.19 = 13.68

19% can be converted to 19/100 or .19 to change out of a percentage. .19 is the multiplied by 72 to find 19% of 72.

For example

a fourth of something is the same as 25%.

if you want to find 1/4 of 8 you would multiply 8 by 1/4.

It is a similar concept with percentages.

Answer:

hello

Step-by-step explanation:

hi

MSA

my milkshake brings all the boys to the yard yeah right its better than yours yeah right its better than yours

The function of  f(x) = (x+4)³ + 3 is one-to-one  then the value of

[tex]f^{-1} (x) = \sqrt[3]{x} - 4[/tex] and,

[tex]f^{-1} (2) = -2.7401[/tex]

The function f(x) = (x+4)³ + 3

Let us assume,

y = (x+4)³ + 3

A function is said to be invertible when it has an inverse. It is represented by [tex]f^{-1}[/tex]. Condition for a function to have a well-defined inverse is that it be one-to-one and Onto or simply bijective.

Then,

y = (x+4)³   and    y = 3

Therefore the inverse of y = 3 is the line x = 3

We can solve,

y = (x+4)³

The solution of Inverse function,

So,

[tex]\sqrt[3]{y} = x+4[/tex]

We can get,

[tex]x = \sqrt[3]{y} -4[/tex]

So the inverse of y is [tex]\sqrt[3]{x} -4[/tex]

f(x) = (x+4)³

So the inverse of f(x) is [tex]\sqrt[3]{x} -4[/tex]

Therefore, [tex]f^{-1}( x)[/tex] = [tex]\sqrt[3]{x} -4[/tex]

Then f(x) = 2

[tex]f^{-1} (x) = \sqrt[3]{x} - 4[/tex]

We can substitute f(x) = 2

[tex]f^{-1} (2) = \sqrt[3]{2} -4[/tex]      

Since, ∛2 = 1.2599

We can substitute this value,

[tex]f^{-1} (2) = 1.2599-4[/tex]

[tex]f^{-1} (2) = -2.7401[/tex]

Therefore,

The value of ,

[tex]f^{-1} (x) = \sqrt[3]{x} - 4[/tex] and,

[tex]f^{-1} (2) = -2.7401[/tex]

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Answer:

When the terminal side is in the first quadrant (angles from 0° to 90°), our reference angle is the same as our given angle. This makes sense, since all the angles in the first quadrant are less than 90°. So, if our given angle is 33°, then its reference angle is also 33°.

When the terminal side is in the second quadrant (angles from 90° to 180°), our reference angle is 180° minus our given angle. So, if our given angle is 110°, then its reference angle is 180° – 110° = 70°.

When the terminal side is in the third quadrant (angles from 180° to 270°), our reference angle is our given angle minus 180°. So, if our given angle is 214°, then its reference angle is 214° – 180° = 34°.

When the terminal side is in the fourth quadrant (angles from 270° to 360°), our reference angle is 360° minus our given angle. So, if our given angle is 332°, then its reference angle is 360° – 332° = 28°.