Is the inverse of every linear function also a function?

Answers

Answer 1

In most cases, the inverse of a linear function is also a linear function.

What is a linear function?

The term "linear function" in mathematics applies to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

A function with the formula f(x) = ax + b, where a and b are real values, is referred to as a linear function.

Here, stands for the line's gradient and b for the y-axis intercept (which is sometimes called the vertical intercept).

These functions' graphs are mirror images of one another when viewed along the line y=x.

As a result, the points on the graph of f(x) are the points on the graph of f(x) that have been turned around.

A linear function's inverse is typically also a linear function.

Therefore, in most cases, the inverse of a linear function is also a linear function.

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Related Questions

To win the game, the team must score at least 8 goals. What inequality represents the number of goals, g, the team must score

Answers

So, on  solving the provided question, we can say that  to form a inequality - x * y > 8

What is inequality?

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

here to form a inequality-

let x = goals by each player

y = no. of players

x * y > 8

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-2n = -1 1/4
................................

Answers

Answer:

n = 5/8

Step-by-step explanation:

-2n = -1 1/4

-1 1/4 = -5/4

So, our equation is

-2n = -5/4

Divided both sides by -2

n = 5/8

So, the answer is

n = 5/8

betsy correctly answered 19 of 25 trivia questions. What percent of the questions did she answer correctly?

Answers

1.14 is the answer just do 19%=1.14

19 divided by 25 is .76
then multiply .76 by 100 to get the percent

or

19/25 • x/100

she answered 76% of the questions correctly

Find the measure of the missing angle? please help :)

Answers

The measure of the angle ∠SUT will be 30°. Then the correct option is C.

What is the triangle?

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The exterior angle of a triangle is almost always equal to the addition of the interior and opposing interior angles. The term "external angle property" refers to this feature.

The measure of the angle ∠SUT is calculated as,

∠SUT + ∠UTS = ∠JST

∠SUT + 80° = 110°

∠SUT = 110° - 80°

∠SUT = 30°

The measure of the angle ∠SUT will be 30°. Then the correct option is C.

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passes through (6,6) and (-2,2)

Answers

Answer: 1/2 is the slope.

Step-by-step explanation: (-2-6)/(2-6) = -8/-4

-8/-4 Simplified is 1/2

Therefore 1/2 is your slope

Hope this helps!

somone please help me with this im begging you

Answers

Answer:

For Q.1, the answer is 9

Step-by-step explanation:

The volume formula for a cylinder is V=πhr^2. The volume formula for a cone is V=(πhr^2)/3. You might notice that the formulas are very similar; the only difference is the divided by three at the end. Because we are going from cylinder to cone, we have to multiply by three instead of dividing. Doing this, we get 3*3=9.

Try solving the rest of the problems using these two formulas by yourself. :)

EMERGENCY NEED HELP PLEASE HELP THE QUESTION IS ATTACHED TO THE QUESTION THING PLEASE HELP!!!

Answers

The required graph of the system of linear equations has been attached below.

What is the Linear equation?

A linear equation is defined as an equation in which the highest power of the variable is always one.

The system of linear equations is given in the question, as follows:

2x + y = 8      .....(i)

-x + 2y = 6    .....(ii)

To graph the equations using the slope and y-intercept,

1) To determine the slope m and the y-intercept, write the equation in the form y = mx + b. (0, b).

Plot the y-intercept next.

3) Depending on whether the slope is positive or negative, go up, down, or left or right from the y-intercept.

Thus, the required graph of the system of linear equations.

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Help please, I need to check my answer

Answers

[tex]\cfrac{45p^5q^4-60p^3q^2 - 15p^2q^3}{15p^2 q^3}\implies \cfrac{45p^5q^4}{15p^2 q^3}-\cfrac{60p^3q^2}{15p^2 q^3}-\cfrac{15p^2q^3}{15p^2 q^3}\implies 3p^3q-\cfrac{4p}{q}-1[/tex]

Given that $k$ is a positive integer less than 6, how many values can $k$ take on such that $3x \equiv k \pmod{6}$ has no solutions in $x$

Answers

Supposing the value of x to be an integer, the values of k that donot

satisfy the given equation 3x = k mod 6 are 1,2,4,5.

What is an integer?

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.

What is the difference between integers and whole numbers?

Integers are a set of numbers that include both positive and negative numbers, as well as zero. Whole numbers, on the other hand, only include the set of non-negative numbers starting from 0 (i.e., 0, 1, 2, 3, 4, ...). In other words, whole numbers are a subset of integers.

If 3x = k mod 6 has no solutions in x, then k must not be divisible by 3. The positive integers less than 6 that are not divisible by 3 are 1, 2, 4, and 5. Therefore, k can take on 4 values: 1, 2, 4, and 5.

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A square board has an area of 144 square units. How long is each side of the board?

Answers

Answer: 12 units

Step-by-step explanation:

∴ Area of Square = side length × side length

⇒144 = lengt²

⇒length = √144

⇒length = 12 units ANSWER

hope that helps...

WILL MARK BRRRRRRRRRRRRRRRRRRAIIIIIINNNNNNNNNNNNNLLLLLLLLLLIIIIIIIIIIIEEEEEEEEESSSSSSSSSSTTTTTTTTTTT

Answers

The volume of the cube, given the lengths of the small cubes used to make the larger cube, is 8 cm ³

The surface area of the cube is 24 cm ²

The total length of the edges of the cube is  24 cm

How to find the volume of a cube ?

The volume of a cube can be found by the formula :

= Side x Side x Side

This is because all the sides of a cube at the same and so the volume would measure them three - dimensionally.

The side length of this cube is the length of two of the smaller cubes as these make up a side of the cube :

= 2 x 1

= 2 cm

The volume is therefore :

= 2 x 2 x 2

= 8 cm ³

How to find the area of a cube ?

The surface area of a cube is:

= 6 x side ²

= 6 x 2 ²

= 24 cm ²

How to find the length of a cube ?

The total length of the edges would be:

= 12 edges on a cube x length of each edge

= 12 x 2

= 24 cm

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11. One side of a kite is 2 cm less than 2 times the length of another. If the perimeter is 38 cm, find the length of each side of the kite. (show work)

Answers

Answer:

Step-by-step explanation:

good

Solution :

Given that,

Perimeter of kite -  38 cm

Let "x" be the one side of kite

Both of the top sides are equal

Therefore, other side = x

One side of a kite is 2 cm less than 2 times the length of another

Therefore,

One of bottom side = 2x - 2

Bottom sides are also equal

Thus, other bottom side = 2x - 5

We know that,

Perimeter = sum of all sides

38 = x + x + 2x - 2 + 2x - 2

38 = 6x - 4

6x = 38 + 4

6x = 42

x = [tex]\frac{42}{6}[/tex]

x = 7

Thus length of each side of kite is:

x = 7

2x - 2 = 2(7) - 2 = 14 - 2 = 12

Thus length of each side of kite is 7 cm , 7 cm , 12cm , 12cm

Please Brainliest

Graph a line given the point A(-2, 3) and the slope of
2|3

Answers

Answer:

Step-by-step explanation:

A kite is shaped like an isosceles triangle. To the nearest tenth what is the length of the spine?​

Answers

Answer: 73.2

Step-by-step explanation:

78/2 is 39. Now, use the pythagorean theorem to find the hypoteuse (in this case the spine), which is about 73.2

we the following mixed operations word problems
During a normal day, there are 782 passengers in average that
are late for their plane each day. However, during the
Christmas holidays, there are 1,835 passengers that are late for
their planes each day which caused delays of 14 planes. How
many more passengers are late for their planes in each day
during the Christmas holidays?

Answers

An average of 782 travelers miss their flight each day during a typical day. In contrast, 1,835 passengers are late for their flights every day over the Christmas holiday, which results in 14 planes being delayed.

1,053 travelers (2,835-782 = 1,053)

During the Christmas holidays, there are 1,053 extra passengers who are late for their flights.

How do you figure out the average number of days late?

In order to compute WADO, we multiply the total amount of each overdue invoice by the number of days past due, then divide that total by the number of days past due. You may figure out your average daily sales by dividing your total sales over a certain period of time by the number of days in that same period.

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Evaluate the infinite geometric series $0.79 0.079 0.0079 0.00079 0.000079 \dotsb$. Express your answer as a fraction with integer numerator and denominator.

Answers

Sum of the infinite geometric series = 79/9

A geometric series, or the first few terms of a geometric sequence, are the sum of an infinite number of terms with a constant ratio between them in mathematics.

Given Geometric sequences,

0.79, 0.079, 0.0079, 0.00079, 0.000079

so, the geometric series is:

0.79 + 0.079 + 0.0079 + 0.00079 + 0.000079 +........

The first term of given geometric series is 0.79

The second term of given series is 0.079

Therefore, the common ration is= 0.079/0.79 = 1/10

The Sum of infinite geometric series is given by, S= a/(1-r)

a here denotes the first term of the series

r denotes the common ration

so,

S = 0.79/{1-(1/10)}

or, S = 0.79/(9/10)

0r, S = 0.79 * (10/9)

0r, S = 79/9

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sort these from least to greatest
0
1
1/2
8/9
49/100
11/10
1/13

Answers

The numbers are sort from least to greatest as 0, 1/13, 49/100, 8/9, 1/2, 1, 11/10

What is a fraction?

A fraction can be defined as the part of a whole number, variable or element.

There are several types of fractions, some of which includes;

Mixed fractionsProper fractionsImproper fractionsComplex fractionsSimple fractions

From the information given, we have the fractions;

0, 1, 1/2, 8/9, 49/100, 11/10, 1/13

To arrange the values from least to greatest, we have to divide the fractions and find their decimal forms, we have;

1/2 = 0.5

8/9 = 0.89

49/100 = 0.49

11/10 = 1.1

1/13 = 0. 08

However, the arrangement is 0, 1/13, 49/100, 8/9, 1/2, 1, 11/10

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Is this right?

If not please help me understand or tell me the answer.

Answers

Answers:Volume = 90 cubic inchesSurface area = 126 square inchesMaterial Cost = Not sure (see the explanation below)

=========================================

Explanation:

L = 6 inches = length

W = 3 inches = width

H = 5 inches = height

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

V = volume

V = L*W*H

V = 6*3*5

V = 90 cubic inches is the volume

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

SA = Surface Area

SA = 2*(LW + LH + WH)

SA = 2*(6*3 + 6*5 + 3*5)

SA = 126 square inches is the surface area

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

Unfortunately there isn't enough information to know the material cost. Please post the full problem, and any other relevant information connected to this question.

Find the distance between point k and point L.

Answers

The distance between points L and K is 4 units.

What is the distance formula between two points?

The distance formula between two points (x₁, y₁) and (x₂, y₂) is gien by,

[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].

Given, Are two points L and K.

The coordinate points of L(- 2, 6) and K(- 2, 2).

Therefore, The distance between points L and K is,

[tex]|LK| = \sqrt{(- 2 + 2)^2 + (2 - 6)^2}[/tex].

[tex]|LK| = \sqrt{16}[/tex].

[tex]|LK| = 4[/tex].

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Is 8 15 and 16 is a Pythagorean triplet?

Answers

No, 8,15 and 16 is not a Pythagorean triplet.

A set of three integers that can be the lengths of the sides of a right triangle is called a Pythagorean triple, it also defines the positive integers a, b, and c which is a right triangle that exists with legs a,b, and hypotenuse c.

By the Pythagorean theorem, this is equivalent to finding positive integers a, b, and c satisfying  a²+b²=c²

One of the simplest Pythagorean triples is the set “3,4,5.”

Now, substitute the values in the above equation:

16²=8²+15²

256=64+225

256[tex]\neq[/tex]289

Therefore, (8,15,16) is not a Pythagorean triplet.

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What is the discriminant of the quadratic equation 2x 5x^2 1?

Answers

The discriminant of the quadratic equation 2x + 5x² = 1 is 24.

The discriminant of a quadratic equation is the value calculated from the coefficients of the quadratic equation and it gives information about the nature of the roots of the equation. The discriminant can be used to determine the number and type of solutions/roots of the equation.

-If the discriminant is greater than zero, the equation has two distinct, real solutions (or roots).

-If the discriminant is equal to zero, the equation has one real solution (or root).

-If the discriminant is less than zero, the equation has no real solutions (or roots), only complex solutions.

The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac.

Plug in the values and solve for the discriminant of the quadratic equation 2x + 5x² = 1.

b² - 4ac = (2)² - 4(5)(-1) = 24

Hence, the discriminant is 24.

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What is the volume of this rectangular prism?

Answers

Answer:

40

Step-by-step explanation:

5 x 4 x 2 = 40

length x width x height = volume

Tickets for all of the described charity raffle games cost $2 per game. James wants to choose three raffles that will give him the best chance of winning. Identify the games that james should play and the games he shouldn’t.

Answers

Answer:

C,A, and F

Step-by-step explanation:

the ones that basically give him a chance is the very first one on the left side and the 3rd one down on the left side and the 2nd column the 2nd one hope this helps

What's the longest UK number 1?

Answers

The person who has the most number 1 in UK is Elvis Presley. He has a total of 21 number 1 which is the highest in history.

The UK Singles Chart is a chart which numbers musician on the basis of their songs and their sales and streams it  was created in 1969. The records and statistics listed here, however, date back to 1952 .

The song which charted the charts was Old Town Road which was recently remixed and launched by Lil Nas X.

Elvis Aaron Presley or more commonly known as Elvis, was an American singer and actor. He dubbed the "King of Rock and Roll", and is now regarded as one of the most significant cultural figures of the 20th century.

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Is this a perfect square trinomial X² 14x 49?

Answers

x² + 14x + 49, this is a perfect square trinomial, which is expressed as

(x + 7)².

What is trinomial?

Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."

An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.

A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.

Given that,

x² + 14x + 49

(x)² + 2(7x) + 49

= (x)² + 2(x)(7) + 7²

This is similar to a² + 2ab + b² = (a + b)²

so, we can write:

= (x + 7)²

= (x +7) (x + 7)

so, this is a perfect square trinomial.

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3. Given: ACAN
m/ATN= (4x + 18)
Find: x so that AT is an altitude
N

Answers

Therefore , the solution of trigonometry function comes out to be tan x tan(4x+18)

What does trigonometry mean exactly?

When it comes to trigonometry, the relationship between the rectangular line segment and The field is believed to have originated in the 1770s, most likely beginning in the third century through the fusion of astrophysics and mathematical sciences. Numerous mathematical equations and their possible uses in calculations are covered by precise mathematical techniques. The basis of trigonometry are the six basic trigonometric operations.

Here,

tan x tan 4x=1

cos 4X cos X - sin 4x sin x=0

cos 5x=0

5x=(n+1/2)π,n ∈ Z

x=(2n+1)/10 π,0 <x <π

π/10, 3π/10, 5π/10, 7π/10,9π/10 (5π/10 is not possible)

Thus, there are only four solutions.

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A laboratory uses liquid nitrogen tanks of two different sizes. The combined volume of 3 large tanks and 2 small tanks is 24 liters. The combined volume of 2 large tanks and 3 small tanks is 21 liters. What is the volume of each size of tank? JUSTIFY YOUR ANSWER.

Answers

The size of the large tank is 6 liters and the size of the small tank is 3 liters.

What is the size of each type of tank?

The first step is to form a system of equations using the information provided in the question:

3l + 2s = 24 equation 1

2l + 3s = 21 equation 2

Where:

l = volume of the large tank s = volume of the small tank

The elimination method would be used to solve the equations:

Multiply equation 1 by 2 and equation 2 by 3:

6l + 4s = 48 equation 3

6l + 9s = 63 equation 4

Subtract equation 3 from equation 4:

5s = 15

Divide both sides of the equation by 5

s = 15 / 5

s = 3 liters

Substitute for s in equation 1 :

3l + 2(3) = 24

3l + 6 = 24

3l = 24 -  6

3l = 18

l = 18 / 3

l = 6

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HELP ME PLEASE . THESE ARE RATIONAL NUMBERS BTW.

Answers

Answer:

15. -3 1/4

16. -4 1/2 OR -4 2/4

17. 1 1/4

18. -5 3/4

19. 1/2 OR 2/4

20. -2 1/2 OR -2 2/4

Step-by-step explanation:

Answer:

15) -3.25

16) -4.5

17)1.25

18)-5.75

19).5

20)-2.5

Which describes why digital signals are a more reliable way to encode and transmit information than analog signals? Multiple choice question. Noise builds up on digital signals only when the signals travel long distances. Noise is easily filtered out without damage to the original signal because only one of two values is expected. Noise is easily filtered out without damage to the original signal because a narrow range of values is expected. Noise does not build up on digital signals when they are transmitted, unlike analog signals.

Answers

The solution is Option B.

Noise is easily filtered out without damage to the original signal because a narrow range of values is expected

What are digital signals?

A digital signal encodes data as a sequence of discrete values. A digital signal can only have one value from a finite set of possible values at any given time. A signal which is a discrete function of time, i.e. non-continuous signal, is known as digital signal. Digital computers and digital phones are some of the examples of digital signals

The three types of digital signals are

Continuous-Time/Analog Signal

Discrete-Time Signal

Digital Signal

Given data ,

The digital signals are a more reliable way to encode and transmit information than analog signals

Because , while transmitting information through digital signals , they have less interference over long distances and digital signals offer better clarity

The digital devices only record pieces of sound waves, not full waves.

Now , Analog technology stores information as sound waves; digital technology stores it as strings of ones and zeroes.

Hence , noise is easily filtered out without damage to the original signal because a narrow range of values is expected

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You found that the area of the quarter circle is 78.50 cm squared. You are right. How was this answer found?
Please help me! It's basically asking how to find the area of this quarter circle. I also have to show how I know that the answer is correct by using these steps to get the area of 78.50 cm squared.

Answers

The area of the quarter of the circle is 78.50 squared centimeters.

How to find the area of quarter of a circle.

A circle is a 2 dimensional plane shape that is bounded by a curve. Its area can be determined by;

area of a circle = [tex]\pi r^{2}[/tex]

where r is the value of the radius of the circle.

The radius of a circle is given as the half of its diameter.

Thus, a quarter of a circle is the 4th part of a given circle. This implies of fraction selected when a circle is divided into 4 equal part.

So that;

area of quarter of a circle = area of a circle/ 4

                                          = [tex]\pi r^{2}[/tex]/ 4

The area of quarter of then given circle = ((22/7)*(10)^2)/ 4

                                                       = 78.50 squared centimeters

Therefore, the answer to the area of the quarter circle was found as explained above.

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