How do you check if an inverse is a function?

Answers

Answer 1

If a value of y relates only to one value of x, then the function does have an inverse function.

Define the term function and its inverse?

A relation between such a collection of inputs and outputs is known as a function.

A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is just the input.If and only if the outcome of reflecting a function's graph about the line y = x is the function's graph, then the function f does have an inverse (passing from the vertical line test).

Thus, if a value of y relates only to one value of x, then the function does have an inverse function.

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Related Questions

Solve the real-world situation by using the substitution method.
1. A standard rectangular highway billboard has a perimeter of 124 ft.
The length is 34 ft. more than the width. Let l represent the length
521 + 2w
124
and w represent the width. The system of equations
1 = 34 + w
Find the length and the width.

Answers

Answer:

521 plus 521 is equal to 10000

If Jamar can run 3/5 of a mile in 2 minutes 30 seconds, what is his rate in miles per minute? (Remember, distance = rate x time)

Answers

Answer:

6/25

Step-by-step explanation:

(3/5) / 2.5 = 6/25

What are personal assets?

Answers

Personal assets are the list of things which are owned by any person for the present or the future use such as house , saving accounts, Cash etc.

Personal assets the list of things all of which are owned by any personal or a family for the present or the future use.When an individual want to take loan of any purpose then bank give the loan by considering the present value of the personal assets.It represent the total property and cash owned by any individual for the present or the future use.Example of personal assets are : house, any other property , cash, certificate representing some value, jewelry, any vehicle etc.

Therefore, the personal assets represent the valuable  items owned by any individual for present or the future use.

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How many 1/9s can go into 2?

Answers

It takes 9, 1/9s to make a whole (1) so double that and it takes 18, 1/9s to make 2

A distribution of exam scores has mean 60 and standard deviation 18. If each score is doubled, and then 5 is subtracted from that result, what will be the mean and standard deviation, respectively, of the new scores

Answers

If each score is doubled, and then 5 is subtracted from that result, then the mean and standard deviation will be 115 and 36 respectively.

What will be the mean and standard deviation?

A huge group of test results has a mean of 60 and a standard deviation of 18. If each score is doubled and then 5 is deducted from the result, the mean and standard deviation are “ mean = 115; standard deviation = 36”. Mean = 2 x 60 -5 = 120 -5 = 115

2 x 18 = 36 standard deviation

The mean is the average and is calculated as the sum of all the results from the example divided by the total number of events.

The standard deviation (SD) is a statistic used to assess the degree of variation or dispersion in a set of data values.

A low standard deviation indicates that the information points slant toward being near the mean of the set, whereas an exclusive expectation deviation or a high standard deviation indicates that the information points tilt toward being near the mean of the set.

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choose the graph of the inequality X< 7
choose one:​

Answers

3rd one. The circle is on 7 and is going to the left.


in one year, the student enrollment increased from 560 to 588. This was an increase of what percent?

Answers

Answer:

5% Increase

Step-by-step explanation:

560 * 0.05 = 28

560 + 28 = 588

Answer: 5%

Step-by-step explanation:

Orig | 560 | 100

Change | 28 | x

new | 588 | n/a

560/28 = 100/x

1 x 5

5%

Help me please I would really appreciate it​

Answers

Step-by-step explanation:

The coordinates of the points are P1(2, 2) and P2(10, 2). The distance d between these two points are given by

[tex]d = \sqrt{ {(x\frac{}{2} - x\frac{}{1} ) }^{2} + ({y\frac{}{2} - y\frac{}{1}) }^{2} } \\ = \sqrt{ ({10 - 2})^{2} +( {2 - 2)}^{2}} \\ = 8[/tex]

Solve for x in this triangle. Round your answer to the nearest tenth. 18 Xº 23​

Answers

Answer:

51.50004959055205

Step-by-step explanation:

[tex]sin (x) = \frac{18}{23}[/tex]

A truck uses 2.5 litres of fuel to travel 8 kilometres.
a How far will the truck travel on 1 litre of fuel?
b How far will the truck travel on 120 litres of fuel?

Answers

To answer these questions, we need to know the fuel efficiency of the truck, which is the distance the truck can travel on one litre of fuel.

a) To find the fuel efficiency, we can divide the distance traveled (8 km) by the amount of fuel used (2.5 L). This gives us a fuel efficiency of 8 km / 2.5 L = 3.2 km/L. So the truck can travel 3.2 km on 1 litre of fuel.

b) To find the distance traveled on 120 litres of fuel, we can multiply the fuel efficiency (3.2 km/L) by the number of litres of fuel (120 L). This gives us a total distance of 3.2 km/L * 120 L = 384 km.

Answer:

a:20 km

b:384

Step-by-step explanation:

a:

[tex] \frac{2.5}{ 8} = \frac{1}{x} [/tex]

[tex]x = 20[/tex]

b:

[tex] \frac{2.5}{8} = \frac{120}{y} [/tex]

[tex]y = 384[/tex]

A recipe ue 1/3 cup of flour and 1/8 cup of ugar. How much flour and ugar doe the recipe ue altogether

Answers

Altogether, the recipe uses 1/2 cup of flour and 1/8 cup of sugar.

What is altogether?

Altogether in math refers to the sum of two or more numbers or values. It is a way of combining two or more items to obtain a total. In math, the term "altogether" is used to denote the sum of all the individual items, as opposed to all of them considered as one. For example, the sum of the numbers 2, 4, and 6 is 12, which is the "altogether" in math.

To calculate this, we must convert the fractions into decimals and then add them together.

The 1/3 cup of flour can be converted to 0.33 cup, and the 1/8 cup of sugar can be converted to 0.125 cup.

When added together, they equal 0.455 cup, or 1/2 cup. Therefore, the recipe uses a total of 1/2 cup of flour and 1/8 cup of sugar.

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How do you find the missing side of an obtuse triangle?

Answers

Answer:

Using the cosines law

Step-by-step explanation:

So, we need to find the length of the other side, we will use the version of the Cosine Rule where a2 is the subject of the formula, which is given by, a2=b2+c2−2bccosA, Side a is the one we are trying to find. Sides band care the other two sides, and angle Ais the angle opposite side a. c2=a2+b2−2abcosC

How are the angles of the two figures related

Answers

Answer:

I believe its A

Step-by-step explanation:

A store creates a mixture using only peanuts and almonds.


There are 20 pounds of the mixture.

Peanuts cost $2. 95 per pound.

Almonds cost $5. 95 per pound.

The mixture costs $4. 00 per pound.

How many pounds of peanuts are in the mixture?

Answers

There are 13 pounds of peanuts present in the mixture.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7. There are different types of equations like linear, quadratic, cubic, etc.

Let's consider Almonds be a and Peanuts be p.

from given conditions,

a + p = 20

and 5.95 a + 2.95 p = 4(20)

5.95 a + 2.95 p = 80

take, a = 20 - p

5.95 (20 - p) + 2.95 p = 80

119 - 5.95 p + 2.95 p =80

119 - 3 p = 80

3p = 39

p = 39/3

p = 13

Therefore, there are 13 pounds of peanuts present in the mixture.

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Find the vertices and foci of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16

Answers

Vertices are at (-7, 5) and (-1, 5) and foci are at (-9, 5) and (1, 5) of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16.

As per the given data the given equation is:

[tex]\\$$\frac{ (x+4)^2}{9} - \frac{(y-5)^2 }{16}=1$$[/tex]

The standard form for the equation of a hyperbola with center (h, k) is [tex]\frac{(x-h)^{2} }{a^{2} } - \frac{(y-k)^2}{b^{2} } =1[/tex]

Your hyperbola opens left/right, because it is of form x - y.

Comparing terms, we find that

h = -4, k = 5, a = 3, y = 4

In the general equation, the coordinates of the vertices are at [tex]$(h \pm a, k)$[/tex].

Thus, the vertices of your hyperbola are at (-7,5) and (-1,5).

The foci are at a distance c from the center, with coordinates [tex]$(\mathrm{h} \pm \mathrm{c}, \mathrm{k})$[/tex], where [tex]$c^2=a^2+b^2$[/tex]

[tex]c^2=9+16=25$[/tex], so c = 5.

The coordinates of the foci are (-9, 5) and (-1, 5).

The Figure below shows the graph of the hyperbola with its vertices and foci.(attached at the end of solution)

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Make a tree diagram to show sample space. Then select the total number of outcomes.
rolling a number cube, tossing a coin and choosing a card from cards marked A and B
a. 24
C.
18
b. 12
d. 6
HELP PLEASE

Answers

Answer:

a. 24

Step-by-step explanation:

Rolling a number cube: 6 outcomes

tossing a coin: 2 outcomes

At this point, we have 6 x 2 = 12 outcomes, because each of the 6 numbers on the cube can each have a heads or tails outcome

Choosing card A or card B gives us 2 more outcomes for each of the 12 outcomes we have so far.

12 x 2 = 24

The level of the tide in a harbor changed from 9 1/4 ft to 4 1/2 ft above sea level over a period of 3 1/4 hr

Answers

Answer:

The answer is "[tex]\bold{- \frac{19}{13} \ / hour}[/tex]"

Step-by-step explanation:

Please find the complete question in the attached file.

Calculating the difference of [tex]9 \frac{1}{4}\ and \ 4 \frac{1}{2}[/tex]  dividing the value by [tex]3 \frac{1}{4}[/tex]

[tex]\to 4 \frac{1}{2} - 9 \frac{1}{4}\\\\ \to \frac{9}{2} - \frac{37}{4}\\\\ \to \frac{18-37}{4} \\\\ \to -\frac{19}{4}\\\\\to -\frac{19}{4} \div \frac{13}{4}= -\frac{19}{4} \times \frac{4}{13} = -\frac{19}{13}\\[/tex]

Find the volume of the prism.

Answers

Answer:

1120

Step-by-step explanation:

What's the domain of a logarithmic function?

Answers

Answer:

  all positive numbers

Step-by-step explanation:

You want to know the domain of the log function.

Log function

The log function ln(x) is defined for all x > 0. A log function with any other base is similarly defined.

  log function domain: all positive numbers

A parent log function has a vertical asymptote at x=0, and an x-intercept at x=1. Its vertical scaling will depend on the base of the logarithm. Like any function, it can be translated and scaled horizontally and vertically.

__

Additional comment

In the field of complex numbers, the log function is defined for any non-zero number. For example, ln(-1) = πi.

The range is all real numbers.

y=-3x+15 create a word problem

Answers

Answer:

John starts with $12 dollars in his bank account, each day he spends $3.

Step-by-step explanation:

Which shape has atleast one pair of perpenicular sides

Answers

The fourth shape which is a square has at least one pair of perpendicular sides.

What is a quadrilateral?

A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.

In the third figure, it is a parallelogram,

In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

The sum of adjacent angles is 180° but individuals are not right angles.

The fourth figure is a square and by the properties of a square, all the interior angles are right angles.

Therefore, It has two pairs of perpendicular sides.

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Martina walked 34 of a mile in 35 of an hour. At this rate, how far can Martina walk in one hour?

Answers

Answer:

34 = 35

Step-by-step explanation:

34x35

Answer:

Martina can walk 1 1/4 miles in one hour.

Step-by-step explanation:

Find the reciprocal of 3/5 (by flipping the fraction)

5/3

Multiply 5/3 by 3/4

3/4(5/3)= 15/12= 1 1/4

​Andy is A years old. His brother Ron is R years old. Andy multiplies his own age by 3. He then subtracts twice Ron's age. ​The answer is 6. ​Ron subtracts his age from Andy's age. ​The answer is −2 a​Write a pair of simultanous equations that model Andy's and Ron's ages.

Answers

Answer:the  pair of simultanous equations that model Andy's and Ron's ages are

3A-2R=6----Equation 1

R-A =2----Equation 2

Andy is 10 Years and Ron is  12 years  

Step-by-step explanation:

Andy's age is represented as A

and Ron';s age is represented as R

Now if Andy multiplies his own age by 3. He then subtracts twice Ron's age. ​The answer is 6 can be expressed mathematically as

3A-2R=6

And if Ron subtracts his age from Andy's age. ​The answer is −2  can be expressed as

R-A =2

Therefore the  pair of simultaneous equations that model Andy's and Ron's ages are

3A-2R=6----Equation 1

R-A =2----Equation 2

Solving becomes

3A-2R=6----Equation 1

R-A =2----Equation 2

Make R subject formulae in equation 2

R =2+A

Putting R =2+A in equation 1

3A-2(2+A)=6

3A -4-2A =6

A-4=6

A=6+4=10

From eqn 2,

R-A =2

R-10 =2

R=10+2=12

Andy is 10 Years and Ron is  12 years  

How many one-cup servings of milk are in a two-liter bottle? Round your answer to the nearest tenth.
____________one-cup servings

Answers

The number of cups of serving that is possible in a two-liter bottle is 8.

What is a unitary method?

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

We know 1 liter is equal to 4 cups.

Therefore, The number of cups serves possible in a two-liter bottle is,

= (2×4) cups.

= 8 cups.

So, 8 cups of servings are possible from a two-liter bottle.

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Use polar coordinates to find the volume of the given solid. Inside the sphere x^2 + y^2 + z^2 = 36 and outside the cylinder x^2 + y^2 = 1.

Answers

The required volume of the given solid is (√16 - r²) -(-√16 - r²).

What is volume?

The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.

Volume and the notion of length are connected.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface.

The cubic meter (m3), a derived unit, is the SI unit of volume.

So, the integrand often takes the form z upper z lower, where z stands for the solid's lower and upper borders.

We are treating the sphere as a hemisphere as of right now, with the XY-plane serving as its lower boundary. Consequently, you must multiply by 2.

The solid's volume is (√16 - r²) -(-√16 - r²).

Therefore, the required volume of the given solid is (√16 - r²) -(-√16 - r²).

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Correct question:

Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.

The total surface area of the prism below is 456 square centimeters. What is the value of the x, height of the prisim?

Answers

*see attachment for the figure

Answer:

x = 17 cm

Step-by-step explanation:

Total surface area of triangular prism = bh + L(s1 + s2 + s3)

Where,

Total surface area = 456 cm²

b = 8 cm

h = 6 cm

s1 = √(8² + 6²) = 10 cm (pythagorean theorem)

s2 = 8 cm

s3 = 6 cm

L = x

Plug in the values

465 = 8*6 + x(10 + 8 + 6)

465 = 48 + x(24)

465 - 48 = 24x

417 = 24x

417/24 = x

17.375 = x

x = 17 cm (approximated)

What is the value of S unit?

Answers

Triangle ABD is a right-angled triangle. The value of s which is the hypotenuse of the triangle ABD is 17 units.

What is triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.

Here,

Given information:

From the given figure, the following information can be extracted:

Triangle ABD is a right-angled triangle.

Base AB is 8 units, Height BD is 15 units.

s is the hypotenuse of the triangle ABD.

Use the Pythagoras theorem to solve for the value of s or AD,

AD²=AB²+BD²

s²=8²+15²

s²=289

s=17 units

Therefore, the value of s which is the hypotenuse of the triangle ABD is 17 units.

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........... I donr know what I'm doing-​

Answers

Intercept = 1

Equation - y = -(2/5)x + 1

University Data Total Receiving Financial Aid Not Receiving Financial Aid Undergraduates 4222 8120 3898 Graduates 1879 731 2610 Total 6101 4629 10730 If a student is selected at random, what is the probability that the student is a graduate (rounded to the nearest percent)​

Answers

Answer:

24%

Step-by-step explanation:

Use the table to find the required data:

P(graduate) = Total graduates / Total studentsP(graduate) = 2610/10730*100% = 24% (rounded)

The probability that a student selected at random is a graduate student is 31%.

What is probability?

The probability of an event happening is represented by a number. The ratio of favourable outcomes to all outcomes is how probability is defined.

The total number of students is 6101, out of which 1879 are graduate students. Therefore, the probability that a student selected at random is a graduate student is:

P(graduate student) = number of graduate students / total number of students

P = 1879 / 6101

P = 0.3078

Therefore, the probability that a student selected at random is a graduate student is 31%.

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Daija is creating a budget, and evaluating his purchases over the last month. Consider the following code segment which attempts to find the sum of all purchases made in the last month, stored in purchased List. N ← 1 sum ← 0 REPEAT UNTIL () { sum ← sum + purchase List[n] n ← n + 1 } What code can replace missing code to assign the total of all values in purchase List to sum

Answers

The missing code that can replace to assign the total of all values in purchase List to sum, is: REPEAT UNTIL (n > purchaseList.length)

What is syntax of REPEAT UNTIL?

The syntax for a REPEAT UNTIL loop in most programming languages is as follows:

REPEAT {

// code to be executed

} UNTIL (condition)

or

DO {

// code to be executed

} UNTIL (condition)

What is looping?

Looping is a programming construct that allows a certain block of code to be executed repeatedly. The two main types of loops are for loops and while loops.

A for loop is used to execute a block of code a specified number of times. It typically starts with a variable initialization, then a condition is checked, and if the condition is true, the code block inside the loop is executed, and then the variable is updated.

The missing code that can replace the empty parentheses in the REPEAT UNTIL statement to assign the total of all values in purchase List to sum, is:

REPEAT UNTIL (n > purchaseList.length)

This means that the loop will continue to execute until the value of n is greater than the length of the purchaseList. In each iteration, the value of purchaseList[n] is added to the sum, and then n is incremented by 1. So, this loop will iterate through all the elements in the purchaseList, adding each one to the sum, until it reaches the end of the list. This will give the total sum of all purchases made in the last month.

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