(20 marks in total) Find the domain of each of the following functions. Write your solutions using interval notation. 3+x (a) (10 marks) f(x) = 3 2x - 1

The discount rate is 15% and the VAT rate is 13%

The following can be deduced:

MP = 2080

Discount = d%

VAT = (d-2)%

Cost = 1997.84

Apply discount:

2080 - d% = 2080*(1 - 0.01d)

Add VAT:

2080*(1 - 0.01d) + (d - 2)%

2080*(1 - 0.01d) * (1 + (d -2)/100)

2080*(1 - 0.01d) * (0.98 + 0.01d)

= 1997.84

(1 - 0.01d)(0.98 + 0.01d) = 1997.84/2080

0.98 + 0.01d - 0.0098d - 0.0001d²

= 0.9605

- 0.0001d² + 0.0002d + 0.98- 0.9605 = 0

0.0001d²- 0.0002d - 0.0195 = 0

d² - 2d + 195 = 0

Solving the quadratic equation we get:

d = 15

Therefore discount is 15%

VAT rate = d - 2 = 15% - 2% = 13%

The concept shown above is the calculation for the discount and the amount of the value added tax.

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Answer:

-9 + ( -16) = -25

( -4) – (-6) + (-5) – (8) =-11

( 3) – (-9) + (-3) – (-2) =11

- ( 5) – (-7) + (-8) =-6

- ( -8) – (-9) + (-4) – (-1) =14

( -5) – (-11) + (10) – (8) =8

( -1) – (-2) + (-3) – (-6) =4

( -4) – ( 4) – (6) + (-5) – (-8) =-11

(-6) + (-5) – (-8) =-3

Step-by-step explanation:

Hope it helps

Answers:

-9 + ( -16) = -25

( -4) – (-6) + (-5) – (8) = -11

( 3) – (-9) + (-3) – (-2) = 11

- ( 5) – (-7) + (-8) = -6

- ( -8) – (-9) + (-4) – (-1) = 14

( -5) – (-11) + (10) – (8) = 8

( -1) – (-2) + (-3) – (-6) = 4

( -4) – ( 4) – (6) + (-5) – (-8) = -11

(-6) + (-5) – (-8) = -3

The triangles ΔKLM and ΔEFG can be proven similar using both SSS and SAS similarity theorems.

In this question, we need to determine whether the triangles can be proven similar using the SSS or SAS similarities theorems.

For given diagrams,

the ratio of the corresponding sides is:

KM/EG = 8/24

            = 1/3

KL/EF = 6/18

          = 1/3

and ML/GF = 5/15

                  = 1/3

The sides of both triangles is proportional .

So by SSS similarity theorem, we have ΔKLM ≈ ΔEFG

Also, ML/GF = 1/3

∠L ≅ ∠F

KL/EF = 1/3

So by SAS similarity theorem, we have ΔKLM ≈ ΔEFG

Therefore, the triangles can be proven similar using both SSS and SAS

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The figure associated to given question is as shown below.

The term "arc" is used to describe units of measure for angular distance because it refers to the length of an arc on a circle.

Angular distance is the measure of the separation between two points on a circle or an arc. The term "arc" is used to describe this measure because it refers to the length of the arc connecting the two points on the circle.

This length is a fraction of the circumference of the circle and is proportional to the angle between the two points. The use of the term "arc" in this context is a nod to the geometric origins of angular measurement, which is based on the properties of circles and their angles.

The most common units of angular measurement are degrees, minutes, and seconds, which are all based on the division of a circle into 360 equal parts (degrees) and further subdivisions (minutes and seconds).

Other units of angular measurement, such as radians and gradians, are also based on the properties of circles and their angles.

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Answer:

Hi! The answer to your question is 8

Step-by-step explanation:

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☆Brainliest is greatly appreciated!☆

Hope this helps!!

- Brooklynn Deka

The probability that Esteban wins the game is 29/49.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, Esteban is playing a matching card game.

If the cards are identical, he wins the game.

Probability of getting cross on both the cards

2/7 × 2/7

= 4/49

Probability of getting star on both the cards

5/7 × 5/7

= 25/49

Probability to win the game is

4/49 + 25/49

= 29/49

Therefore, the probability that Esteban wins the game is 29/49.

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The target population is the population of interest that researchers aim to generalize their findings to.

The correct answer is c. sample.

In a research study, the population of interest is often too large or too difficult to access entirely. Therefore, researchers select a representative subset of the population to study, which is called a sample. In this case, patients with inflammatory bowel disease are the population of interest, and those who participate in the study are the sample.

The accessible population refers to the portion of the population that is accessible to the researcher. For example, if a researcher is studying the prevalence of a disease in a certain region, the accessible population would be the individuals living in that region.

An element refers to a single member of the population or sample.

The target population is the population of interest that researchers aim to generalize their findings to.

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Answer:

the X is 35

Step-by-step explanation:

la respuesta para la ecuación es -5

Answer:

7u-21+5u=39 12u-21=39 12u=39+21 19u=60 u=5

Answer:

A

Step-by-step explanation:

the exact number is 1,000 miles per hour

so the closest answer is A

Answer:

solid A

Step-by-step explanation:

I'm sorry for late

Answer:

Step-by-step explanation:

Happy Ramadan!

Hope this help :)

The probability of the number of systems sold being more than 2 standard deviations from the mean will depend on the sample size and the sample statistics.

In the event that we need to discover the probability that the number of systems sold is more than 2 standard deviations from the cruel, we ought to discover the zone beneath the typical bend past 2 standard deviations from the cruel in both headings (i.e., within the tails).

Agreeing to the observational run of the show (moreover known as the 68-95-99.7 run of the show), roughly 95% of the perceptions in a typical conveyance drop inside 2 standard deviations of the cruel. Hence, the likelihood of a perception being more than 2 standard deviations from the cruel is roughly 1 - 0.95 = 0.05.

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The value of r/s is equal to 9.

There exists a theorem that states that the square of a hypotenuse in a right-angled triangle is equal to the sum of squares of the perpendicular side and the base side.  This theorem is known as Pythagoras theorem. By applying Pythagoras' theorem in this right-angled triangle formed in our image, we obtain the given formula

\(H^2 = P^2 + B^2\)

\((r + s)^2 = (r - s)^2 + (r - 3s)^2\)

\(r^2 + 2r.s + s^2 = 2r^2 - 8r.s + 10.s^2\)

\(r^2 - 10.r.s + 9s^2 = 0\)

(r - 9s) (r - s) = 0

Now we will equate these two factors to 0.

By equating, we get r/s = 9 and r/s = 1.

r/s = 1 does not apply to the geometry in this question.

So, r/s = 9 is the solution for the given equation.

Therefore, our answer is 9.

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The complete question is -

"Three circles of radius s are drawn in the first quadrant of the xy-plane. The first circle is tangent to both axes, the second is tangent to the first circle and the x-axis, and the third is tangent to the first circle and the y-axis. A circle of radius r>s is tangent to both axes and to the second and third circles. What is r/s? "

Answer

This statement is not correct.

Explanation

Not every straight line is a graph of a function.

Although, nearly all linear equations are functions because they pass the vertical line test. That is, most linear equations are set up that you can obtain a value for y, given a value for x.

Examples of linear equations that are functions include

y = 10

y = x

y = 2x

y = 7x + 14

y = − 2x − 7

The exceptions are relations that fail the vertical line test. The ones that don't give a y-value for every x.

Examples of linear equations that are not functions include

x = some constant

That is,

x = 7

x = -100 etc.

Hope this Helps!!!

The Length of the conjugate axis is equal to 2b. The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola.

In a hyperbola, the name of the green segment is called the transverse axis. The transverse axis is the longest distance between any two points on the hyperbola, and it passes through the center of the hyperbola. It divides the hyperbola into two separate parts called branches.

The transverse axis of a hyperbola lies along the major axis, which is perpendicular to the minor axis. Therefore, it is also sometimes called the major axis.

The other axis of a hyperbola is called the conjugate axis or minor axis. It is perpendicular to the transverse axis and passes through the center of the hyperbola. The length of the conjugate axis is usually shorter than the transverse axis.In the hyperbola above, the green segment is the transverse axis, and it is represented by the letters "2a". Therefore, the length of the transverse axis is equal to 2a.

The blue segment is the conjugate axis, and it is represented by the letters "2b".

Therefore, the length of the conjugate axis is equal to 2b.The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola. In particular, the distance between the two branches of the hyperbola is determined by the length of the transverse axis.

If the transverse axis is longer, then the branches of the hyperbola will be further apart, and the hyperbola will look more stretched out. Conversely, if the transverse axis is shorter, then the branches of the hyperbola will be closer together, and the hyperbola will look more compressed.

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Step-by-step explanation:

5 sandwiches plus 7 pies =12

12×7 days (week) =84 were sold

Answer:

1. City A
2. Exponential Growth
3. Linear

Step-by-step explanation:

The equation for exponential growth is f(x)=a(1+r/100)^x, where a is the initial growth/starting population, r is the growth rate, and x is the time intervals.

City A
f(x)=200(1+1.05/100)^x
Simplify:
f(x)=200(1.105)^x

City B
An increase in 20 people each year is NOT exponential but linear:
f(x)=20x+200

Now we plug in x for 1 to stand for 1 year and see which city has a greater number:
City A:
f(1)=200(1.105)^1
f(1)=200 x 1.105
f(1)=221

City B:
f(1)=20(1)+200

f(1)=20+200

f(1)=220

City A will have more people.

City A is an exponential function because there's a percent increase every year, and there will be more people every year because there are more people. This is kind of how compound interest also works

City B is a linear equation because a set number of people are added every year and doesn't change based on the amount of people already in it.

1. City B will have more population after 1 year.

In this case, we have been given of both the cities A and B with each year's growth factor and we have been told to find out, which city will have more population after 1 year. So to find out the comparison, first we need to find out the individual popoulation of both the cities after 1 year of interval.

So, population of City A after 1 year will be 200 * 1.05 = 210

Similarly,  population of City B after 1 year will be 200 + 20 = 220

It is clear that City B has more population as compared to City A.

Therefore, after 1 year City B has more population.

2. equation for City A is Exponential Growth Equation.

Exponential growth is the growth which takes place when a particular quantity increases at a constant rate over a fixed time period. It is given in the form of \(P = P_{0} * (1 + r)^t\), where P is population, \(P_{0}\) is initial population, r is the growth rate, and t is time period.

3. equation for City B is Linear Equation.

Linear equation is a representation of a straight line when graphed on paper. It has constant coefficients and variables raised to power 1. It is given in the form of \(P = P_{0} + rt\), where P is population, \(P_{0}\) is initial population, r is the growth rate, and t is time period.

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In an incidence geometry with the additional axiom that every line has exactly three points lying on it, the minimum number of points required is 4.

This is because a line must have at least two-points to exist, and if it has only two points, it is not possible to have another point lying on it (since every line must have exactly three points).

Hence, there must be at least 4-points to create two lines such that each line contains exactly three points.

Also, with 4 points, it is possible to create 6 lines such that each line contains exactly 3 points, forming a configuration known as the Fano-plane, which is the smallest example of an incidence geometry that satisfies the given axiom.

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Answer:

515.

Step-by-step explanation:

40 x 12 = 480

480 + 35 =515

Answer:

The answer would be $515

Step-by-step explanation:

40x+35=t

40(12)+35=t

40 times 12 = 480

480 + 35 =515

Answer: About 31%

Step-by-step explanation:

1. Divide 114 to 361

Answer:

4 1/3 - 2 1/4 = 25/12 or 2 1/12

Step-by-step explanation:

Answer:

This is gebber gabber but yes

Step-by-step explanation:

Hello there. To graph this function, the best way is to find two points that are into the line and then pass a line through them.

Since the image of a line is all the real numbers, we can pick any point for x and find y that satisfy it.

Starting with x = 0, we have that f(0) = -3 * 0 + 4 = 4.

So the point (0, 4) is in the line.

Now, making x = 1, we have that f(1) = -3 * 1 + 4 = -3 + 4 = 1

So the point (1, 1) is in the line.

Graphing the function, we have:

This is the graph of this function.

Answer:

#1: 146 degrees #2: 111 degrees

Step-by-step explanation:

The angles of a heptagon (a shape with 7 sides) are supposed to add up to 900 degrees, so just add up all the sides that you know and subtract it from 900 and you will have x! Do the same thing with the second one, except is is a hexagon and all the angles should add up to 720 degrees. (Don't forget to add the right angle, which is 90 degrees) So add up all the sides you know and subtract from 720 to get x.

P.S. If correct, please give Brainliest?

Answer:

N = number of sides

The sum of the interior angles of a polygon is equal to (N x 180)-360.

The first problem has 7 sides so the interior angle total = 900 degrees.

Add up all the known interior angles:

96+105+161+123+155+114+x = 900

x = 900-754 = 146 degrees

The second problem has 6 sides so the interior angle total = 720 degrees.

Add up all the known interior angles:

127+40+202+90+150+x = 720

x = 720-609 = 111 degrees

The  rate of change of Wayne's hours of sleep with respect to each day is  5  hours per day.

The rate of change of Wayne's hours of sleep with respect to each day is calculated as follows;

Mathematically, the formula is given as;

rate of change of sleep = change in sleep / change in time of sleep

The change in the sleep pattern = 30 - 15 = 15 hours

The change in the time of sleep = 6 - 3 = 3 days

The  rate of change of Wayne's hours of sleep with respect to each day is calculated as

rate of change of sleep = ( 15 hours ) / ( 3 days )

rate of change of sleep = 5  hours per day

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