Let f(x) = 4x + 3 and g(x)=x²-x+1. Perform the function operation and then find the domain.
g(x)-f(x)
g(x)-f(x) = (Simplify your answer.)

Using Arithmetic progression, There were 4,13,22,31 pupils chosen out of the applicants.

The professor desires to choose four students at random.

A sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence. The common difference of the sequence is d, and the number an is the first term. An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.

The fourth student was chosen at random, followed by every ninth student.

The fourth student is chosen first.

Using the following term formula, which is

=>a + d(n-1) (n-1)

The second student is the one after that.

=>4 + 9(2-1) (2-1)

=>4 + 9(1) (1)

=>4 + 9

=> 13

The third pupil will be

=>4 + 9(3-1) (3-1)

=>4 + 9(2) (2)

=>4 + 18

=> 22

The fourth pupil will be

=>4 + 9(4-1) (4-1)

=>4 + 9(3) (3)

=> 4+ 27

=> 31

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The expression that represents the number of seconds Jacob has been running is t - 7.

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. An expression's structure is as follows: (Math Operator, Number/Variable, Math Operator). The two integers are connected by a mathematical operator.

Since Jacob started running 7 seconds after Alma, the number of seconds Jacob has been running can be represented as t - 7. So the expression that represents the number of seconds Jacob has been running is: t - 7.

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Answer: We can set up a system of equations to represent the information given:

Let x = length of Barbary River

Howler River = x + 230

Gin River = x + 150

Retinal River = x - 30

Total length = x + (x + 230) + (x + 150) + (x - 30) = 19,230

We can then use substitution and the equations above to solve for the length of each river:

x + (x + 230) + (x + 150) + (x - 30) = 19,230

4x + 350 = 19,230

4x = 18,880

x = 4720 (length of Barbary River)

Howler River = x + 230 = 4720 + 230 = 4950 mi

Gin River = x + 150 = 4720 + 150 = 4870 mi

Retinal River = x - 30 = 4720 - 30 = 4690 mi

Step-by-step explanation:

The equation 6x + 8 = 2(3x + 4) had infinitely many solutions.

The equation 6x + 8 = 2(3x + 4) can be solved by isolating x on one side of the equation. To do this, we can first distribute the 2 on the right side of the equation:

6x + 8 = 6x + 8

Then we can subtract 8 from both sides:

6x + 8 - 8 = 6x + 8 - 8

6x = 6x

Divide both sides by 6

6x/6 = 6x/6

x = x

This means x can assume any value which will make the equation true.

Therefore, the equation had infinitely many solutions.

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The domain of the function f(x) - g(x) is given as follows:

[tex][-6, -\sqrt{3}] \cup [\sqrt{3},6][/tex]

The domain of a function is the set composed by all the input values that the function accepts.

For a square root, the inner term cannot be negative, hence the domain of f(x) is given as follows:

x² - 3 >= 0

|x| >= sqrt(3)

x <= -sqrt(3) or x >= sqrt(3).

For function g(x), the domain is given as follows:

36 - x² >= 0

x² <= 36

|x| <= square root (36)

|x| <= 6.

-6 <= x <= 6.

The domain of the subtraction function is the intersection of the domain of both functions, hence:

[tex][-6, -\sqrt{3}] \cup [\sqrt{3},6][/tex]

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Answer: 5.4h -13 -1.9d

Step-by-step explanation:

combine the like terms together.

Price paid for car = $23622, The loss value is $3742 and total distance the car was used for is 18000 kilometres.

Distance is a measurement of how far apart two objects or points are. It is the length of the actual route taken to get from one place to another. In physics, distance is frequently used to refer to a physical length or an estimation based on other criteria, such as "a few kilometres apart" or "some miles away."

However, the distance travelled by an object to move from its initial position to its final position will be the same as the distance travelled to move from its final position to its initial position. As a result, distance is independent of a body's motion.

a. Price paid for car = $23622

Discount = 7%

Sale price = $19880

b. The loss value is $3742

c. Let total distance travelled be d

Fuel consumption=10km per litre

Cost of fuel =1.4 per litre

Cost of fuel per kilometre =1.410= 0.14

Other cost = 938

Cost of usage =0.14*d +938

Total cost including loss = 0.14*d +938+3742

The cost per kilometre has been provided as 0.4

Total cost of the vehicle's use = 0.4*d

B=A0.4*d = 0.14*d +938+37420.26*d = 4680d = 18000

Thus, Total distance the car was used for is 18000 kilometres.

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Answer: 5s + 28.3

Step-by-step explanation:

Elizabeth's annual Social Security deduction is $72580, Medicare deduction is $1053.71 per year, biweekly gross pay is $2796.15, total amount withheld for federal tax is $15336.80, amount deducted is $66.50 and annual salary is $79,307.38

a) Social Security deduction is 6.2% of Elizabeth's annual salary, which is $72,580 x 6.2% = $4,486.76 per year.

b) Medicare deduction is 1.45% of Elizabeth's annual salary, which is $72,580 x 1.45% = $1,053.71 per year.

c) Elizabeth is paid every other week, so her bi-weekly gross pay is $72,580 / 26 = $2,796.15.

d) The total amount withheld for federal tax from Elizabeth's annual salary is $72,580 x 21% = $15,336.80.

e) The amount deducted from Elizabeth's salary per paycheck for city tax is ($72,580 x 2.875%) / 26 = $66.50.

f) As of January 1, Elizabeth will receive a 9.1% raise, so her annual salary will be $72,580 x (1 + 0.091) = $79,307.38.

Correct Question :

Elizabeth works for Picasso Paint Supplies. Her annual salary is $72,580.

a) What is Elizabeth's annual Social Security deduction?

b) What is Elizabeth's annual Medicare deduction?

c) Elizabeth is paid every other week. What is her biweekly gross pay?

d) Each pay period, Elizabeth's employer deducts 21% for federal withholding tax. What is the total amount withheld for federal tax from Elizabeth's annual salary?

e) If Elizabeth is taxed at an annual rate of 2.875% for city tax, how much is deducted from her salary per paycheck to withhold that tax?

f) As of January 1, Elizabeth will receive a 9.1% raise. What will Elizabeth's annual salary be?

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So, the average speed of the train is 54.09 miles per hour.

To calculate the average speed of the train for the entire trip, you need to find the total distance traveled and the total time traveled.

First, you can convert the time traveled at each speed to hours. 40 minutes is equal to 40/60=0.67 hours. So the total time traveled is 1+0.67=1.67 hours.

To find the total distance traveled, you can use the formula: distance = speed x time. At 45 mph, the distance traveled is 45 x 0.67 = 30.15 miles. At 60 mph, the distance traveled is 60 x 1 = 60 miles. Therefore, the total distance traveled is 30.15 + 60 = 90.15 miles.

Finally, you can use the formula: average speed = total distance / total time.

Average speed = 90.15 miles / 1.67 hours = 54.09 miles per hour.

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Sid has a total of 32 caps.

In mathematics →

Given is that Sid has a baseball cap collection. 75% of his caps have sports team symbols. 24 of the caps have the team symbols.

Let the total number of caps be {x}. Then, we can write -

24 = 75% of {x}

24 = (75/100) {x}

24 = 3/4 {x}

{x} = 24 x 4/3

{x} = 32

Therefore, Sid has a total of 32 caps.

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Answer:

42/6 = 7 Minutes

Step-by-step explanation:

Answer:

(3,2)

Step-by-step explanation:

 2(y = 5x - 13)

-(2y = -5x + 19)

0 = 15x - 45

15x = 45 --> x=3

y = 5(3) - 13

y = 2

Answer: x=-4/3,      y=19/3

Step-by-step explanation:  According to the formula,  

x=(mx2+nx1)/(m+n) ,     y=(my2+ny1)/(m+n)

Here the ratio is 1:5

m=1 ,   n=5

x1 = -4,  x2 = 12

y1 = 5,   y2 = 13

Now put in the formula,

[tex]x=\frac{1*12+5(-4)}{1+5}[/tex] ,     [tex]y=\frac{1*13+5*5}{1+5}[/tex]

x=(12-20)/6 ,      y= (13+25)/6

x=-8/6         ,      y=38/6

x=-4/3          ,     y=19/3

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Answer:

D: 39

Step-by-step explanation: Using the steps of the Pythagorean theorem.

On the graph:

A  represents the reactants

B represents the activated complex

C represents the products

D represents the activation energy

The path of energy changes that take place in a reaction, as well as the energy content of the reactants and products, are depicted in the energy profile diagram.

The letters shown in the diagram represents the following:

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The correct answer is 500 yards. The largest area for the field will be when the cube is a forecourt. With 2000 yds. of fencing, each side would be 2000/4 =  500 yds.

Long, or 500 yds.  If there were no swash also, the largest area would be given by a square configuration since adding the length and dwindling the range of a square by the same value, t will drop the area by a square with sides of length.  Now add the swash on one side. The swash acts like a glass.

As we guard in a cube on one side of the swash, imagine an identical cube on the other side. The maximum area is given when the two blocks form a square, that's when we have a cube doubly as long as wide.

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The value of the largest area of the field will be 5000 sq. ft.

From the given data,

Total pasture area of fencing =2,000 feet

The shape of the field =rectangular

As the area of the rectangle = l*b

So, we can write it as;

2000=x+2y, (As the area of surrounded by a river from one side, so we need to only fence twice of width and only one length (Side) of the rectangle.

Now applying the formula of the area of the rectangle

we will get it as:

[tex]$$\begin{aligned}& A(x)=x\left(\frac{2000-x}{2}\right)=\frac{1}{2}\left[2000 x-x^2\right] \\& A^{\prime}(x)=\frac{1}{2}[2000-2 x]=0 \\\end{aligned}$$[/tex]

Solving the value,

We will get: x=100 ft y=50 ft

So, determining the value of the largest area,

We will get it as:

A_{max}=(100)(50)=5000 Sq. ft.

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Answer:

(i) 11 years old

(ii) 30 years old

Step-by-step explanation:

K is x

In four years, he will be x+4 and his mother will therefore be 3(x+4)

Six years ago, he was x-6 and his mother was 7(x-6).

In 10 years his mother went from 7(x-6) to 3(x+4)

so their difference is 10

7x-42+10=3(x+4), since 7x-42 is 10 years less than 3x+12

7x-32=3x+12

4x=44

x=11 age of K now

in 4 years he will be 15 and his mother 45.

Six years ago he was 5 and his mother 35

Therefore, his mother was 30 when he was born.

She is now 41.

Imran is currently 10 years old. His mother's current age is 34 years old and she was 24 years old when Imran was born.

The question involves a system of equations based on the relationship between Imran and his mother's ages. We can define Imran's current age as i and his mother's current age as m. From the problem we have the following two equations:

By solving this system of equations, we can determine that Imran's current age (i) is 10 years old and his mother's current age (m) is 34 years old. To find the age of Imran's mother when he was born, we would subtract Imran's age from his mother's, i.e., 34 - 10, so Imran's mother was 24 years old when Imran was born.

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In a data set, the number of observations will always be the same as the group of answer choices number of variables is the number of elements.

A data set is a collection of data. It is a set that corresponds to one or more database tables, where every column of a table represents a particular variable, and each row corresponds to a given record of the data set in question.

The data set lists values for each of the variables, such as example height and weight of an object, for each member of the data set. Data sets can also consist of a collection of documents or files.

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(0, -26) and (0,25 )is the focus of the hyberbola.

Any point in a hyperbola has distances from the two foci that are fixedly different from each other.

Every hyperbola has two foci (plural for focus). The hyperbola's branches are encircling both of them.

(0,-26) is inside the lower branch (0,-24) is not inside the lower branch (0,25) is inside the upper branch (0,30) is inside the upper branch

Lower branch is our main focus. We must examine the image to determine which of two potential solutions is correct. From the maxima to the focus for the lower branch is one distance. The top branch needs the same, which we must discover. Distances between points (0,30) and (0.25) are 1 and 6, respectively.

(0, -26) and (0,25).

The complete question is,

What is the depicted hyperbola's point of focus? (0, −26) (0, −24) (0, 25) (0, 30) (0, 30) BRAINLIESTT.

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It is impossible to create a Gaussian surface that makes it easy to calculate the electric field around a charged dipole. Thus, the response is no.

According to Gauss's law, the enclosed electric charge directly affects how much an electric field's net flux is moving over a closed surface. This is given by, [tex]\phi=\frac{Q}{\epsilon_0}[/tex], where the electric flux is represented by Ф, the permittivity of free space is represented by [tex]\epsilon_0[/tex], and the enclosed charge is represented by Q.

Gauss's law must be applied for the symmetric charge distribution required for the given surface in the equation [tex]\frac{Q}{\epsilon_0}=\int\vec{E}\cdot d\vec{A}[/tex] to have a single value of the electric field.

The electric field surrounding a charged particle can be estimated using the Gaussian surface. Gauss' Law cannot be applied to the dipoles because electric dipoles lack a surface with a symmetric distribution of the electric field all around them.

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The exponential function that satisfies the given conditions is given as follows:

[tex]f(t) = 4e^{1.099t}[/tex]

The format of the exponential function for this problem is given as follows:

f(t) = 4e^(kt).

In which k is the exponential growth rate.

After five hours, there was 972 bacteria, meaning that when t = 5, f(t) = 972, hence the growth rate is obtained as follows:

[tex]972 = 4e^{5k}[/tex]

[tex]e^{5k} = 243[/tex]

5k = ln(243)

k = ln(243)/5

k = 1.099.

Meaning that the function is defined as follows:

[tex]f(t) = 4e^{1.099t}[/tex]

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The perimeter of the triangle BCD is 17.25 centimeters.

A closed route that covers, encircles, or outlines a one-dimensional length or a two-dimensional form is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are several uses in real life for perimeter calculations.

so, perimeter of the triangle is the sum of all its side length.

Perimeter of one triangle / perimeter of another triangle= side of one triangle by side of another triangle.

let us suppose that the perimeter of triangle BCD is equal to X

27.6/x = 9.6/6

x = 17.25 cm

therefore, the perimeter of triangle BCD is equal to 17.25 centimeters.

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Answer:38.6

Step-by-step explanation:

The solutions to the equations is the point of intersection of graphs and the points are ( 0 , 2 ) and ( 1 , 1.25 )

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the first equation be represented as A

Now , the value of A is

y = ( -3/4 )x + 2   be equation (1)

Let the second equation be represented as B

Now , the value of B is

y = ( 1/4 )ˣ + 1   be equation (2)

Now , to calculate the solutions to the equations , plot the equations in the graph

The point of intersection of equation of lines represents the solution to the equation

Substituting the values in the equation , we get

( -3/4 )x + 2 = ( 1/4 )ˣ + 1

The first point of intersection is ( 0 , 2 )

when x = 0 , y = 2

( -3/4 ) (0) + 2 = ( 1/4 )⁰ + 1

On simplifying the equation , we get

0 + 2 = 1 + 1

2 = 2

So , the solution is ( 0 , 2 )

Hence , the equations are solved

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35% can be represented in equivalent decimal form and fraction form 0.35 and 7/20

35% is equivalent to 0.35 in decimal form. Divide the percentage by 100 to get the decimal equivalent. 35 / 100 = 0.35.

35% is equivalent to 7/20 as a fraction. A percentage must be multiplied by 100 before being simplified to become a fraction. 35/100 = 0.35, or 7/20, can be written more simply.

Although both forms are equal, they are employed in various contexts. The fraction form is more frequently used in probability and statistics while the decimal form is more frequently used in calculations.

It's also important to keep in mind that percentages are a technique to express numbers as fractions of 100. For example, 35% is the same as 35/100, or 7/20.

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Answer: (7)^-2 and 1/49 are equivalent

Step-by-step explanation:

Answer: To find the rotation in revolutions per minute (RPM) given the angular speed and the radius, we can use the formula:

RPM = (Angular Speed (rad/s)) / (2 * pi)

To find the RPM, we first need to convert the linear speed to angular speed. We can do this by using the formula:

Angular Speed (rad/s) = Linear Speed (m/s) / Radius (m)

Angular Speed = 82.3 m/s / 0.131 m = 630 rad/s

RPM = (630 rad/s) / (2 * pi) = 131 rev/min

To find the RPM, we first need to convert the linear speed to angular speed. We can do this by using the formula:

Angular Speed (rad/s) = Linear Speed (ft/min) / (Radius (ft) * 12)

Angular Speed = 144.2 ft/min / (10.9 ft * 12) = 10.9 rad/s

RPM = (10.9 rad/s) / (2 * pi) = 10.9 rev/min

To find the RPM, we first need to convert the linear speed to angular speed. We can do this by using the formula:

Angular Speed (rad/s) = Linear Speed (in/h) / (Radius (in) * 3600)

Angular Speed = 553 in/h / (553 in * 3600) = 0.09 rad/s

RPM = (0.09 rad/s) / (2 * pi) = 0.09 rev/min

Step-by-step explanation: