Express the length a, b, c, and d in the figure in terms of the trigonometric ratios of θ.
a = b = c = d =

Therefore , the solution of the given problem of function comes out to be  f(g(x)) = x[tex]X^{2}[/tex]−4[tex]X^{2}[/tex]−28x−32/(x−4)

Each x value in the domain has one but only one y value range, according to the rule of a function. Definition. If there is only one and only one value of x such that f(x) = y, then the function is one-to-one

Here,

Given : f(x) =X² - 8x+16/2 + 2x

g(x) =(6x)/(x-4)

To find the f(g(x)) :

=> f(g(x)) = f(6x/(x-4))

=>  f(6x/(x-4)) =  (6x/(x-4) )^2 - 8((6x)/(x-4)) +16/2 + 2(6x)/(x-4)

=>  f(6x/(x-4)) = 36[tex]x^{2}[/tex]/ ( [tex]x^{2}[/tex]+ 16 - 8x) - 36[tex]x^{2}[/tex]/(x+4) +8

=> f(6x/(x-4)) = x[tex]X^{2}[/tex]−4[tex]X^{2}[/tex]−28x−32/(x−4)

Therefore , the solution of the given problem of function comes out to be  

f(g(x)) = x[tex]X^{2}[/tex]−4[tex]X^{2}[/tex]−28x−32/(x−4)

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Explanation:

The confidence interval spans from 440 to 472. This is a width of 472-440 = 32 units. It divides in half to get 32/2 = 16. We can think of this as the "radius" of the confidence interval, and it represents the margin of error. It's the distance from the center to either endpoint of the interval.

Side note: use the midpoint formula to determine the center.

The inverse of a function is a function that "undoes" the original function. If f is a function and x is an element in the domain of f, then the inverse of f is denoted as f^-1(x) and is defined as the element in the domain of f such that f(f^-1(x)) = x.

The symbol "φ" (phi) is not a commonly used notation for any function. It is a Greek letter and can be used in different fields such as physics, mathematics, and engineering to represent different things depending on the context.

It is important to note that not all functions have inverses. A function has an inverse only if it is a bijective function, which is a function that is both injective and surjective, meaning that it maps every element of the domain to a unique element in the range and vice-versa.

So to find the inverse of a function, you have to first make sure that the function is bijective. If so, you can find the inverse function by switching the positions of x and y, then replacing y with f^-1(x) or x with f^-1(y) and solving for the new x or y.

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The solution for given question of algebra are 10, -42, -38 for question 1st, 2nd and 3rd.

There are several sub-branches of algebra, including commutative algebra, abstract algebra, linear algebra, and elementary algebra.

x + 6/x + 3 = 4/7

7x + 42 = 4x + 12

7x - 4x = 42-12

3x = 30

x = 10

2/x+8 = 3/x+9

2x - 18 = 3x + 24

x = -42

x+2/6 = x-4/7

7x+14 = 6x-24

x = -38

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On sectional charts, the graticules are the lines that separate each 30 minutes of latitude and each 30 minutes of longitude. One tick mark equals one minute of latitude or longitude. Moving northward increases latitude while moving westward increases longitude. The coordinates of the Garrison (Pvt) airport are 47° 40' 00" N and 101° 26' 00" W.

Direction is characterised as the course that something follows, the route that must be taken to get to a particular location, the direction in which something is beginning to take shape, or the direction you are facing. When you turn right instead of left, that is an illustration of direction.

Identifying whether a direction is clockwise or anticlockwise is a straightforward method for resolving direction problems. If we turn right, the direction will be entirely clockwise. Therefore, when starting from the correct point at North, every right movement will lead in the clockwise directions of East, South, and West.

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The like terms in 3x (3 - 2y) and 2 (xy + x²) are -6xy and 2xy.

Like terms are terms which have the same variables and exponents. In this case, the like terms are -6xy and 2xy because they both have the same variable (xy) and exponents (1). In algebra, like terms can be added or subtracted to simplify an expression.  Like terms are terms which have the same variables and exponents.

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(0.818  , 1.546)  is the point that is part of solution.

point (0,2) and (2,0) are not the part of solutions.

3y - 2x ≤ 3

y + 3x  ≤ 4

these are the system of inequalities.

What are Inequalities?

Inequality is a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

Given in this question,

There are two lines L1 and L2.

From the graph we can find the two points that lies on the line L1 be

(0,1) and (3,3).

similarly From the graph we can find the two points that lies on the line L2 be

(0,4) and (2,-2).

From the two points (x1 , y1) and (x2,y2) we can write the equation of the Line from the following formula :

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex].   This is the equation of line for given two points.

Equation of line L1 :

[tex]y-1=\frac{3-1}{3-0} (x-0)[/tex]

3y - 3 = 2x ----------(ii)

Equation of line L1 : 3y - 2x = 3.

Equation of line L2 :

[tex]y-4=\frac{-2-4}{2-0} (x-0)[/tex]

y   = -3x + 4 ----------(ii)

Equation of line L2 : y + 3x = 4.

The point that is the part of the solution :

putting the value of y from equation (ii) in equation (i).

3(-3x+4) -3 = 2x

-9x-2x = -12+3

-11x = -9

  x = 0.818

y = -3(0.818) +4 = +1.546

so Point of intersection is (0.818  , 1.546)

This is the point that is part of solution.

The point that is not below both the lines are not part of solution.

the point that are not part of solution are:

3y - 2x ≥ 3  ->  (0,2)

y + 3x  ≥ 4   ->  (2,0)

point (0,2) and (2,0) are not the part of solutions.

Inequalities are for shaded portion :

3y - 2x ≤ 3

y + 3x  ≤ 4

these are the system of inequalities.

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The perimeter of the parallelogram with the given vertices is 33.

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.

Given that:

A = (3, 6)

B = (-5, 6)

C= (6 , -1)

D = (-2, -1)

The length of side is given by the formula:

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

Substitute the values in the formula to find the sides of the parallelogram.

[tex]AB= \sqrt{(-5 -3)^2 + (6-6)^2} = 8\\ \\BC = \sqrt{(6+5)^2 + (-1 - 6)^2} = 13\\\\CD= \sqrt{(-2+6)^2 + (-1 +1)^2} = 4\\\\\DA= \sqrt{(3+2)^2 + (6+1)^2} = 8[/tex]

The perimeter is obtained by adding all the sides of the given two-dimensional shape.

P = 8+13+4+8

P = 33

Hence the perimeter of the parallelogram is 33.

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No, one mole is not equal to one gram. For an object, the mole and gram numerical values differ.

1 gram, what is it?

One mole consists of an Avogadro number of atoms. If you are aware of the mole quantity, you can convert a mole into grams.

The mole (symbol: mol) is the unit of material quantity used by the International System of Units. The amount of a substance determines how many elementary entities of that substance are present in an object or sample. The mole must contain precisely 6.02214076×10²³ elementary entities.

A mole's relationship to a gram is

The product of the number of Moles of an object to its atomic weight equals one gram.

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The Construction is shown below.

Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Given:

a) Steps for perpendicular line:

b) Perpendicular Bisector for triangle

So, if we extend the bisector they can meet inside, at center and outside the triangle.

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Answer:

x = 2

Step-by-step explanation:

If you look at the equation:

(x + 2) = 4

We just need to solve for x.

To solve for x, we can subtract the total by the addend, to get the variables value.

4 - 2 = 2

Therefore, the value of x is 2.

To complete the table, we can simply multiply the number of calories by 0.239 to find the equivalent amount of Joules.

The equation relates Joules to calories as j = 0.239c, where c stands for calories and j stands for joules. For example, 1 calorie is equal to 0.239 Joules, 2 calories is equal to 0.478 Joules, and so on.

Joules (j)              Calories (c)

0.239c                  1

0.478c                  2

0.717c                  3

0.956c                  4

1.195c                  5

1.434c                      6

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Answer:

[tex]y=\frac{9}{10}x-\frac{7}{5}[/tex]

Step-by-step explanation:

Using the points [tex](-4,-5)[/tex] and [tex](6,4)[/tex], the slope is [tex]m=\frac{-5-4}{-4-6}=\frac{9}{10}[/tex].

Using point-slope form:

[tex]y+5=\frac{9}{10}(x+4) \\ \\ y+5=\frac{9}{10}x+\frac{18}{5} \\ \\ y=\frac{9}{10}x-\frac{7}{5}[/tex]

Answer:

Step-by-step explanation:

You need to add both of the angles you already know (1 and 2). If you add angle 1 and angle 2 you get 74. This means m < J K M would be 74°.

Answer:

74 degrees

Step-by-step explanation:

You have to add angles 1 and 2

35 +39=74

Therefore, 74 is the answer

Answer:

Step-by-step explanation:

To find values of y we substitute values of x in the given expression so when x = 0

y = (0)^2 - 6(0) + 3

  = 3.

x = 1, y = 1^2 - 6(1) + 3 = -2

x = 3, y = 3^2 - 6(2) + 3 = 0.

Use these values to draw the graph

(a)  Read this from the graph

Coordinates of the minimum should be 3, -6)

(b) Equation of the line of symmetry is the vertical line through the minimum point ( x = 3).

(c)  Read these from the graph.

(the points where the graph cut the x-axis).

(d) and e - read the values from your graph.

Answer:

Translate(1.3, -1)

Scale Factor: 2/3

Step-by-step explanation:

First, perform a dilation about the origin. This will make the original shape smaller.

From the given diagram, we can see that R'S' is 10 units long. RS is 15 units long. Using this information, we can create this ratio.

[tex]\frac{10}{15}[/tex]

This means that Triangle R'S'T' is 2/3 of Triangle RST. Construct lines from the origin (the center of dilation) to each point on the original triangle. Then, find two thirds of that line. The new point will be the new y-coordinate.

The new coordinates will (approx.) be:

R = (-2, 4.7)

S = (-2, -5.3)

Only two coordinates are necessary to perform this translation. As per the graph, this triangle must shift approximately 1.3 units up and 1 unit to the left. Thus, the final translation is:

Translate(1.3, -1)

Scale Factor: 2/3

For the given principal and two different rate of interest for the 15 years of time period the cost of four points is given by  $26786.2.

As given in the question,

Principal amount 'P' = $128,000

Time 't' = 15 years

Rate of interest 'r' = 5.5%

                             = 0.055

Total amount 'A' received is given by the formula :

A = P ( 1 + r/100 )^n

  = 128,000 ( 1 + 5.5 / 100 )^15

  = $285756.99

Now when the rate of interest is changed to

Rate of interest 'r' = 4.81%

                             = 0.0481

Total amount 'A' received is given by the formula :

A = P ( 1 + r/100 )^n

  = 128,000 ( 1 + 4.81 / 100 )^15

  = $258970.79

Now, the cost of four points is given by:

= $( 285756.99 - 258970.79 )

= $ 26786.2

Therefore, for the given principal amount with two different rate of interest for the time period of 15 years the cost of four points is equal to  $26786.2.

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The cost of a carpet of the same quality, measuring 5m by 3m is $129.

We can use the unitary method to solve this problem. The unitary method is a technique used for solving a problem by first finding the value of a single unit, and finding the necessary value by multiplying the single unit value.

In this question, it is given that a carpet measuring 4m × 2.5m costs $86. That means the 10m² area of carpet costs $86 if we divide 10 by both the cost and area of the carpet we will find that, 1 m² area of carpet will cost $8.6. So the cost of a carpet of 5m × 3m will be the area of the carpet multiplied by the cost of the carpet per 1 m² i.e, 15m² of carpet will cost $8.6 × 15 which is equal to $129.

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(A) (x+4)(x-1)=0 is the proper factors form of the given equation x²+3x-4=0.

A factor is a number that completely divides another number.

To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

So, we have the equation:

x²+ 3x - 4 = 0

By dividing the center term, this quadratic equation can be reduced to its simplest form.

The result of dividing the middle word is:

x² + 4x - x - 4 = 0

One way to spell it is as:

x (x + 4) - 1 (x + 4) = 0

Now, we obtain:

(x + 4) (x - 1) = 0

Therefore, (A) (x+4)(x-1)=0 is the proper factors form of the given equation x²+3x-4=0.

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Correct question:

Which of the following is the correct factored form of the given equation x2+ 3x - 4 = 0?

(A) (x +4) (x - 1) = 0

(B) (x - 4) (x - 1) = 0

(C) (x - 4) (x +1)= 0

Therefore , the solution of the given problem of triangle comes out to be  ΔA"B"C "≅ ΔABC is congruent.

The fact that a triangle has sides or vertices qualifies it as a polygon. It is an elementary geometric form. The name given to a triangle with vertices A, B, & C is Triangle ABC. A singular planes and triangle are obtained in Euclidean geometry when the vertices are not collinear. Any triangle that has three sides and three corners is a polygon.

Here,

Triangle A'B'C' is created by reflecting triangle ABC across the y-axis.

Afterward, it was dilated by a ratio of 1/3 to create triangle A "B"C".

Find the right answer for the triangles ABC and A"B"C."

So,

We are aware that reflection undergoes a rigorous transformation, meaning the shape and size of the original object do not change.

As a result, after reflection, figures always match their pictures.

"ABC," "A'B'C," etc (i)

The process of dilation is flexible. Although the size is changed, the shape is still the same.

Figures after dilatation therefore always resemble their photographs.

ΔA'B'C' ≅ ΔA "B"C" ... (ii)

With I and (ii), we obtain

ΔA"B"C "≅ ΔABC

Similar triangles include ABC and ABC.

As a result, choice A is the right one.

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The slope shows a change in the amount of fuel left in each mile. Since the slope is -0.04, the amount of fuel left drops by 0.04 gallons each mile

The slope of a line governs its steepness. Using mathematics, the gradient is expressed as "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical (rise) to the horizontal (run) change in distance between any two sites. Every time the equation for a straight line is written as y = mx + b, the slope-intercept representation of the equation is utilized. At the location of the y-intercept, the line has a slope of m, b, and c. (0, b). As an example, the y-intercept of the equation y = 3x - 7 has a value of 3. (0, 7).

given

It is evident that with each additional row, the distance is increased by one mile and the fuel level is altered.

From one row to the next in the table, the amount of fuel left changes by -0.04 gallons.

The distance in the table that changes from one row to the next is 1 mile.

The slope is the pace at which the amount of fuel left changes in relation to the change in distance.

The line that passes through the places listed in the table has a slope of -0.04 degrees.

The slope shows a change in the amount of fuel left in each mile. Since the slope is -0.04, the amount of fuel left drops by 0.04 gallons each mile.

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I don't see the image. Can you send it in the message.

Answer: y<-5x+9

Step-by-step explanation:

Slope is -5, y-intercept is 9 and the shaded area is on the left side (meaning y is less than the line). The line is dotted which means that the answer will less than but not equal to.

The y-intercept of the quadratic function f(x) = (x - 8)(x + 3) is (0, -24).

The graph's intersection with the y-axis is known as the y-intercept. Finding the intercepts for any function with the formula y = f(x) is crucial when graphing the function. An intercept can be one of two different forms for a function. The x-intercept and the y-intercept are what they are. A function's intercept is the location on the axis where the function's graph crosses it.

This is an illustration of a y-intercept. Think about the line y = x + 3. The point where this graph crosses the y-axis is (0,3). Therefore, the y-intercept of the line y = x+ 3 is (0,3).

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The equation indicates that the given equation's constant variable is 8.

In other words, you may claim that y directly depends on x or that y is directly proportional to x. The continuity equation or the constant variable variation in this function is m (or k). a direct variation's product of two variables or the result of two variables in such an inverse variation K is the constant of variation in the direct variation equations.

"X fluctuates directly as Y" denotes that as y rises, x also rises by the same amount. In other words, the ratio between y and x is constant and is:

                            x = k × y                

where k is the constant of variation.

Here,

it is given that y varies as  x,

if y=24 and x=3,

therefore,

y = kx

24 = 3k

∴ k = 8

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5/32 of the time, the product of the two numbers on the face-up sides will be greater than 36.

The likelihood of an event happening is gauged by probability. Many things are impossible to completely predict in advance. Using it, we can only make predictions about how probable an event is to happen, or its chance of happening.

There are 64 possible options to look at (8 x 8).

If one die is a 1, then no combinations will be possible, even if the other die is an 8.

If one dice is a 2, then no combinations will be possible, even if the other die is an 8.

If one dice is a 3, then no combinations will be possible, even if the other die is an 8.

If one die is a 4, then no combinations will be possible, even if the other die is an 8.

If one die is a 5, the second die must be an 8 for the result to be more than 36. So, (5, 8) is effective.

If one die is a 6, the second die must be a 7 or an 8 to produce a result greater than 36. Therefore, both (6, 7) and (6, 8) are valid.

If one die is a 7, the other die can be a 6, 7, or 8 to get a result that is more than 36. As a result, (7, 6), (7, 7) and (7, 8) all function.

If one die is an 8, the other die can be a 5, 6, 7, or 8 to get a result that is more than 36. Therefore, (8, 5), (8,6), (8,7), and (8,8) are valid.

Out of a total of 64 possible combinations, there are a total of 1 + 2 + 3 + 4 = 10 that are successful.

As a result, the response is 5/32 because 10/64 = 5/32.

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The length of the arc that subtended an angle of 120° with a radius of 27 m is 18π m.

We know that the length of the arc of a circle = Radius of the circle × angle subtended by the arc (in radians)

Here radius of the circle is 27 m

The angle subtended is 120°

Hence we will first convert the angle into radians

Angle in radians = Angle in degree X π/180

= 120 X π/180

= 2π/3

Therefore, the length of the arc = 27 X 2π/3

= 18π m

Therefore, the length of the arc that subtended an angle of 120° with a radius of 27 m is 18π m.

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Answer: N= x24 over 3

Step-by-step explanation: