How to solve this problem

The inverse of the function is f⁻¹(x)=3+√18+x, 3-√18+x

A relation is a function if it has only One y-value for each x-value.

Let us consider the function f(x)=(x-3)²

Where x belongs to [1, 2]

f(x)=x²+9-6x

y=x²+9-6x

Interchange the variables.

x=y²+9-6y

y=3+√18+x

y=3-√18+x

Relace y with f⁻¹(x)

f⁻¹(x)=3+√18+x, 3-√18+x

Hence, the inverse of the function is f⁻¹(x)=3+√18+x, 3-√18+x

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Answer:

3c=3x+6

Step-by-step explanation:

-2+3c=2x+6+x

-2+3c=3x+6      First combine the x on the right side.

-2+3c=3x+6

+2            +2    Add 2 to both sides to eliminate 2 on the left side.

3c=3x+6

By  exponential expressions  3(5x + 3).(27)x as 3f(x)  this we get value 3.5x(27.3,x(x)f) + 3.3(27.3,x(x)f) .

Simply put, exponential expressions are a condensed approach to express powers. The base's frequency of use as a factor is indicated by the exponent.

f(x) = ax, where x is the input variable and is expressed as an exponent, is the formula for an exponential function.

In addition to being dependent on the exponential function, the exponential curve also depends on the value of x. Whenever a>0 and a1 are not equal.

Example :

3(5x + 3).(27)x as 3f(x) : 3.5x(27.3,x(x)f) +3 .3 (27 .3,x(x)f)

Steps

3(5x+3)(27x , 3f(x))

= 3(5x + 3)(27.3,x(x)f)

Apply the distributive law :

a(b + c) = ab + ac

a = 3(27x,3f(x)), b=5x,c = 3

=3(27x,3f(x)). 5x + 3(27x,3f(x)).3

=3.5x(27.3,x(x)f) + 3.3(27.3,x(x)f)

The Complete Question.

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Based on the table, a statement which is true include the following: C. The table shows a linear relationship, but not a proportional relationship.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 6/2 ≠ 11/4 ≠ 34/9 ≠ 81/16

In this context, we can reasonably infer and logically deduce that the table shows a linear relationship because as the value of time (in hours) increases, the value of distance (miles) also increases. However, it does not show a proportional relationship.

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The missing coordinate of P, using the fact that P lies on the unit circle in the given quadrant is √(2/7) or √(2/7)

The unit circle is a circle with a radius of 1 centered at the origin (0,0) on a coordinate plane. If a point P lies on the unit circle, then the distance from the origin to P is 1.

We can use the distance formula to find out the missing coordinate of P.

The distance formula:   [tex]d = \sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]

where (x1, y1) is origin and (x2, y2) is the point P.

Given in the problem that P is in Quadrant IV, then the (x, y)-coordinate is negative.

So we can use the given information and the distance formula to find out the missing coordinate.

[tex]d = \sqrt((x2 - 0)^2 + (y2 - 0)^2) = 1[/tex]

x2 = -5/7, y2 = -5/7

[tex]d = \sqrt((-5/7 - 0)^2 + (-5/7 - 0)^2) = \sqrt((-5/7)^2 + (-5/7)^2) = \sqrt(25/49 + 25/49) = \sqrt(50/49) = \sqrt(2/7) = 1[/tex]

Therefore, the missing x coordinate of P is √(2/7) or √(2/7)

P = (-5/7,√(2/7))

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The spaceship's velocity modulus increased due to the firing of the brake rocket in order to transfer the spacecraft into a circular orbit of the Moon satellite.

When approaching the Moon, a spacecraft follows a parabolic trajectory which is almost tangent to the Moon's surface. At the moment of maximum approach, the brake rocket is fired for a short time interval. This causes a decrease in the spacecraft's velocity and an increase in its centripetal force. This, in turn, causes the spacecraft to move away from the Moon and into a circular orbit of a Moon satellite. The increased centripetal force causes the spacecraft to accelerate, and thus its velocity modulus increases. The magnitude of this increase in velocity modulus depends on the duration and power of the brake rocket. In conclusion, the velocity modulus of the spacecraft increases due to the firing of the brake rocket.

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The change in y between x = 5 and x = 9 is 2572.

What is a function?

An assignment of a Y element to every X element constitutes a function from X to Y. Both the set X and the set Y are referred to as the function's domain and codomain, respectively.

Here, the function is given as y(x) = 4x ^ 3 + 3x ^ 2 - 3x.

we'll find the value of given function i.e. y when x = 5 and 9.

when x = 5,   y(5) = 4(5) ^ 3 + 3(5) ^ 2 - 3(5)

                            = 4(125) + 3(25) - 15

                            = 500 + 75 - 15

                            = 560.

when x = 9,   y(9) = 4(9) ^ 3 + 3(9) ^ 2 - 3(9)

                            = 4(729) + 3(81) - 27

                            = 2916 + 243 - 27

                            = 3132.

So, the change in y is  2572 (3132 - 560).

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Here proof i.e. ∠1=∠3 is also given in the image for the given geometric shape.

What are geometric shapes?

In Mathematics, Geometric shapes are the figures which demonstrate the shape of the objects we see in our everyday life. In geometry, shapes are the forms of objects which have boundary lines, angles and surfaces. There are different types of 2d shapes and 3d shapes.

Shapes are also classified with respect to their regularity or uniformity. A regular shape is usually symmetrical such as a square, circle, etc. Irregular shapes are asymmetrical. They are also called freeform shapes or organic shapes. For example, the shape of a tree is irregular or organic.

In plane geometry, the two-dimensional shapes are flat shapes and closed figures such as circles, squares, rectangles, rhombus, etc.  In solid geometry, the three-dimensional shapes are cube, cuboid, cone, sphere and cylinder. We can observe all these shapes in our daily existence also. For example books (cuboid shape), glasses (cylindrical shape), traffic cones (conical shape) and so on.

Now

To prove   ∠1=∠3

Here as given ∠1+∠4=180°

and also ∠2+∠3=180°    (supplementary angles)

therefore,

∠1+∠4=∠2+∠3

and also ∠2=∠4  ( complementary angles)

Hence,

          ∠1=∠3

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Answer:

Bottom model and has 60 toys in all

Step-by-step explanation:

here is ur answer seeee now

The time that is taken to fall is  3.1 s.

In this case, we have been told that A rock is thrown upward with a velocity of 18 meters per second from the top of a 36 meter high cliff, and it misses the cliff on the way back down.

We have to know that the maximum height that the rock has attained by the use of the formula;

v^2 = u^2 - 2gh

v = final velocity

u = initial velocity

g = acceleration

h= distance

v = 0 m/s at the maximum height

h = u^2/2g

h = (18)^2/2 * 9.8

h = 324/19.6

h = 16.5 m

The height from the cliff upwards is; 16.5 m + 36 m = 52.5 m

The distance that is covered when falling is;  52.5 m - 4 m = 48.5 m

If it is falling then it is dropped from a height and u = 0 m/s

h = 1/2gt^2

48.5 = 0.5 * 9.8 * t^2

t = √48.5/0.5 * 9.8

t = 3.1 s

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The polynomial that represents the perimeter of the figure is 3x

From the question, we have the following parameters that can be used in our computation:

Side length = x

Triangle type = equilateral triangle

See attachment for the figure

The perimeter of an equilateral triangle can be calculated as

P = 3 * side length

substitute the known values in the above equation, so, we have the following representation

P = 3 * x

So, we have the following representation

P =3x

Hence, the perimeter expression is 3x

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The missing angle measure is of:

1. 25º.

The missing side length is of:

2. 12 cm.

Triangles ABC and ACD(3) are similar by the AAS theorem.

Similar triangles are triangles that share these following two features:

For this problem, we have that the segment SSC is the bisection of angle A, hence:

We have two similar angle measures, C and 25º, along with the opposite length, hence the AAS theorem is used.

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Explanation

The ratio 1:2:3 refers to the idea we could have: 1 red, 2 green, 3 blue. The order of the colors is important. Follow the order mentioned in the 1st sentence of the instructions. That order being red:green:blue.

Then the instructions mention that there are actually 5 red (instead of 1 red). This means we multiply each part of the ratio by 5

The ratio 1:2:3 scales up to 5:10:15

We see that there are 15 blue marbles

The equation -1.5x = 4(x + 2.18) solved for x is -1.59. Option C

Algebraic expressions are described as expressions that are mainly composed of variables, terms, constants, coefficients and factors.

These expressions are also composed of arithmetic operations, such as;

From the information given, we have that;

-1.5x = 4(x + 2.18)

expand the bracket

-1. 5x = 4x + 8.72

Now, collect like terms, we get;

-1.5x - 4x = 8.72

subtract the like terms

-5.5x = 8.72

Divide both sides by the coefficient of x

x = -1.59

Hence, the correct option is Option C

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Complete question:

Solve the following equation for x. Round the answer to the nearest hundredth.

−1.5x= 4(x + 2.18)

A. 0.63

B. 3.49

C. -1.59

D. -0.40

Step-by-step explanation:

g(-4) = 3(-4)-12

= -24

f(g(-4)) = f(-24)

f(-24) = 2(-24)+7

= -41

i don't know it is true i'm just trying:)

The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a polygon with n sides is given as follows:

S(n) = 180 x (n - 2).

Hence, for an hexagon, with six sides, the sum is given as follows:

S(6) = 180 x (6 - 2)

S(6) = 720º.

A regular hexagon has all angle measures equal, hence the measure of each angle is given as follows:

720/6 = 120º.

The segment FB is a bisection of the angle F of the hexagon, dividing it into two equal angles, hence the angle measures are given as follows:

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(a) Any number could represent the amount of current flowing through the capacitor in decimal form. So that the electric capacitor is Continuous.

(b) There are exactly that many players. So On-line gaming system is Discrete.

(c) The number of flights or their proportion depend on the aircraft, which are expressed as whole numbers. So an airport is continuous.

In the question, we have to classify the systems as being either discrete or continuous:

Discrete data, often known as discrete values, is information that only accepts specific values. This type of data, which typically takes the form of whole numbers or integers, can be counted and has a finite set of possible values.

Data that can be measured is referred to as continuous data. There are an endless number of alternative possibilities for the values in this data, which are not fixed.

Nevertheless, the main distinction between discrete and continuous data is that the former has a finite value that can be counted while the latter has an infinite range of possible values that can be measured.

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All real numbers, with the exception of -6 , are the solution to a rational equation. The quotient of two polynomials is the definition of a rational expression.

[tex]$\frac{(x-2)(x+6)}{7(x+6)}=\frac{x-2}{7} \quad: \quad x \neq-6$[/tex]

[tex]$\frac{(x-2)(x+6)}{7(x+6)}=\frac{x-2}{7}$[/tex]

Simplify

[tex]$\frac{(x-2)(x+6)}{7(x+6)}: \quad \frac{x-2}{7}$[/tex]

[tex]$\frac{x-2}{7}=\frac{x-2}{7}$[/tex]

Seven times both sides

[tex]$\frac{x-2}{7} \cdot 7=\frac{x-2}{7} \cdot 7$[/tex]

Simplify

[tex]$x-2=x-2$[/tex]

There is equality between the two sides.

For every x Verify Solutions, true

Search for ill-defined (singularity) points: [tex]$x=-6$[/tex]

Because -6, the equation is undefined.

[tex]x \neq -6[/tex]

Therefore the correct answer is option C ) All real numbers except -6 .

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The inverse of the given function is [tex]f^{-1}(x) = (x-7)^2[/tex].

A function that may reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.

Given that the equation of the function is:

f(x) = √x + 7

Covert the given function into an equation:

y = √x + 7

Interchange the variables in the equation:

x = √y + 7

Isolate the value of y.

Subtract, 7 from both sides of the equation:

x - 7 = √y + 7 - 7

x - 7 = √y

Take square on both sides of the equation:

(x-7)² = (√y)²

(x-7)² = y

Replace, y with [tex]f^{-1}(x)[/tex].

[tex]f^{-1}(x) = (x-7)^2[/tex]

Hence, the inverse of the given function is [tex]f^{-1}(x) = (x-7)^2[/tex].

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The rate of change In gallons of gas per year from 1995 to 1997 is: C. Δg/Δt = 4 gal/year.

In Geometry, the rate of change of the data in this table can be calculated by using this mathematical equation;

Rate of change (slope), m = (Change in y-axis, Δg)/(Change in x-axis, Δt)

Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)

From the information provided in the graph above, we can logically deduce the following data points located on the line:

Substituting the given data points into the rate of change formula, we have the following;

Rate of change (slope), Δg/Δt = (y₂ - y₁)/(x₂ - x₁)

Rate of change (slope), Δg/Δt = (538 - 530)/(1997 - 1995)

Rate of change (slope), Δg/Δt = 8/2

Rate of change (slope), Δg/Δt = 4 gallon/year.

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The amount of tin was used to make the can of cylindrical can is 478 cm²

An equation is an expression that shows the relationship between numbers and variables.

Area is the amount of space occupied by a figure. Area is usually calculated for a two dimensional shape while volume is calculated for a three dimensional shape.

The surface area of cylindrical can = 2π(radius * height + radius²)

From the image:

radius = 9 cm/2 = 4.5 cm, height = 12.4 cm

Hence, substituting:

The surface area of cylindrical can = 2(3.14)(4.5 * 12.4 + 4.5²) = 478 cm²

The surface area of cylindrical can is 478 cm²

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The two supplementary angles are 155 and 25.

Two angels whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

Given;

Two angles are supplementary

One is 150 degrees more than 1/5 of the others

Let one angle be x

Then the other angle will be x/5+150

Now,

x+ x/5+150=180

6x/5+150=180

6x/5=180-150

6x/5=30

x=150/6

x=25

Other angle= x/5+150=25/5+150

=155

Therefore, the angles will be 155 and 25.

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The required roster form of the given sets are C ∩ (B’ ∪ A) = {p, q}.

The roster form of a set is defined as a set that can be represented mathematically in a precise way using a roster notation. In a roster notation, if the set has more than one element, a comma is used to denote the separation between every pair of elements.

The given sets are defined as follows:

U = {f, g, h, p, q, r, x, y, z}

A = {f, g, p, q}

B = {g, h, q, x, y}

C = {p, q, x, y, z}

The complement of set B is the set of all elements in the universal set U that are not in set B.

U = {f, g, h, p, q, r, x, y, z}

B = {g, h, q, x, y}

B’ = {f, p, r, z}

The union of set B' and A is the set of all elements that are in set B' or in set A.

A = {f, g, p, q}

B’ = {f, p, r, z}

B’ ∪ A = {f, g, p, q, r, z}

The intersection of set C and (B’ ∪ A) is the set of all elements that are in both set C and set (B’ ∪ A).

C = {p, q, x, y, z}

B’ ∪ A = {f, g, p, q, r, z}

C ∩ (B’ ∪ A) = {p, q}

So, C ∩ (B’ ∪ A) = {p, q}

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The polynomial equation with the given zeros is something like:

p(x) = a*(x - 1)²*(x + 2)²*(x - 5)²

Remember that for a polynomial of degree a with the zeros {x₁, x₂, ...} the polynomial can be written as:

p(x) = a*(x - x₁)*(x - x₂)*...

Here we don't know the leading coefficient, and we know that the zeros are:

{1, 1, -2, -2, 5, 5}

These appear twice because all have a multiplicity of 2.

Then the equation is:

p(x) = a*(x - 1)*(x - 1)*(x + 2)*(x + 2)*(x - 5)*(x - 5)

p(x) = a*(x - 1)²*(x + 2)²*(x - 5)²

Where a can be any real number different than zero.

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The function f(x) = x^2 + 1 can be graphed using the coordinates (x, y) where x is the x-coordinate, and y is the y-coordinate.

This function can be written as y = x^2 + 1. Using this equation, we can plot the graph of the function. To plot the graph, we need to plot points on the x-axis and y-axis. The x-axis is the horizontal line and the y-axis is the vertical line.

For example, let us take a point x = 0. Substituting x = 0 in the equation f(x) = x^2 + 1, we get y = 0^2 + 1, which is equal to 1. So, we can plot the point (0,1) on the graph. Similarly, we can plot the point (1,2), (2,5), (3,10), (4,17), (5,26), and so on.

By plotting all these points, we can get the graph of the function f(x) = x^2 + 1. This graph is a parabola with vertex at (0,1). It is an increasing function, which means that as the value of x increases, the value of y also increases. The graph is also symmetric about the y-axis.

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Answer:

I'm not understanding can you say it in a similar way?

Answer:

Step-by-step explanation:

Opportunity cost and production possibilities

Shen is a talented artist who sells hand-crafted goods on his website. Shen currently crafts and sells both crochet hats and baskets. He spends 8 hours

a day working on crafts. The following table gives different daily output scenarios depending on how much of his time is spent on each good

As per the given equation of the least squares regression line y=10+0.9x the score of Carla's final exam is 95.5.

As given in the question,

Given equation of the least squares regression line is :

y = 10 + 0.9x

Where 'y' shows the predicted final exam score

And 'x' represents the score of the first exam.

Carla's first exam score is equal to 95

Then predicted value 'y' of the Carla's final exam score is given by :

y = 10 + ( 0.9 ) × 95

⇒ y = 10 + 85.5

⇒ y = 95.5

Therefore, the predicted final score of Carla's as per the given least squares regression line is equal to 95.5.

The above question is incomplete, the complete question is :

In a statistics course a linear regression equation was computed to predict the final exam score from the score

on the first test. The equation of the least-squares regression line was y=10+0.9x where y represents the predicted final exam score and x is the score on the first exam.

Carla scored 95 on the first test. What is the predicted value of the Carla's score on the final exam?

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The range of sina(3cos2a cos4a 3sin2a sin2a cos2a) ^ tan a(sec a -sina tana) where a is not an integer multiple of 7t/2.

The range of sina(3cos2a cos4a 3sin2a sin2a cos2a) ^ tan a(sec a -sina tana) where a is not an integer multiple of 7t/2 can be calculated using the following formula:

Range = Maximum Value - Minimum Value

The expression inside the parentheses can be simplified to 3cos2a cos4a + 3sin2a sin4a and the expression inside the exponential can be simplified to tan2a (1 / cos2a - sin2a). This gives us the expression

Range = 3cos2a cos4a + 3sin2a sin4a ^ tan2a (1 / cos2a - sin2a)

To calculate the maximum and minimum values, we can use derivatives to find the critical points of the expression. Taking the first derivative with respect to a, we get

d/da (3cos2a cos4a + 3sin2a sin4a ^ tan2a (1 / cos2a - sin2a)) = 0

Solving this equation gives us the critical points of a = ±7t/6. Using these values, we can calculate the maximum and minimum values of the expression.

Maximum Value = 3cos14t/6 cos8t/6 + 3sin14t/6 sin8t/6 ^ tan4t/3 (1 / cos14t/6 - sin14t/6)

Minimum Value = 3cos22t/6 cos16t/6 + 3sin22t/6 sin16t/6 ^ tan4t/3 (1 / cos22t/6 - sin22t/6)

Finally, using the formula for the range, we can calculate the range of the expression to be

Range = 3cos14t/6 cos8t/6 + 3sin14t/6 sin8t/6 ^ tan4t/3 (1 / cos14t/6 - sin14t/6) - (3cos22t/6 cos16t/6 + 3sin22t/6 sin16t/6 ^ tan4t/3 (1 / cos22t/6 - sin22t/6))

This expression gives us the range of sina(3cos2a cos4a 3sin2a sin2a cos2a) ^ tan a(sec a -sina tana) where a is not an integer multiple of 7t/2.

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The simplified expression is ab∛ 3ab².

The correct option is (C).

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.

Given:

2ab (∛192ab²) -5(∛81 [tex]a^4b^5[/tex])

Now, factorizing the terms as

192ab² = 2 x 2 x 2 x 2 x 2 x 2 x 3 x a x b x b

81 [tex]a^4b^5[/tex] = 3 x 3 x 3 x 3 x a x a x a x a x b x b x b x b x b

So, 2ab (∛192ab²) -5(∛81 [tex]a^4b^5[/tex])

= 2ab (∛2 x 2 x 2 x 2 x 2 x 2 x 3 x a x b x b) -5(∛3 x 3 x 3 x 3 x a x a x a x

                                                                                    a x b x b x b x b x b)

= 2ab ( 2 x 2 ∛ 3 x a x b x b) -5( 3 x a x b ∛3 x a x b x b )    

= 8ab ∛ 3ab² - 15ab∛ 3ab²                            

= -7ab ∛ 3ab²

Hence, the simplified expression is ab∛ 3ab².

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