What is the rational function?

Answer:

mx=4

Step-by-step explanation:

Following the slope formula y2-y1/x2-x1, we can find our solution. Follow steps in image.

-Hope this helped

Answer:

Step-by-step explanation:

480 miles/5 hours=x miles/8 hours

x=480*8/5

x=768 miles(distance)

480/5=96 mph(speed)

The value of the the expression 3x - 2y when x = 2 and y = 1 is 4

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

In this case, we want to find the expression 3x - 2y when x = 2 and y = 1. This will be:

= 3x - 2y

= 3(2) - 2(1)

= 6 - 2

= 4

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Complete question

Find the expression 3x - 2y when x = 2 and y = 1. Substitute given values of variables and evaluate expression

I recently dropped a large cube, leaving a dent in my floor. The floor's surface contains a triangular hole with sides that are $68, $75, and $77 long. The hole is about this deep:  [tex]$d=12 \sqrt{6}[/tex]

Three sides, three angles, and three vertices make up the closed, two-dimensional shape of a triangle. Polygons include triangles. Triangle ABC is seen in the above figure. Triangle examples. Sandwiches, traffic signals, clothing hangers, and a billiards rack are a few instances of triangles in everyday life.

To start, you can determine the sides of the tetrahedron whose apex corresponds to the dent's deepest point. Three of its sides are previously known to be $68,75,77, and since we have perpendicular planes, if these side lengths are x, y, and z, then

[tex]$x^2+y^2=68^2, x^2+z^2=75^2, y^2+z^2=77^2$[/tex] and these three equations solve to

[tex]$x=12 \sqrt{15}, y=4 \sqrt{154}, z=3 \sqrt{385}[/tex]

When the origin of a coordinate frame is located at the point where three perpendicular planes cross and the axes are placed along the edges, the equation for the plane of the triangle hole is

[tex]$\frac{x}{12 \sqrt{15}}+\frac{y}{4 \sqrt{154}}+\frac{z}{3 \sqrt{385}}=1[/tex]

As a result, the distance from the origin, which is the hole's deepest point, to its plane is

[tex]$d=\frac{1}{\sqrt{\frac{1}{144(15)}+\frac{1}{16(154)}+\frac{1}{9(385)}}}[/tex]

Then we get,

[tex]$d=12 \sqrt{6}[/tex]

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When x = 4, x⁴ × x⁻¹  will be 1. So correct option is C.

In mathematics, an exponential function is a function in which the variable (usually denoted by "x") is in the exponent. The most common exponential function is f(x) = b^x, where b is a constant called the base of the exponential function. For example, f(x) = 2^x is an exponential function with base 2. The graph of an exponential function is a curve that increases or decreases at an ever-accelerating rate as x increases. The exponential function is useful in many areas of mathematics and science, including finance, population growth, and radioactive decay.

To evaluate x⁴ × x⁻¹ when x = 4, we first substitute 4 for x in the expression:

x⁴ × x⁻¹ = 4⁴ × 4⁻¹

Now we can simplify the exponent by multiplying 4 × -1 = -4

x⁴ × x⁻¹ = 4⁴ × 4⁻⁴

Now we can simplify the exponent by applying the rule (aᵇ) × (aⁿ) = a⁽ᵇ⁺ⁿ⁾

x⁴ × x⁻¹ = 4⁽⁴⁺⁽⁻⁴⁾⁾

We now have 4⁰ which is equal to 1, so the final answer is 1.

Therefore the answer is C. 1

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After rounding off the median of the given data would be 38.

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory.

It could be referred to as "the middle" value for a data set.

The fundamental difference between the mean and the median when describing data is that the median is more representative of the "normal" value because it is not skewed by a tiny fraction of exceptionally big or small values.

So, calculate as follows:

22, 25, 25, 36, 39, 48, 53, 70

TErms are even: Average of two middle terms to get median.

Median = 36 + 39/2

Median = 37.5

Rounding off: 38

Therefore, after rounding off the median of the given data would be 38.

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Recent findings have revealed strong evidence amount for the theory that there is a black hole that lies at the center of the Milky Way and of many other galaxies in the universe.

Recent scientific studies have provided strong evidence for the theory that there is a black hole lying at the center of the Milky Way and of many other galaxies in the universe. This theory is supported by findings such as the detection of gravitational waves caused by the collision of two black holes, which is indicative of the existence of black holes in the universe. Additionally, the discovery of high-energy X-ray emissions from regions near the center of the Milky Way suggests the presence of a supermassive black hole. These findings, combined with other evidence, provide strong support for the theory that a black hole lies at the center of the Milky Way and of many other galaxies in the universe.

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The correct answer is U - II = I + III + IV.

In order to solve problems based on these sets, we can use a Venn diagram to depict the logical relationship between sets and their components. Although other closed figures like squares may be used, a Venn diagram commonly uses intersecting and non-intersecting circles to indicate the relationship between sets.

c represent the compliment of the particular state.

U is the union set

∩ represent intersection between the neighbouring sets

Therefore,

Bc = U - B = I + II

Bc∩A = Area common in Bc and A = II

(Bc∩A)c = Area in U but not in (Bc∩A) = U - II = I + III + IV

So, answer is d.

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The direct variation equation that relates x and y is 2y = 5x.

A type of proportionality known as "direct variation" occurs when one quantity directly changes in response to a change in another quantity.

This implies that if one quantity increases, the other quantity will also increase proportionately. Similarly, if one quantity decreases, the other amount also drops.  

The symbol '∝' is used to represent the relation of Direct variation between two quantities.

Here we have

y varies directly with x

=> y ∝ x

=> y = kx ----(1)

where k is the proportionality constant  

Given that x = 2 and y = 5

Now substitute given values in (1)

=> 5 = k(2)

=> 2k = 5

=> k = 5/2

Now substitute k = 5/2 in equation (1)

=> y = (5/2)x

=> 2y = 5x

Therefore  

The direct variation equation that relates x and y is 2y = 5x.

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Answer:

16.89 cubic inches

Step-by-step explanation:

r = 2.25/2 = 1.125

h = 4.25

[tex]\pi[/tex] = 3.14

V = h[tex]\pi[/tex]r^2

V = (4.25)*(3.14)*(1.125)^2

V = 16.889765625

A linear programming problem consists of a linear function to be to be maximized or minimized. It is subject to a set of constraints given in the form of linear equations or inequalities.

Linear programming is the programming in which selecting the best possible choice from those available alternatives whose constraint function and the objective function can be referred to as the linear mathematical function.

Linear programming is used for the optimization of linear objective.

It is used as constrained optimization, from where the objective functions and constraints all are linear.

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables

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Answer: 8.995437384 cm or roughly 9 cm

Step-by-step explanation:

V = 1/3 pi r^3 * h

75.36 = 1/3 pi 2^3 * h

h = 8.995437384 cm

Thus, we have shown that the equation [tex]\frac{d^2y}{dx^2} - 2tanx\frac{dy}{dx} = 0[/tex] is true using differentiation.

A part from integration, differentiation is one of the two key principles. A technique for determining a function's derivative is differentiation.

Given y * cos x = e^x

By implicit differentiation, the first derivative is

-y * sin x + y' * cos x = e^x

By implicit differentiation, the second derivative is

-y cos x - y' sin x - y' sin x + y'' cos x

= e^x-y cos x - 2 * y' sin x + y'' * cos x

= e^x <--- combines the two like terms in the middle on left side

-y cos x - 2 * y' sin x + y'' * cos x = y * cos x <--- substitutes the original function y*cosx

= e^x-2y cos x - 2 * y' sin x + y''  * cos x = 0  <--- subtracts y*cos x from both sides

-2y - 2 * y' tan x + y'' = 0  <--- divides both sides by cos x

y'' - 2*tanx * y' - 2y = 0

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Answer:

x = 38°

Step-by-step explanation:

sum of interior angle

=(n - 2 )180

=(8 - 2)180

=(6)180

=1080°.

the value of x

=(x + 55)° + (3x + 20)° + 4x° + (4x - 10)° + (6x - 55)° + (3x + 52)° + 3x° + (2x + 30)° = 1080°

= x + 3x + 4x + 4x + 6x + 3x + 3x + 2x + 55 + 20 - 10 - =55 + 52 + 30 = 1080.

=26x + 92 = 1080

=26x = 1080 - 92

=26x = 988

=26x/26 = 988/26

x = 38°

The equation for the amount charged by the company in Charlotte for m number of miles is c = 2m + 25.

The equation in standard form to represent the amount charged, c, for m number of miles by the company in Charlotte is c = 2m + 5. This means that the cost of utilizing the company is $2 per mile plus a flat fee of $5.This equation is in standard form, in which c represents the amount charged, m represents the number of miles and 25 represents the flat rate fee. To calculate the cost of a certain number of miles, we first multiply the number of miles by 2, then add 25 to the result. For example, if m = 10, then c = 2(10) + 25 = 45. In other words, if someone in Charlotte wanted to travel 10 miles, they would be charged 45 dollars.

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You can find the sales price history of a car by looking up the VIN

D=P(1−E%) 2

Or equivalently:

D=P(1− E/100 )^ 2

The exponential depreciation equation is of the form y=P(1-r)^xy=P(1−r) X With PP the original value, rr the depreciation rate per period and xx the number of periods.

The Kelley Blue Book, as well as its equally prominent website, is one of the most reliable sources for vehicle price, utilized by individuals buying or selling cars. Kelley evaluates the following values: private party, trade-in, recommended retail, and certified pre-owned (CPO). Check the vehicle history record while looking for a secondhand automobile online. If the original car window sticker is submitted with the report, you may sometimes figure out the MSRP of a vehicle.

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The length of the diagonal of the rectangular box with the origin O(0, 0, 0) and A(2, 4, 5) as opposite vertices is 6.708203932499369.

Let the origin be O(0, 0, 0) and A(2, 4, 5).

The length of the diagonal of the box can be calculated using the distance formula.

Diagonal = √((2-0)^2 + (4-0)^2 + (5-0)^2)

= √(4 + 16 + 25)

= √45

= 6.708203932499369

1. We are given the coordinates of two opposite vertices of a rectangular box, the origin O(0, 0, 0) and A(2, 4, 5).

2. To calculate the length of the diagonal of the box, we need to use the distance formula.

3. The length of the diagonal can be calculated as Diagonal = √((2-0)^2 + (4-0)^2 + (5-0)^2)

4. By substituting the values of the coordinates in the formula, we get Diagonal = √45

5. Simplifying the expression, we get Diagonal = 6.708203932499369.

The length of the diagonal of the rectangular box with the origin O(0, 0, 0) and A(2, 4, 5) as opposite vertices is 6.708203932499369.

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In this situation, the independent variable is x, which is the number of groups, and the dependent variable is y, which is the number of exercises needed.

To model this situation with an equation, we need to calculate the number of exercises needed for each group. Since we have x groups, and each group needs a unique exercise, we can calculate the number of exercises needed by multiplying the number of groups by 5, since each group has 5 members. Thus, the equation would be y = 5x. This equation uses the fact that each group is made up of 5 members, so each group needs a unique exercise. In order to determine the number of exercises needed, we can solve the equation for x by dividing both sides by 5. This gives us x=y/5, which indicates that the number of exercises (x) is equal to the number of groups (y) divided by 5.For example, if we have 8 groups, then the number of exercises needed would be 5*8 = 40.In this situation, the independent variable is x, which is the number of groups, and the dependent variable is y, which is the number of exercises needed.

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The algorithm appears to be an O(n^2) complexity algorithm, as the number of steps taken grows quadratically with the number of items n.

This can be demonstrated by calculating the slope of the line formed by the given values. The slope of the line formed by the given values is m = (3,500 - 100) / (60 - 10) = 33. This means that for every increase in the number of items of 10, the number of steps taken increases by 33. This indicates that the algorithm is O(n^2) complexity, as for every increase of 10 items, the number of steps taken increases by 33. This pattern will continue for larger values of n, meaning that for very large values of n, the algorithm will be O(n^2) complexity.

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Answer:

150

Step-by-step explanation:

x - .14x = 129

.86x = 129   Divide both sides by .86

x = 150

The solution for this equation is (3¹)⁴=81.

The power of a number defines how many times to use the number in multiplication, Powers are also called Exponents or Indices.

If the power is positive, multiply the number by itself that many times. If the power is negative, multiply the number's reciprocal by itself that many times. If the power is zero, the result will always be 1.

For example, 8^2 could be called “8 to the power 2” “8 to the second power”, or simply “8 squared”.

A number, ​X​, to the power of 2 is also referred to as ​X​ squared.

X​ is called the base number.

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All solutions to the system of equations created by the linear equation and the quadratic equation y=x^2+9 are (3,18), (-3,-18), (0,9), (-2,13), and (2,13).

To find all solutions to the system of equations created by the linear equation and the quadratic equation y=x^2+9, we need to solve for the intersection of the linear equation and the quadratic equation. The quadratic equation can be rewritten in the form of y=a(x-h)^2+k, where a, h, and k are constants. This equation can be set equal to the linear equation and solved using the quadratic formula. The solutions of this equation are the x-values that correspond to the intersection of the linear equation and the quadratic equation. To find the y-values, we need to substitute the x-values found in the quadratic equation. Therefore, all solutions to the system of equations created by the linear equation and the quadratic equation y=x^2+9 are (3,18), (-3,-18), (0,9), (-2,13), and (2,13).

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The vertex for the given function is (1, -25) and the zeros are (6, 0)(-4, 0).

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.

Given y = (x - 1)² - 25

converting the equation in form of y = ax² + bx + c

y = x² + 1 - 2x - 25

y = x² - 2x - 24

vertex of a quadratic equation is given by (-b/2a, -D/4a)

b = -2, a = 1, c = -24

D = b² - 4ac

D = (-2)² - 4(-24)

D = 4 + 96

D = 100

vertex is, -b/2a = -(-2)/2 = 1

and -D/4a = -100/4 = -25

vertex are (1, -25)

and for zeros put y = 0

y = x² - 2x - 24

x² - 2x - 24 = 0

x² - 6x + 4x - 24 = 0

x(x - 6) + 4(x - 6) = 0

(x - 6)(x + 4) = 0

x = 6 and x = -4

zeros are (6, 0)(-4, 0)

Hence option C is correct.

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Answer:

10d

Step-by-step explanation:

p = d

10p = ?

Cross multiply

(10pd)/p = 10d

Answer:  The equation that represents the situation is d = k/p, where k is a constant.

This equation states that the number of days taken to complete the work (d) is inversely proportional to the number of people working on the job (p).

Given that 10 people work on the job and it takes them d days to complete it, we can substitute these values into the equation:

d = k/10

We don't know the value of k, so we can't find out the number of days it takes with 10 people working.

Step-by-step explanation:

Triangle ABC and triangle XYZ are not congruent because they do not have the same side lengths or angles. To be congruent, two triangles must have the same side lengths and the same angles.

To determine if two triangles are congruent, we first need to check if they have the same side lengths. If the two triangles have the same side lengths, then we can move on to check if the angles of the two triangles are the same. If the two triangles have the same side lengths and the same angles, then we can conclude that the two triangles are congruent. If the two triangles do not have the same side lengths and the same angles, then we can conclude that the two triangles are not congruent. In the case of triangle ABC and triangle XYZ, they do not have the same side lengths or angles, so they are not congruent. To be congruent, two triangles must have the same side lengths and the same angles.

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The value of x = 4 and y = 5.

What is congruence?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Here, we have

Given: triangles ABC and DEC are congruent, then:

3y + 1 = 4x

4y - 6 = 2x + 6

We need to solve the system of equations above.

Rearranging both equations:

-4x + 3y = -1       [1]

-2x + 4y = 12      [2]

Multiplying [2] by -2:

4x - 8y = -24      [3]

Adding [1] and [3]:

-5y = -25

Dividing by -5:

y = 5

Substituting in [1]:

-4x + 3(5) = -1

-4x + 15 = -1

Subtracting 15:

-4x = -16

Dividing by -4:

x = 4.

Hence, the value of x = 4 and y = 5.

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If you want to reach Alpha Centauri you will need to go at a speed of 29,666,095,890,410 km/hr.

Alpha Centauri is 4.4 lightyears away from your location, now let's convert this distance into kilometers:

1 lightyear = 9.46 trillion kilometers

4.4 x 9.45 trillion kilometers = 41.58 trillion kilometers

Now, let's calculate the time available:

If there are 24 hours in a day, then in a year there are 24 x 365 = 8760, hours, which means in 160 years there are 1,401,600. Using this, calculate the speed:

41.58 trillion kilometers/ 1,401,600 hours = 29,666,095,890,410 kilometers per hour.

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Answer:

3

Step-by-step explanation:

√25 = .5

Answer:

the answer is Number 3 = v25