Will mark as brainliest if correct

Answer:

La ecuación de la recta es \(y = -6\cdot x +23\).

Step-by-step explanation:

Para construir la ecuación de la recta podemos utilizar un punto contenido en la recta y su pendiente. En primer punto, hallamos el punto con la resolución del siguiente sistema de ecuaciones lineales:

\(x+4\cdot y = 0\) (1)

\(x-3\cdot y = 7\) (2)

La solución del sistema de ecuaciones es \((x,y) = (4,-1)\).

Por Geometría Analítica, sabemos que la Ecuación de la Recta en su forma explícita es:

\(y = m\cdot x + b\) (3)

Donde:

\(x\) - Variable independiente.

\(y\) - Variable dependiente.

\(m\) - Pendiente.

\(b\) - Intercepto.

Si sabemos que \((x,y) = (4,-1)\) y \(m = -6\), entonces el intercepto de la recta es:

\(b = y-m\cdot x\)

\(b = 23\)

Ahora, la ecuación de la recta es \(y = -6\cdot x +23\).

Answer:

53/100

Step-by-step explanation:

Answer: 4 ) 5/9

Step-by-step explanation:

Using the simplex method, the maximum value of Z=5A+4B is found to be 19.2 when A=3.6 and B=1.2. The calculations can be confirmed by using any software that solves linear programming problems.

To solve the given linear programming problem using the simplex method, we start by converting the problem into standard form. We introduce slack variables to convert the inequalities into equations.The initial tableau is as follows:

      | A | B | S1 | S2 | S3 | S4 |   RHS

------------------------------------------

 Z    | -5 | -4 | 0  | 0  | 0  | 0  |    0

------------------------------------------

 S1   |  6 |  4 | 1  | 0  | 0  | 0  |   24

 S2   |  1 |  2 | 0  | 1  | 0  | 0  |    6

 S3   | -1 |  1 | 0  | 0  | 1  | 0  |    1

 S4   |  0 |  1 | 0  | 0  | 0  | 1  |    2

We perform the simplex iterations until the optimal solution is reached. After applying the simplex method, the final tableau is obtained as follows:

      |  A  |  B  |  S1  |  S2  |  S3  |  S4  |   RHS

------------------------------------------------------

 Z    |  0  | 1.8 | 0.2  | -1   | -0.4 |  0.4 | 19.2

------------------------------------------------------

 S1   |  0  |  0  |  0   | 1.5  | -1   |  1   |  3

 S2   |  1  |  0  | -0.5 |  0.5 |  0.5 | -0.5 | 1.5

 A    |  1  |  0  | 0.5  | -0.5 | -0.5 |  0.5 |  0.5

 S4   |  0  |  0  |  1   | -1   | -1   |  1   |  1

From the final tableau, we can see that the maximum value of Z is 19.2 when A=3.6 and B=1.2. This solution satisfies all the constraints of the problem. The calculations can be verified using any software that solves linear programming problems, which should yield the same optimal solution.

Learn more about  linear programming  here:- brainly.com/question/30763902

#SPJ11

Answer:

none

Step-by-step explanation:

it doesn't have any information or content

The minimum number of colors needed to vertex-color the graph \(W_n\) is n + 1. We need to remove 2 edges from \(W_n\) to leave a spanning tree.

To determine the number of colors needed to vertex-color the graph \(W_n\), let's first understand the structure of the graph.

The graph \(W_n\), also known as the wheel graph, consists of a cycle of n vertices connected to a central vertex. Each vertex in the cycle is connected to the central vertex.

To vertex-color the graph, we can assign colors to the vertices in a way that no two adjacent vertices have the same color. The goal is to find the minimum number of colors required for this coloring.

To justify the answer, we need to show that it is possible to color the graph with the proposed number of colors and that it is impossible to color it with fewer.

To show that it is possible to color the graph with the proposed number of colors:

We can use n colors to color the n vertices in the cycle. Each vertex in the cycle is adjacent to two other vertices, and we can assign a different color to each of these vertices. This ensures that no two adjacent vertices in the cycle have the same color.

For the central vertex, we can use an additional color that is different from any color used for the cycle vertices. Since the central vertex is connected to all the vertices in the cycle, this coloring scheme guarantees that no two adjacent vertices in the entire graph have the same color.

Therefore, it is possible to color the graph \(W_n\) with n + 1 colors.

To show that it is impossible to color the graph with fewer colors:

Consider the case when we attempt to color the graph with fewer than n + 1 colors. Since each vertex in the cycle is adjacent to two other vertices, at least two adjacent vertices in the cycle would need to share the same color if we use fewer colors.

However, this violates the condition that no two adjacent vertices should have the same color in a proper vertex coloring. Therefore, it is impossible to color the graph \(W_n\) with fewer than n + 1 colors.

Hence, the minimum number of colors needed to vertex-color the graph \(W_n\) is n + 1.

For the second part of the question, when n ≥ 4, we know that \(W_n\) is not a tree because it contains cycles. To leave a spanning tree, we need to remove edges from the graph.

The graph \(W_n\) has n vertices and n + 1 edges. To leave a spanning tree, we need to remove (n + 1) - (n - 1) = 2 edges. Removing any two edges from the graph will result in a spanning tree.

Therefore, we need to remove 2 edges from \(W_n\) to leave a spanning tree.

For more details about spanning tree

https://brainly.com/question/13148966

#SPJ4

Answer:

diameter(d)=8 in.

radius(r)= d/2= 4 in.

height(h)= 3r = 3(4) = 12 in.

Volume=r ² h

          =(3.14)(4)²(12)

          =(3.14)(16)(12)

          =602.88 in.

      Therefore, the volume of the cylinder is 602.88 in.

Step-by-step explanation:

Answer:

Im literally learning the same thing go to math     way and type the equation word for word

Step-by-step explanation:

The direction of vector R with respect to the positive x-axis is approximately −16.70i − 20.00j. The magnitude and direction of vector R are option (d) 16.7,309.0.

To find the magnitude of the vector R=B⋅A, we first need to calculate the dot product of vectors A and B:
B⋅A = (4.50i − 5.00j)⋅(−6.00i + 8.00j)
    = 4.50(−6.00) + (−5.00)(8.00)
    = −27.00
The magnitude of vector R is equal to the absolute value of the dot product of A and B:
|R| = |B⋅A| = 27.00
To find the direction of vector R with respect to the positive x-axis, we need to calculate the angle between vector R and the positive x-axis. We can do this by finding the angle between vector R and the positive x-axis using the arctangent function:
θ = tan⁻¹(Ry/Rx)
where Rx and Ry are the x and y components of vector R, respectively. To find Rx and Ry, we first need to calculate the components of vector R:
R = B⋅A = −27.00
Rx = R cos(θ) = R cos(tan⁻¹(Ry/Rx)) = −27.00 cos(51.10∘) ≈ −16.70
Ry = R sin(θ) = R sin(tan⁻¹(Ry/Rx)) = −27.00 sin(51.10∘) ≈ −20.00
Therefore, the direction of vector R with respect to the positive x-axis is approximately −16.70i − 20.00j. The magnitude and direction of vector R are option (d) 16.7,309.0.

Learn more about arctangent here : https://brainly.com/question/29198131

#SPJ11

Learn more about correlation coefficient on the given link:

https://brainly.com/question/4219149

#SPJ11

Answer:

The distributive property states that you can "distribute" the contents of one parentheses into the other to find an answer.

Let's first break down the larger number in the second parentheses:

400 + 10 + 5.

Then, let's multiply all those numbers by 3.

400 x 3 = 1200. 10 x 3 = 30. 5 x 3 = 15.

Then add up all the numbers and you get 1245.

Answer:

1245

Step-by-step explanation:

400+10+5

400×3=1200. 10×3=30. 5×3=15

An expression for cos(2θ) in terms of x is cos(2θ) = 1 - 2x²

To find an expression for cos(2θ) in terms of x, we can use the double angle identity for cosine:

cos(2θ) = 2cos²(θ) - 1

Since we know sin(θ) = x, we can use the Pythagorean identity for sine and cosine to find cos(θ):

cos²(θ) = 1 - sin²(θ) = 1 - x²

Now we can substitute this expression for cos²(θ) into the double angle identity:

cos(2θ) = 2(1 - x²) - 1 = 1 - 2x²

Therefore, an expression for cos(2θ) in terms of x is:

cos(2θ) = 1 - 2x²

Learn more about expression

brainly.com/question/14083225

#SPJ11

Answer:

c

Step-by-step explanation:

The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

The critical value(s) and rejection region(s) for the type of z-test with a level of significance a = 0.03 and a right-tailed test are as follows :Step 1: Determine the critical value of  zThe critical value is calculated by using the normal distribution table and the level of significance. A right-tailed test will have a critical value of zα. For a level of significance of 0.03, we will look for the z-value that corresponds to 0.03 in the normal distribution table.Critical value for a = 0.03 is z = 1.88 (approx).Step 2: Determine the Rejection Region The rejection region for a right-tailed test is defined as any z-value that is greater than the critical value. That is, if the test statistic is greater than 1.88, we reject the null hypothesis at the 0.03 level of significance, and if it is less than or equal to 1.88, we fail to reject the null hypothesis.Therefore, the rejection region for a right-tailed test with a level of significance of 0.03 is as follows:Rejection Region: Z > 1.88  OR  Z ≤ -1.88Graph: The graph for the given values will be as follows:The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

To know more about  critical value Visit:

https://brainly.com/question/32607910

#SPJ11

The Area of given shape is 170 square inches. The shape is combination of two rectangle.

A shape that is made by combination of two or more basic shape is termed as composite shape. As example the shape in the figure is a composite shape of two rectangle.

we need to calculate the area of each shape seperately then the two result is added or subtracted depending on the position of those shape.

In this figure, there are two rectangles, one has 11 in length and 10 in width, the other has 15 in length and 4 in width.

the area of each rectangle is = 11x10 =110 in²

and 15x4 = 60 in²

total area of shape is the sum of two shape= (110+60) in² = 170 in²

hence, the area is 170 square inches.

to learn more about Area of rectangle visit:

https://brainly.com/question/27683633

#SPJ1

The density of the material is 4 g/cm³.

What is the density of the material?

Density is a physical property that describes the amount of mass per unit volume of a substance. It is typically represented by the symbol "ρ" (rho) and is calculated by dividing the mass of an object by its volume. The units of density are usually expressed as mass per unit volume, such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).

Density is defined as mass per unit volume. We can use the formula:

density = mass/volume

Substituting the given values:

density = 48g / 12cm³

Simplifying:

density = 4g/cm³

Therefore, the density of the material is 4 g/cm³.

To learn more about the density visit:

https://brainly.com/question/1354972

#SPJ1

Answer:

\(\frac{b}{a}\) is the total time taken to clean the house.

Step-by-step explanation:

Given that:

Betsy cleans \(\frac{a}{b}\) of the house.

Time taken = 1 hour

To find:

Time taken to clean the whole house = ?

Solution:

We can use unitary method here to solve this problem.

We are given that \(\frac{a}{b}\) of the house is cleaned in 1 hour.

We have to find that a total of 1 house will be cleaned in how much time.

(1 house because Betsy's house can be considered as a single unit).

To find this we will divide 1 hour with \(\frac{a}{b}\).

Now, Let us solve this mathematically:

\(\frac{a}{b}\) of the house is cleaned in = 1 hour

1 of the house will be cleaned in =  1 hour divided by \(\frac{a}{b}\)

\(\dfrac{1}{\dfrac{a}{b}}\ hours\\\Rightarrow \dfrac{1 \times b}{a}\ hours\\\Rightarrow \dfrac{b}{a}\ hours\)

So, the answer is:

\(\frac{b}{a}\) is the total time taken to clean the house.

The number of tickets that they give away to employees is 33.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenarios.

Let the number of employees be x

Therefore, number of listener = 5x

Total number of people = 198

Therefore, this will be illustrated thus:

x + 5x = 198

6x = 198

Divide

x = 198/6

x = 33

Therefore 33 tickets are given to employees.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

Characteristic polynomial of the matrix \(p(x) = (x+1)(x-2)^2\)

For the matrix [8 -4 0 -4], the characteristic polynomial is found by taking the determinant of the matrix [8-x -4 0 -4; 0 8-x -4 0; 0 0 8-x -4; 0 0 0 8-x] and simplifying it. This results in p(x) = \((x-8)^4\).

For the matrix [3 0 4 -3 -4 -1 0 -1 0], the characteristic polynomial is found by taking the determinant of the matrix [3-x 0 4; -3 -4-x -1; 0 -1 -x 0;] and simplifying it. This results in \(p(x) = (x+1)(x-2)^2\).

The determinant of the matrix (A - lam*I), where I is the identity matrix of the same size as A, is found by computing the characteristic polynomial of a square matrix A, represented by P(lam), which is a polynomial function of a scalar variable lambda. We refer to the eigenvalues of the matrix A as the roots of the characteristic polynomial. Important details about the matrix, including its diagonalizability, rank, trace, and determinant, are revealed by the characteristic polynomial. It frequently appears in applications like systems of linear equations, differential equations, and linear transformations.

Learn more about matrix here:

https://brainly.com/question/31982832

#SPJ11

Answer:

(-4, 5)

Step-by-step explanation:

Hi there!
We are given the following system:
x+11y=51

3x+5y=13
And we want to solve it by substitution.
When we solve a system by substitution, we want to solve one of the equations for a variable; the variable should equal an expression containing the other variable. Then, we substitute that expression into the other equation as the variable we solve for, solve for that variable, and then use the value of the solve variable to find the value of the first variable

It's easier to solve for a variable if the leading coefficient in front of that variable is 1, like with x in the first equation (x+11y=51)
To solve this equation for x, we can subtract 11y from both sides.

x+11y=51

  -11y   -11y

_____________
x=51-11y
Now substitute 51-11y as x in 3x+5y=13:

3(51-11y)+5y=13

Multiply

153-33y+5y=13

Combine like terms.

153-28y=13

Subtract 153 from both sides

-28y=-140

Divide both sides by 28

y=5
Now substitute 5 as y in 51-11y to solve for x.

x=51-11y

x=51-11(5)
multiply

x=51-55

Subtract

x=-4

The answer is x=-4, y=5, or as a point, (-4, 5)
Hope this helps!

See more on solving systems of equations by substitution here: https://brainly.com/question/26578968

Answer:

A, D, E

Step-by-step explanation:

The solutions to the equation 3x^2 - 9x - 12 = 0 are x = 4 and x = -1.

To solve the quadratic equation 3x^2 - 9x - 12 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a),

where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 3, b = -9, and c = -12. Substituting these values into the quadratic formula, we have:

x = (-(-9) ± √((-9)^2 - 4 * 3 * (-12))) / (2 * 3)

= (9 ± √(81 + 144)) / 6

= (9 ± √(225)) / 6

= (9 ± 15) / 6.

We have two possible solutions:

For the positive root:

x = (9 + 15) / 6

= 24 / 6

= 4.

For the negative root:

x = (9 - 15) / 6

= -6 / 6

= -1.

The solutions to the equation 3x^2 - 9x - 12 = 0 are x = 4 and x = -1.

for such more question on equation

https://brainly.com/question/17145398

#SPJ8

The correct option will be that S T is congruent to segment W V.

Given the triangles STU and WVX, if the triangje are congruent, then the measure of their sides will be the same.

Since the corresponding angles are congruent, hence the equivalent sides will be:

ST = WV

Su = WX

TU = VX

Based on these, the correct option will be that S T is congruent to segment W V.

Learn more on congruent triangles here: https://brainly.com/question/2938476

Answer:

Step-by-step explanation:

Answer: 486 sq. feet.

Step-by-step explanation:

Given, w represents the width of the room, such that

. The polynomial (w+2) (2w-5) or \(2w^2- w -10\)gives the new area of any room in the house.

If current width of the kitchen is 16 feet, the put w= 16 in the above expression, we get

Area of the new kitchen = \((16+2) (2(16)-5)\) sq. feet  

\(=(18)(27)=486\text{ sq. feet}\)

Hence, the area of the new kitchen = 486 sq. feet.

To express the given system of differential equation as an almost linear system, we need to find the partial derivatives of the given functions with respect to x and y.

∂f/∂x = -ex
∂f/∂y = 2
∂g/∂x = -1
∂g/∂y = -4cosy

Now, substituting these values in the general form of an almost linear system,

x′(t) = ax + by + r(x,y)
y′(t) = cx + dy + s(x,y)

we get,

x′(t) = -ex + 2y
y′(t) = -x - 4cosy

So,

a = -e, b = 2, c = -1, d = 0

At the critical point (0,0), the Jacobian matrix is

J(0,0) = ⎡⎣⎢⎢⎢-1 2⎤⎦⎥⎥⎥

The eigenvalues of this matrix can be found by solving the characteristic equation,

det(J - λI) = 0

where I is the identity matrix of the same size as J.

det ⎡⎣⎢⎢⎢-1-λ 2⎤⎦⎥⎥⎥ = (-1-λ)(-λ) - 2(2) = λ^2 + λ - 4

Using the quadratic formula, we get the eigenvalues as

λ1 = (-1 + sqrt(17))/2 ≈ 0.56
λ2 = (-1 - sqrt(17))/2 ≈ -2.56

Since the eigenvalues have opposite signs, the critical point is a saddle.

Learn more about differential equation

https://brainly.com/question/31492438

#SPJ11

Solution:

First, we need to find out the amount for one kilogram. Since 100 grams = 30 pesos, and 1000 grams = 1 kilogram, we need to multiply it by 10.

30 x 10 = 300

Now we have the amount for 1 kilogram. Now in order to get the amount for 8 kilograms, we need to multiply it by 8.

300 x 8 = 2400 pesos

Answer:

The answer is 2,400 pesos.

Check:

30 x 10 = 300 So 300 pesos for a kilogram

300 x 8 = 2400 So 2400 pesos for 8 kilograms.

Answer:

pqoejbbbsvbhxncbqbqheeirowoqpnabzvxjsmqkw

The standard equation of a hyperbola with a vertical transverse axis, centered at the origin, and values of a = 9 and b = 4 is y^2/81 - x^2/16 = 1.

The standard equation of a hyperbola centered at the origin with a vertical transverse axis is given by (y^2/a^2) - (x^2/b^2) = 1. In this case, we are given that a = 9 and b = 4, so substituting these values into the equation, we get:

(y^2/81) - (x^2/16) = 1

This is the standard equation of the hyperbola in question. It tells us that the center of the hyperbola is at the origin (0,0), the transverse axis is vertical (parallel to the y-axis), and the distance from the center to the vertices is 9 units (which is the value of a).

The distance from the center to the foci is given by c = sqrt (a^2 + b^2), which in this case is sqrt (81 + 16) = sqrt (97). The asymptotes of the hyperbola are the lines y = (a/b) x and y = -(a/b) x, which in this case are y = (3/4) x and y = -(3/4) x.

Learn more about equation here:

brainly.com/question/1462469

#SPJ11

any number multiplied by 0 is 0. a single value cant be assigned to a fraction where the denominator is 0 so the value remains undefined.

Answer:

Since the definition x0 = 1 is based upon division, and division by 0 is not possible, we have stated that x is not equal to 0. Actually, the expression 00 (0 to the zero power) is one of several indeterminate expressions in mathematics. It is not possible to assign a value to an indeterminate expression.Thus making it unsolved

Step-by-step explanation:

The probability of at least one loud noise exceeding 80db in an hour is:

p(at least one loud noise > 80db) = 1 - p(y ≤ 80)

please note that to calculate the exact probability, we need to perform the integration and numerical calculations.

to find the probability of at least one loud noise exceeding 80db in an hour, we need to calculate the complement of the event where no loud noise exceeds 80db.

let's define the random variable x as the number of sudden horrible sounds within an hour. since x follows a poisson distribution with parameter λ = 3, we have p(x = k) = e⁽⁻λ⁾ * (λᵏ) / k!

next, let's define the random variable y as the loudness of a single noise, which follows an exponential distribution with rate parameter λ = 0.01. the probability density function of y is given by f(y) = λ * e⁽⁻λʸ⁾ for y ≥ 0.

we want to calculate the probability of at least one loud noise exceeding 80db, which can be expressed as p(y > 80).

the probability of no loud noise exceeding 80db can be calculated as p(y ≤ 80), which is the complement of p(y > 80).

p(y ≤ 80) = ∫[0 to 80] λ * e⁽⁻λʸ⁾ dy

integrating this expression gives us:

p(y ≤ 80) = [0 to 80] (0.01 * e⁽⁻⁰.⁰¹ʸ⁾) dy

now, we can calculate the complement probability:

p(y > 80) = 1 - p(y ≤ 80)

Learn more about probability here:

https://brainly.com/question/32117953

#SPJ11