PLEASE HELP WILL GIVE BRANI FOR ANY RIGHT ANSWER

The set of all points equidistant from the points A(-2, 4, 4) and B(5, 2, -3) forms a plane. This plane can be described by an equation that represents the locus of points equidistant from A and B.

To find the equation of the plane, we can first calculate the midpoint M between points A and B, which is given by the coordinates (x₀, y₀, z₀) of M, where x₀ = (x₁ + x₂)/2, y₀ = (y₁ + y₂)/2, and z₀ = (z₁ + z₂)/2.
Midpoint M:
x₀ = (-2 + 5)/2 = 3/2
y₀ = (4 + 2)/2 = 3
z₀ = (4 - 3)/2 = 1/2
Next, we calculate the direction vector D from A to B, which is obtained by subtracting the coordinates of A from those of B.
Direction vector D:
dx = 5 - (-2) = 7
dy = 2 - 4 = -2
dz = -3 - 4 = -7
Using the midpoint M and the direction vector D, we can write the equation of the plane as follows:
(x - x₀)/dx = (y - y₀)/dy = (z - z₀)dz
Substituting the values we calculated earlier, the equation becomes:
(x - 3/2)/7 = (y - 3)/(-2) = (z - 1/2)/(-7)
This equation represents the set of all points equidistant from points A(-2, 4, 4) and B(5, 2, -3), and it describes a plane in three-dimensional space.

Learn more about equidistant here
https://brainly.com/question/29886221



#SPJ11

Answer:

To find out how many gallons of Bear's Blue paint are needed to cover the entire floor of the church, we need to calculate the total area of the floor and divide that by the coverage area of one gallon of paint.

The floor of the church measures 80 ft by 40 ft, so its total area is:

Area = Length x Width = 80 ft x 40 ft = 3200 square feet

Each gallon of Bear's Blue paint covers 50 square feet, so the number of gallons needed is:

Gallons = Total Area ÷ Coverage per Gallon

Gallons = 3200 sq ft ÷ 50 sq ft/gallon

Gallons = 64 gallons

Therefore, 64 gallons of Bear's Blue paint are needed to cover the entire floor of the church.

Answer:

A quadratic equation is second degree equation with the standard form ax^2+bx+c=0 as the highest power is 2.

__________________.

The Elementary Matrix E is \(\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right]\).

We know that the Matrix

\(A = \left[\begin{array}{ccc}2&1&3\\-2&4&5\\3&1&4\end{array}\right] , B = \left[\begin{array}{ccc}2&1&3\\3&1&4\\-2&4&5\end{array}\right]\)

\(EA = B\)

⇒ \(E = B A^{-1}\)

\(A^{-1} = \frac{1}{|A|} \times \left[\begin{array}{ccc}A_{11}&A_{12}&A_{13}\\A_{21}&A_{22}&A_{23}\\A_{31}&A_{32}&A_{33}\end{array}\right]\)

\(|A| = \left|\begin{array}{ccc}2&1&3\\-2&4&5\\3&1&4\end{array}\right|\)

\(= 2 \times4\times4-2\times5\times1 - 1\times(-2)\times4+1\times5\times3+3\times(-2)\times1 - 3\times4\times3\\= 32 -10+8+15-6-36 = 3\)

\(A^{-1} = \frac{1}{3} \left[\begin{array}{ccc}11&-1&-7\\23&-1&-16\\-14&1&10\end{array}\right] \\A^{-1} = \left[\begin{array}{ccc}\frac{11}{3} &\frac{-1}{3}&\frac{-7}{3}\\\frac{23}{3}&\frac{-1}{3}&\frac{-16}{3}\\\frac{-14}{3}&\frac{1}{3}&\frac{10}{3}\end{array}\right]\)

\(\therefore E =\left[\begin{array}{ccc}2&1&3\\3&1&4\\-2&4&5\end{array}\right] \times \left[\begin{array}{ccc}\frac{11}{3} &\frac{-1}{3}&\frac{-7}{3}\\\frac{23}{3}&\frac{-1}{3}&\frac{-16}{3}\\\frac{-14}{3}&\frac{1}{3}&\frac{10}{3}\end{array}\right]\)

\(E = \left[\begin{array}{ccc}\frac{22+23-42}{3}&\frac{2+1-3}{3}&\frac{-14-16+30}{3}\\\frac{33+23-56}{3}&\frac{-3-1+4}{3}&\frac{-21-16+41}{3}\\\frac{-22+92-70}{3}&\frac{2-4+5}{3}&\frac{14-64+50}{3}\end{array}\right]\)

\(E = \left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right]\)

To learn more about matrices, visit: brainly.com/question/11367104

#SPJ4

The coordinate matrix of x in the basis b' is calculated to be,

[-2    1      6]

[ 1     0     4]

[ 0   10    6]

To find the coordinate matrix of x in the basis b', we need to express x as a linear combination of the basis vectors in b', and then use the coefficients of the linear combination as the entries of the coordinate matrix.

So we want to find scalars a, b, and c such that:

(4, 30, -8) = a(8, 11, 0) + b(7, 0, 10) + c(1, 4, 6)

Expanding this equation, we get a system of linear equations,

8a + 7b + c = 4

11a + 4c = 30

10b + 6c = -8

Solving the above  system of equations, we will get:

a = -2, b = 1, and c = 6

Hence , the required coordinate matrix of x in the basis b' is found to be :

[-2  1  6]

[ 1  0  4]

[ 0 10  6]

Learn more about coordinate matrix :

https://brainly.com/question/28194667

#SPJ4

(a) The number of different color combinations for filling up a jar with 50 jellybeans of 4 different colors, with no restrictions on the distribution of colors, is 4^50.

(b) The number of distinct non-negative integer solutions to the equation x1 +x2+x3 + x4 +x5 +x6 +x7 =20 is 230,230, which is found using the stars and bars method.

(a) Since there are 4 colors of jellybeans and no restrictions on the distribution of colors, we can choose any combination of colors to fill up the jar. Each jellybean can be one of 4 colors, so the number of different color combinations is 4^50.

(b) This is a classic stars and bars problem. We need to find the number of non-negative integer solutions to the equation x1 +x2+x3 + x4 +x5 +x6 +x7 =20. To solve this, we can imagine representing each x variable with a star ( * ), and using bars ( | ) to separate the stars into 7 groups, with each group representing one of the x variables. For example, the solution x1=2, x2=3, x3=0, x4=5, x5=4, x6=1, x7=5 would be represented as:

**|***||*****|||||||||

There are a total of 20 stars in this diagram, and 6 bars separating them into 7 groups. The number of solutions is equal to the number of ways to arrange the 20 stars and 6 bars, which is (20+6) choose 6, or 26 choose 6, which is equal to 230,230. Therefore, there are 230,230 distinct solutions to the equation x1 +x2+x3 + x4 +x5 +x6 +x7 =20.

Learn more about non-negative integer solutions:

https://brainly.com/question/15024048

#SPJ11

It is true that  the graph of the equation  \(\frac{x^2/a^2}{y^2/b^2} = 1\)represents a hyperbola with a horizontal transverse axis.

In general, a hyperbola is defined as the set of all points (x, y) in a coordinate plane such that the absolute difference between the distances from each point to two fixed points, called the foci, is constant. The equation \(\frac{x^2/a^2}{y^2/b^2} = 1\) represents a hyperbola with a horizontal transverse axis.

The center of the hyperbola is at the origin (0, 0), and the foci are located at (±c, 0), where \(c = \sqrt{(a^2 + b^2)}\). The vertices are at (±a, 0), and the asymptotes of the hyperbola have slopes of ±(b/a).

In the given equation,\(\frac{x^2/a^2}{y^2/b^2} = 1\), the terms \(\frac{x^2}{a^2}\)and \(\frac{y^2}{b^2}\)have opposite signs, which indicates a hyperbola. The coefficient of  determines the horizontal distance of the hyperbola branches, and the coefficient of \(\frac{x^2}{a^2}\)and \(\frac{y^2}{b^2}\) determines the vertical distance.

Therefore, the graph of the equation  \(\frac{x^2/a^2}{y^2/b^2} = 1\)represents a hyperbola with a horizontal transverse axis.

To know more about "Traverse axis" refer here:

https://brainly.com/question/30349519#

#SPJ11

The maximum greatest common divisor is n! + 1

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

a(n) = n! + n

When expanded, we have

a(n) = n(n - 1)! + n

So, we have

a(n) = n((n - 1)! + 1)

Calculate a(n + 1)

a(n + 1) = (n + 1)((n + 1 - 1)! + 1)

a(n + 1) = (n + 1)(n! + 1)

So, we have

a(n) = n((n - 1)! + 1)

a(n + 1) = (n + 1)(n! + 1)

From the above, we have

GCD = n! + 1

Read more about sequence at

https://brainly.com/question/30499691

#SPJ4

The equation that represents the linear equation is t = 4d + 5.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

The table is given in the attached image.

To find the equation:

First, find the common difference.

So,

13 - 9 = 4

17 - 13 = 4

21 - 17 = 4

25 - 21 = 4

Here, the first difference 4 is common.

That means, the equation is a linear equation.

And the general form of the linear equation is,

t = md + c

Here, m = 4

So,

t = 4d + c

To find C:

Substitute the value of t = 9 and d = 1,

So, c = 5

So, the linear equation is t = 4d + 5.

Therefore, t = 4d + 5 is the linear equation.

To learn more about the linear equation;

https://brainly.com/question/29739212

#SPJ1

Answer: -3/4

Step-by-step explanation:

change of y/change if x

so 7-4/2-6 which gets you -3/4

Lemme know if you need a better explanation hope this helps

The distance of the losing shot from the center is also uniformly distributed from 0 to 1.  To find the PDF of the distance of the losing shot from the center, we need to first determine the probability of one shot being closer to the center than the other.

Let X be the distance of the first shot from the center, and Y be the distance of the second shot from the center. Then, the probability that X is closer to the center than Y is given by the area of the region where X < Y, which is a triangular region with base 1 and height 1/2 (since the probability of X being closer to the center than Y is the same as the probability of Y being closer to the center than X). Therefore, the probability of X being closer to the center than Y is 1/4.

Now, let Z be the distance of the losing shot from the center. We know that Z is equal to the distance of the second shot from the center if the second shot is closer to the center than the first shot, and it is equal to the distance of the first shot from the center if the first shot is closer to the center than the second shot. Therefore, the PDF of Z is given by:

fZ(z) = (1/4)fY(z) + (3/4)fX(z)

where fX(x) and fY(y) are the PDFs of X and Y, respectively. Since X and Y are uniformly distributed from 0 to 1, their PDFs are both equal to 1 for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. Therefore, we have:

fZ(z) = (1/4) + (3/4) = 1

for 0 ≤ z ≤ 1. This means that the distance of the losing shot from the center is also uniformly distributed from 0 to 1.

Learn more about distance here:

https://brainly.com/question/15172156

#SPJ11

Probability is the measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.

We need to find out how many combinations of pants, shirts, and shoes the software engineer can wear without repeating any combination.

1. Pants: The software engineer has 3 pairs of pants to choose from.
2. Shirts: They have 4 shirts to choose from.
3. Shoes: They have 3 pairs of shoes to choose from.

To find the total number of combinations, simply multiply the number of choices for each item together:

Combinations = (Number of pants) x (Number of shirts) x (Number of shoes)

Combinations = 3 (pants) x 4 (shirts) x 3 (shoes)

Combinations = 36

So, the software engineer can go 36 days without wearing the same combination of three items.

To know more about Probability visit:

https://brainly.com/question/30034780

#SPJ11

Answer:

Step-by-step explanation:

jjjjjjjj

Answer:

\(\huge\boxed{\sf Yes.}\)

Step-by-step explanation:

y = 6x - 9 ---------------(1)

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

So,

x = 3, y = 9

Put this in Eq. (1) to verify.

9 = 6(3) - 9

9 = 18 - 9

9 = 9 [Equation satisfied]

Now, put x = 3, y = 9 in Eq. (2)

9 = 2(3) + 3

9 = 6 + 3

9 = 9 [Equation satisfied]

Since, both the equations are satisfied by the values of x and y, we can say that x = 3 and y = 9 is the solution to the system.

\(\rule[225]{225}{2}\)

Answer: Yes, it is a solution

Step-by-step explanation:

Plug (x,y) values into the equations.

Plug in (3,9)

y=6x-9  ---->.  (9)=6(3)-9 ----> 9=18-9 ----->   9=9

y=2x+3 ------>.  (9)=2(3)+3 ----> 9=6+3 ----> 9=9

When know (3,9) is a solution because each side has the same value.

Example:

8=9 Not a solution

5=5 A solution

Answer:

$32.55

Step-by-step explanation:

93 * .35 = 32.55

Answer:

125.55

Step-by-step explanation:

35% of 93 is32.55

Answer: polar form

Step-by-step explanation:

The distance from the sun to the other focus is 5.01 × 10⁹ m.

(a) The distance from the center of an ellipse to a focus is an where a is the semi major axis and e is the eccentricity. Thus, the separation of the foci ( in the case of Earth's orbit ) is;

2ae = 2(1.50 × 10¹¹)(0.0167) = 5.01 × 10⁹ m.

(b) To express this in terms of solar radii, we set up a ratio;

(5.01 × 10⁹)/(6.96 × 10⁸) = 7.2

Thus, we can conclude that the distance from the sun to the other focus is 5.01 × 10⁹ m.

Read more about Distance from Sun at; https://brainly.com/question/11494894

#SPJ1

Complete question is;

The Sun's center is at one focus of Earth's orbit. How far from this focus is the other focus, (a) in meters and (b) in terms of the solar radius, 6.96 × 10⁸ m? The eccentricity is 0.0167, and the semimajor axis is 1.50 × 10¹¹ m.

Answer:

The answer to this depends on the accuracy of the way this is transcribed.  If the value on the left side of the equals sign is indeed x, then it would be a rational equation.  If it is meant to be another scalar value though, then this would be a quadratic equation.

Step-by-step explanation:

This depends on the what is on the other side of the equals sign.  If it is a scalar value, then you are guaranteed a proper quadratic equation.  In the example given though:

\(x = ax^2 + bx + c\)

This is not actually true.  In this example, we can divide both sides by x, giving us a very different equation:

\(x = ax^2 + bx + c\\1 = ax + b + c/x\\ax + c/x = 1b\)

and this equation actually a rational one.

msin²x+cos²x=m-1

since the interval are 0 and π/4

Therefore

msin²(0)+cos²(0)=m-1

m(0)+1=m-1

1=m-1

m=2

use π/4 now

msin²(π/4)+cos²(π/4)=m-1

m(1/2)+(1/2)=m-1

m+1=2(m-1)

m+1=2m-2

-m=-3

m=3

Therefore

m=2 or 3

After taking Math 1010, their hourly wage increases to $12, which is a raise of 20%. They now make 20% more than their coworker. the person's new wage is $12 and the coworker's wage is $11, the person now makes ($12 - $11) / $11 * 100 ≈ 9.09% more than the coworker.the raise is 57.4%.

The hourly wage of the person is $10, while their coworker earns 10% more, making it $11 per hour.
Let's denote the person's hourly wage as x. According to the given information, the coworker earns 10% more than the person. This means the coworker's hourly wage is x + 0.10x = 1.10x.
Together, they make $16 per hour, so their combined wages are x + 1.10x = 2.10x. Since this equals $16, we can solve for x: 2.10x = $16, which gives x = $7.62.
After taking Math 1010, the person's hourly wage increases to $12. The raise amount can be calculated as the difference between the new wage and the previous wage, which is $12 - $7.62 = $4.38. To calculate the raise percentage, we divide the raise amount by the previous wage and multiply by 100: (4.38 / 7.62) * 100 ≈ 57.4%. Therefore, the raise is approximately 57.4%.
Since the person's new wage is $12 and the coworker's wage is $11, the person now makes ($12 - $11) / $11 * 100 ≈ 9.09% more than the coworker.

Learn more about hourly wage here
https://brainly.com/question/1582269



#SPJ11

Answer:

d = 24.

Step-by-step explanation:

Answer:

Each one can lead up to 180 (that's a hint)

A fraction that is sometimes used to approximate pi is 22/7.

One example of a fraction that is sometimes used to approximate pi is 22/7. This fraction is an approximation of pi that has been used for centuries, even though it is not an exact value of pi.

It is a good approximation that is accurate to within about 0.04%, which makes it useful in many practical applications.

The fraction 22/7 comes from dividing the circumference of a circle by its diameter, which is the definition of pi. While the exact value of pi is an irrational number that cannot be expressed as a fraction, 22/7 is a commonly used approximation that is easy to remember and calculate with. However,

there are more accurate approximations of pi that can be used for more precise calculations, such as 355/113 or 3.14159265359.

To know more about Greek symbols visit:

brainly.com/question/7269995

#SPJ1

Answer:

It is better to buy 8 eggs for 12 rupees.

Step-by-step explanation:

21/12 = 1.75

It cost 1.75 rupees per egg.

12/8 = 1.5

It costs 1.5 rupees per egg.

Answer: 11/4n + 2 = -3 +3/2n

Step-by-step explanation:

1) Solve the given equation

-5n + 31 = -14n -5

9n = -36 (Move like terms)

n = -4

2) Solve every other equation until match

1a)

11/4n + 2 = -3 +3/2n

11/4n = -5 + 6/4n (Change fraction and move like terms)

5/4n = -5 (minus fraction)

n =  -4 Correct

The minimum number amount of light energy that can exist in Hasbrouck 20 is zero due to the divisibility of light.

According to quantum theory, light is composed of particles called photons. Each photon carries a certain amount of energy, which is directly proportional to its frequency.

However, the size of the lecture hall being 9 m across does not impose any constraints on the minimum amount of light energy. In the quantum realm, light can be continuously divided, and there is no lower limit to the amount of light energy that can exist.

Therefore, the minimum amount of light energy in Hasbrouck 20 is considered to be zero.

This implies that arbitrarily small quantities of light can exist, and the division of light energy can continue indefinitely.

Learn more about Number click here :brainly.com/question/3589540

#SPJ11

Answer:

The diver's position in feet (depth) when she swims with dolphins is -83 feet.

Step-by-step explanation:

First highlight the important information from the question.

A diver sits on a boat at the surface of the ocean preparing to dive. She dives in and descends to -128 feet. After a few minutes, she ascends 45 feet to swim with a pod of dolphins that has appeared. What integer represents the diver's position in feet (depth) when she swims with the dolphins?

So, first she descends -128 feet, then she ascends 45 feet to swim with dolphins. So, now that we have the important information highlighted we can solve the problem.

-128+45=-83.

The diver's position in feet (depth) when she swims with dolphins is -83 feet.

Hope this helps!

If not, I am sorry.

Answer:

The number 3.99 as a fraction in its simplest form is 3 and 99/100. In its simplest form of a mixed fraction is 399/100.

Step-by-step explanation:

hope that helps>3

Answer:

- 3 99/100

= - 399/100

Step-by-step explanation:

we have

Company A = 0 + 0.70m

Company B = 50 + 0.20m

we will find A > B, so

answer: more 100 miles

Answer:

1334.1312

Step-by-step explanation:

Answer:

1334.1312

Step-by-step explanation: