Parallel lines Q and M are cut by transversal lines j and k.

1) What is the measure in degrees of ∠ 1?

2) What is the measure in degrees of ∠ 2?

3) What is the measure in degrees of ∠ 3?

4) What is the measure in degrees of ∠ 4?

5) What is the measure in degrees of ∠ 6?

Explain how you found∠" 6?".

Answer:

The answer is (2,1)

Step-by-step explanation:

Given a vector in the plane, we can describe the rotation as a function :

X is the vector

T is the function that represents the rotation

[tex]T(X)=AX[/tex]

Where A is the rotation matrix

The rotation matrix about the origin in counterclockwise sense for an angle ''a'' is :

[tex]A=\left[\begin{array}{cc}cos(a)&-sin(a)\\sin(a)&cos(a)\end{array}\right][/tex]

If we replace ''a'' by 90 ⇒

[tex]\left[\begin{array}{cc}cos(90)&-sin(90)\\sin(90)&cos(90)\\\end{array}\right][/tex]

[tex]A=\left[\begin{array}{cc}0&-1\\1&0\\\end{array}\right][/tex]

If we want to rotate the vector D = (1,-2) :

[tex]T(D)=AD=\left[\begin{array}{cc}0&-1\\1&0\\\end{array}\right]\left[\begin{array}{c}1&-2\end{array}\right]=\left[\begin{array}{c}2&1\end{array}\right][/tex]

The rotation of the vector (1,-2) about the origin for an angle of 90 and in counterclockwise sense is (2,1)

Answer:

the correct answer is 18 i hope this helps you

The length of each edge of a cube with a total surface area of 486 square units is 9 units, obtained by dividing the total surface area by 6 to get the area of one face and then taking the square root.

To find the length of each edge of a cube when you have the total surface area, you need to understand that a cube has 6 faces that are all squares of the same size. Since the total surface area of the cube is given as 486 square units, we can find the area of one face by dividing the total surface area by 6. Once we have the area of one face, we can find the length of one edge by taking the square root of that area because the area of a square is equal to the length of one side squared (Area = side x side).

Let's calculate:

Therefore, the length of each edge of the cube is 9 units.

The slope of the line passing through the given points (2, 0) and (2, 4) is ∞ (undefined).

Given the following data:

To find the slope of the line passing through the given points (2, 0) and (2, 4):

Mathematically, the slope of a line is given by the following formula;

[tex]Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Substituting the points into the formula, we have;

[tex]Slope, \;m = \frac{4 - 0}{2 - 2}\\\\Slope, \;m = \frac{4}{0}[/tex]

Slope, m  = ∞ (undefined).

Note: A mathematical expression is considered to be undefined when its denominator is zero (0).

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The reciprocal of number 4 3/7 is 7/31.

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.

Given the mixed number

4 3/7 = (7×4 + 3)/7

⇒ 31/7

Now reciprocal is nothing but an interchange of numerator and denominator.

So

Reciprocal of 31/7 → 7/31

Hence "The reciprocal of number 4 3/7 is 7/31".

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Answer:

Let x represent the number of blueberry muffins [tex]x\geq 0[/tex]

Let y represent the number of bran muffins [tex]y\geq 0[/tex]

Tray of blueberry muffins: 1/3 cup of oil & 2 eggs

Tray of bran muffins: 1/2 cup of oil & 1 egg

Alan has 4 cups of oil and 12 eggs on hand.

He sells a tray of blueberry muffins for $12 each.

He sells a tray of bran muffins for $9 each.

[tex]\frac{x}{3}+\frac{y}{2}\leq 12[/tex]

The constraints for the problem are 4 cups of oil and 12 eggs.

Alan should not exceed 4 cups of oil and 12 eggs as it will create shortage. He should get the correct proportion of both the muffins to maximize his profit.

In equation form it is : [tex]\frac{x}{3}+\frac{y}{2}\leq 4[/tex]

Answer:

One of this ordered pairs: [tex]\left ( 1,3 \right )\,,\,\left (1 ,-2 \right )[/tex] should be removed

Step-by-step explanation:

A relation f is said to be a function if for each and every element of it's domain there exists a unique image in it's codomain.

As per the graph, ordered pairs are [tex]\left ( 1,3 \right )\,,\,\left ( 2,1 \right )\,,\,\left ( -2,2 \right )\,,\,\left (1 ,-2 \right )\,,\,\left ( 5,-4 \right )\,,\,\left ( -4,-4 \right )\,,\,\left ( -5,-3 \right )[/tex]

Here,  all the ordered pairs have unique image except [tex]\left ( 1,3 \right )\,,\,\left (1 ,-2 \right )[/tex]

Here , element 1 of domain has two images 3 and - 2 .

We know that as per definition for each and every element of the domain there should be a unique image in the codomain.

So, one of this ordered pairs: [tex]\left ( 1,3 \right )\,,\,\left (1 ,-2 \right )[/tex] should be removed in order to make it a function.

To find the number of students in a group who spent a total of $15.20, with each student spending $1.90, divide the total amount by the amount each student spent, resulting in 8 students.

The question asks how many students were in a group if they spent $15.20 altogether, with each student spending $1.90. To find the number of students, divide the total amount spent by the amount each student spent. This calculation is performed by dividing $15.20 by $1.90.

Calculation: $15.20 ÷ $1.90 = 8 students

Therefore, there were 8 students in the group.

The average rate of change of the function over the interval is 3

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

f(x) = 6 + 3x

The interval is given as

From x = 1 to x = 8

The function is a linear function

This means that it has a constant average rate of change

So, we have

f(1) = 6 + 3(1) = 9

f(8) = 6 + 3(8) = 30

Next, we have

Rate = (30 - 9)/(8 - 1)

Evaluate

Rate = 3

Hence, the rate is 3

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Question

Find the average value gave of the function g on the given interval. g(x) = 6 + 3x , [1, 8]

Answer:

Inequality for the given condition for the weight (m) ≥ 100 (greater than or equal to)

Explanation:

let suppose weight of Jared is "m" according to the given question.

His weight should be atleast (greater than or equal to ) 100 kilogram in order to box is heavy weight class.

So, our inequality equation for the above condition is :

m is greater than or equal to 100

m ≥ 100   That's the final answer.

I hope it will help you.

The cost formula for maintenance cost is : y = 3.33x + 10000

The cost formula for maintenance cost can be written in the form :

Using the pair of points ;

Slope = (14000 - 20000) / (7200 - 9000)

Slope = -6000 / 1800

Slope, b = 3.33

We have ;

y = 3.33x + c

Using the point (9000, 20000)

20000 = 3.33(9000) + c

20000 = 30000 + c

c = 10000

Now we have;

y = 3.33x + 10000

The cost formula for maintenance cost is : y = 3.33x + 10000

Answer:

b)the results of the survey cannot reliably be extended and generalized.

Step-by-step explanation:

Voluntary sampling is a type of convenience sample; it is convenient for the researcher to perform.  

However, voluntary sampling can lead to bias; usually only people who feel strongly one way or the other about the survey will volunteer to be members of a sample.

Since there is a possibility of bias, the results of the survey cannot reliably be extended and generalized.

The correct statement is,

b) the results of the survey cannot reliably be extended and generalized.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Since, We know that;

Voluntary sampling is a type of convenience sample and it is convenient for the researcher to perform.  

However, voluntary sampling can lead to bias; usually only people who feel strongly one way or the other about the survey will volunteer to be members of a sample.

Now, Since there is a possibility of bias,

Hence, the results of the survey cannot reliably be extended and generalized.

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Answer: B)  [tex]V=\pi r^2 h[/tex]

Step-by-step explanation:

Given: DeAndre has two glass cylinders .

To determine which cylinder will hold the most water, we need to find the volume of both the containers.

We know that the volume of cylinder is given by :-

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

Therefore, the formulas will help him determine which cylinder could hold the most water will be :

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

Answer:

V = 6w² + 12w

Step-by-step explanation: