X 4 ? 36 42
y 20 120 180 210

16
20
24
28

Answer:

3y+8=x

Step-by-step explanation:

School X School Y

y+8=x

3y=x

3y+8=x

Answer:

There are 27,720 ways to select the committee

Step-by-step explanation:

First, it is necessary to know how many ways are there to select 3 members, if there are 9 members of the mathematics department. This can be found using the following equation:

Where nCk gives as the number of ways in which we can select k elements from a group of n elements. So, replacing n by 9 and k by 3 members, we get:

So, there are 84 ways to select 3 members from 9 members of the mathematics department.

At the same way, we can calculate that there are 330 ways to select 4 members from the 11 that belong to the Computer science department as:

Finally the total number of ways in which we can form a committee with 3 faculty members from mathematics and 4 from the computer science department is calculated as:

9C3 * 11C4 = 84 * 330 = 27,720

Option c) x² + 11x - 1 = 0 is the correct quadratic equation that can be used to determine the thickness of the frame.

In this problem, Emily wants to hang a painting in a gallery, and she needs to determine the thickness of the frame, denoted by "x," surrounding the painting. The painting and frame together should have an area of 31 square feet. The dimensions of the painting are given as 5 feet in width and 6 feet in length. To find the equation that will help us determine the thickness of the frame, we need to set up a quadratic equation based on the given information.

Let's start by visualizing the problem. The painting is a rectangle, and the frame around it will also form a rectangle. So, we can find the area of the frame by subtracting the area of the painting from the total area of the painting and the frame.

The area of a rectangle can be calculated by multiplying its length and width. For the painting, we have:

Painting's area  = Length * Width

                          = 6 feet * 5 feet

                          = 30 square feet

Now, we know that the total area of the painting and frame together is 31 square feet. So, we can set up the following equation:

Total area (painting + frame) = Painting's area + Frame's area

31 square feet = 30 square feet + Frame's area

Frame's area = 31 square feet - 30 square feet = 1 square foot

The frame's area is given by the product of its width (which is the thickness "x") and the length of the painting (6 feet):

Frame's area = x * 6 feet

Since the frame's area is equal to 1 square foot, we can write:

x * 6 = 1

Now, let's rearrange the equation to set it to zero on one side:

6x - 1 = 0

We have now derived the quadratic equation that represents the problem:

6x - 1 = 0

The correct answer is not directly provided among the options. However, let's manipulate the equation to put it in standard quadratic form (ax² + bx + c = 0):

Multiply the equation by -1 to change the sign of each term:

-6x + 1 = 0

Now, it matches option c) x² + 11x - 1 = 0.

Thus, option c) is the correct quadratic equation that can be used to determine the thickness of the frame, "x," for the given problem.

To know more about Quadratic Equation here

brainly.com/question/17177510

#SPJ2

The correct answer is 4x2 + 22x − 1 = 0  

That's what you get when you (5 + 2x)(6 + 2x) = 31

And you get to expand that based on the data that is already provided in the question.

Cot² x - tan² x = 1 is not true for all the values of x, where x is a trigonometric angle.

What is a trigonometric angle?

Trigonometric angles are the ratios of trigonometric functions.

If we consider a right-angle triangle with an angle between base and hypotenuse is Ф then:

tan Ф = (height/base), and

cot Ф  = 1/tan Ф = base/height

Given, Cot² x - tan² x = 1

This is not true for all the values of x. Here, x is a trigonometric angle.

If we take x = 45°, then: Cot² x - tan² x = (1)² - (1)² = 0.

Hence, the statement is not true for all the values of x.

Learn more about trigonometric angles here: brainly.com/question/14235900

#SPJ2