- Triangle ABC has vertices A(1,2), B(7,0), and


C(3,-2). Prove triangle ABC is an isosceles triangle.



Please help! Thanks

Answers

Answer 1

Triangle ABC can be proven to be an isosceles triangle by showing that two of its sides have equal lengths.

To prove that triangle ABC is isosceles, we need to demonstrate that at least two of its sides have equal lengths. Let's calculate the lengths of the sides AB, BC, and AC using the distance formula.

The length of side AB can be found using the coordinates of points A(1,2) and B(7,0):

AB = √((7-1)² + (0-2)²) = √(36 + 4) = √40 = 2√10

The length of side BC can be calculated using the coordinates of points B(7,0) and C(3,-2):

BC = √((3-7)² + (-2-0)²) = √((-4)² + (-2)²) = √(16 + 4) = √20 = 2√5

The length of side AC can be determined using the coordinates of points A(1,2) and C(3,-2):

AC = √((3-1)² + (-2-2)²) = √((2)² + (-4)²) = √(4 + 16) = √20 = 2√5

Comparing the lengths of the sides, we see that AB = AC = 2√10 = 2√5. Therefore, two sides of triangle ABC have equal lengths, indicating that it is an isosceles triangle.

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Related Questions

QUESTION 2 The Operating Systems interactions are primarily with the _____________. Applications user glue throughput

Answers

The primary interaction of operating systems is with applications and users.

Operating systems serve as a bridge between applications and users, facilitating their interactions and enabling the smooth execution of tasks. When a user interacts with an application, such as opening a document or launching a web browser, the operating system plays a crucial role in managing the underlying resources and coordinating the necessary actions.

At the application level, the operating system provides a platform for software developers to create and run their programs. It offers various services and APIs (Application Programming Interfaces) that applications can utilize to access system resources like memory, storage, and network connectivity. The operating system also handles process management, ensuring that multiple applications can run concurrently and share system resources efficiently. It manages processes' execution, scheduling, and synchronization, allowing for smooth multitasking and resource allocation.

Additionally, the operating system provides a user interface through which users can interact with applications and control the system. This can be in the form of a graphical user interface (GUI), command-line interface (CLI), or a combination of both. The operating system handles user input, such as mouse clicks or keyboard strokes, and translates them into actions that the applications can understand. It also manages output, displaying application windows, menus, and dialog boxes on the screen, and relaying information to the user.

In terms of throughput, the operating system plays a crucial role in optimizing resource allocation and managing system performance. It allocates CPU time, memory, and other resources to applications based on their priority and demand, ensuring fair and efficient resource utilization. By monitoring system performance, the operating system can identify bottlenecks and optimize resource usage to enhance overall throughput.

In summary, the operating system's interactions are primarily with applications and users. It provides a platform for applications to run, manages system resources, facilitates user interactions, and optimizes throughput to ensure efficient operation of the system.

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what is a fee that broadcasters must pay to musicians for using their songs in public? royalty, copyright,collaboration, or fair use?

Answers

Answer:

Royalty Payment

hope this answered your question!

What is the advantage of 2022 rogue’s manual shift mode?.

Answers

The 2022 Nissan Rogue has a new manual shift mode. The advantage of this manual shift mode is that it gives drivers greater control over the driving experience. It also provides drivers with an enhanced level of engagement with the vehicle.

Manual shift mode is becoming increasingly popular in modern cars. It allows drivers to manually shift gears, rather than relying on an automatic transmission to do it for them. This gives drivers more control over the vehicle, and can help to improve driving performance. The 2022 Nissan Rogue is equipped with a Continuously Variable Transmission (CVT) that is designed to provide a smooth and efficient ride.

However, some drivers may prefer the experience of shifting gears manually. The manual shift mode in the 2022 Rogue allows drivers to do just that.This provides drivers with a more engaging driving experience and allows them to get the most out of the Rogue's performance capabilities. Overall, the advantage of the 2022 Rogue's manual shift mode is that it provides drivers with a greater level of control over the vehicle, and can help to enhance the driving experience.

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why do most highlights on plastic objects look white, while those on gold metal look gold

Answers

When light is shone on an object, it gets absorbed and reflected by the object’s surface. This is why we see different colors of objects and why most highlights on plastic objects look white, while those on gold metal look gold.

Most highlights on plastic objects look white because the surface of plastic is not as smooth as that of metal. The light is scattered on the rough surface of the plastic object, causing the colors to mix and appear white. As a result, the color of the highlight is lost in the overall whiteness of the scattered light. On the other hand, gold metal is smooth, and light reflects off it more easily.

When light falls on the gold surface, the electrons on the surface of the metal move around, causing the light to reflect in a specific way that creates the color gold. The highlight on the gold metal will also be gold as the surface is smooth, and the light is reflected in a specific way to give it that golden color. In conclusion, highlights on plastic objects look white because the surface of the plastic is rough, while those on gold metal look gold because the surface of the gold metal is smooth, which allows light to reflect in a specific way that creates the color gold.

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By the mid 1980s, the ARPANET had grown into what we now call the Internet, connecting computers owned by large institutions, small organizations, and individuals all over the world. True False

Answers

True. By the mid-1980s, the ARPANET had indeed evolved into what we now recognize as the Internet, linking computers owned by various entities worldwide.

True. The ARPANET, initially created by the U.S. Department of Defense's Advanced Research Projects Agency (ARPA) in the late 1960s, served as the foundation for the development of the Internet. It started as a network connecting a few large institutions, such as universities and research centers, facilitating communication and resource-sharing between them. Over time, the network expanded, incorporating smaller organizations and eventually reaching individual users around the globe.

By the mid-1980s, the Internet had become a decentralized network, consisting of interconnected networks using the Transmission Control Protocol/Internet Protocol (TCP/IP) suite as its underlying communication protocol. This expansion allowed for the exchange of data and information on a much broader scale, enabling global communication and collaboration. The Internet's growth during this period laid the groundwork for its exponential development in the subsequent decades, revolutionizing the way people communicate, access information, conduct business, and engage in various online activities.

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Which question should a programmer ask when evaluating a game


development project's limitations?


O A. What features are going to be the most difficult to build?


O B. What features are players most likely to want in the game?


O C. What is the best way to describe the game to prospective players?


O D. What types of people are likely to be interested in playing the


game?

Answers

The question a programmer should ask when evaluating a game development project's limitations is:

A. What features are going to be the most difficult to build?This question helps the programmer assess the technical challenges and limitations they may encounter during the development process. By identifying the most challenging features, the programmer can plan and allocate resources accordingly, ensuring the project stays within scope and budget.

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You received someone’s public key as (55, 7), and you want to encrypt the plaintext value of 8. Using RSA encryption, what is the corresponding ciphertext?

Answers

The corresponding ciphertext for encrypting the plaintext value of 8 using RSA encryption with a public key of (55, 7) is 32.

RSA encryption is a public-key encryption algorithm that relies on the mathematical properties of prime numbers. In this case, the public key provided consists of two values, (55, 7), where 55 represents the modulus and 7 represents the public exponent. To encrypt the plaintext value of 8, we raise it to the power of the public exponent and take the modulus of the result with the modulus value.

To encrypt the plaintext value of 8, we perform the following calculation:

ciphertext = (plaintext ^ public_exponent) % modulus

= (8 ^ 7) % 55

= 2097152 % 55

= 32

Therefore, the corresponding ciphertext for encrypting the plaintext value of 8 with the given public key (55, 7) is 32.

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Which documentation tool is MOST useful for designing a whole system when databases are involved?

Answers

When designing a whole system involving databases, the documentation tool that is most useful is the Entity Relationship Diagram (ERD). An ERD provides a graphical representation of the entities, attributes, and relationships in a database system.

It is a modeling technique used to visualize and describe the data that is used by a business or organization. ERD is the most popular and widely used documentation tool for designing systems that involve databases. It helps to create a clear picture of the system and its different components, including tables, attributes, and relationships. The key components of an ERD include entities, attributes, and relationships.

Entities are objects or concepts that are represented by tables in the database. Attributes are the characteristics of the entities, and relationships describe how the entities are related to each other. With an ERD, it is easy to identify the different tables in the system, the fields within each table, and how the tables relate to one another.

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If you have multiple projects, and if you need to check for new updates, every five minutes, which is the correct CRON expression that Jenkins can use to avoid polling of all the projects at the same time.


Choose the correct option from below list


(1)*/5 * * *


(2)None of the options


(3)5 * * * *


(4)H/5 * * * *

Answers

The correct CRON expression for Jenkins to check for updates every five minutes without polling all projects at the same time is option (1) */5 * * *.

The CRON expression "*/5 * * *" specifies that Jenkins should run the task every five minutes. The asterisk (*) in the first position means "every" or "any" value, so */5 indicates every fifth minute. The remaining fields are left as asterisks to denote any value for the other components (hour, day, month, etc.). This expression ensures that Jenkins will check for updates every five minutes without having all projects polled simultaneously. By using this expression, Jenkins will stagger the polling of projects and avoid overwhelming the system with simultaneous requests.

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Choose the term described. : End of Line indicator : the directory, folders, and subfolders in which a file is located

Answers

The term described as "End of Line indicator" is used to mark the termination of a line of text, which is often indicated by the characters "\n" or "\r\n". The end of line indicator is used by text editors, word processors, and other programs that manipulate text to separate lines of text.

In computing, the term "directory" refers to a container that holds files and other directories. The directory contains the folders and subfolders in which a file is located. It provides a hierarchical organization structure for files and directories that makes it easier to manage large volumes of data.

In summary, the end of line indicator is a character that marks the end of a line of text, while a directory is a container that holds files and other directories and provides a hierarchical structure for organizing files.

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What is not one of the three characteristics of tcp in its role as a reliable delivery protocol?.

Answers

Transmission Control Protocol (TCP) is the most popular protocol utilized for communication across the internet. TCP, as a reliable delivery protocol, has several characteristics. However, one of the three characteristics of TCP in its role as a reliable delivery protocol is the ability to perform a quick, continuous, and reliable flow control.


The first characteristic of TCP is connection-oriented communication. The connection-oriented communication guarantees that the sending device is connected to the receiving device before data transmission. TCP guarantees that the receiver is ready to receive data before transmission occurs. Therefore, the receiver will have a buffer ready to store incoming data.

Therefore, Flow control is one of the three characteristics of TCP in its role as a reliable delivery protocol. It allows the sender to control the flow of data based on the receiver's buffer size, preventing buffer overflow or congestion.

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