Yes, both triangles are constructible. A triangle is constructible if its three sides can be constructed using a straightedge and compass. In the case of the first triangle, we can construct the sides of length 3, 4, and 5 using the Pythagorean theorem. For the second triangle, we can construct the sides of length 5, 7, and 8 using the Pythagorean theorem as well. Therefore, both triangles are constructible. **

A triangle is constructible when its three sides can be constructed using a straightedge and compass. In other words, a triangle is constructible if its sides can be formed by straight lines and its vertices can be created by the intersection of those lines. This means that the sides of the triangle must be able to be drawn using only a straightedge and compass, without the use of any other tools or measurements. **

The triangle is not constructible. This is because the given side lengths do not satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, the sum of the two shorter sides is equal to the length of the longest side, making it impossible to construct a valid triangle. **

Yes, there are coin-operated vending machines in Flensburg. These machines can be found in various locations such as train stations, shopping centers, and public buildings. They offer a variety of products including snacks, drinks, and even everyday essentials like toiletries and phone chargers. Customers can use coins to make purchases from these vending machines. **

The huge ships depicted in the movie 2012, known as "arks," are designed to withstand catastrophic events such as massive floods. While the concept of building large ships to save a portion of the population from a global disaster is theoretically possible, the specific design and scale of the arks in the movie may not be realistic. Constructing such massive ships would require an enormous amount of resources, engineering expertise, and logistical challenges that may make it impractical in reality. Additionally, the feasibility of such a project would depend on the specific details of the disaster scenario and the availability of suitable construction materials and technology. **

At the first coin-operated vending machine, which was created in the early 1880s by Percival Everett, customers could purchase postcards for their money. The machine was installed in the railway stations and post offices in London, and for a penny, customers could receive a postcard featuring a picture of the surrounding area. This early vending machine was a novelty at the time and provided customers with a convenient way to purchase postcards without the need for human interaction. **

Yes, there are rules that can be used to determine when a triangle is uniquely constructible. One such rule is the side-angle-side (SAS) congruence criterion, which states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent and can be uniquely constructed. Another rule is the side-side-side (SSS) congruence criterion, which states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent and can be uniquely constructed. These rules can be used to determine when a triangle is uniquely constructible based on the given information. **

The answer to this question depends on individual preferences and needs. A cashier-operated checkout provides the opportunity for human interaction and personalized service, which some people may prefer. On the other hand, a self-service store offers convenience and efficiency, allowing customers to complete their purchases quickly and without waiting in line. Ultimately, the better option is subjective and varies from person to person. **