Mathematic question answer

1. In the figure below, the line segment AB is equal in length to the line segment BC. If point C lies on the segment AB, what is the length of the segment AC? 2.

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A city hall has a square area of 20,000 square meters and a perimeter of 4 kilometers. If the area of a circle of radius 2,000 meters is half this area, what is the radius of this circle? 3. A square with sides of length 5 meters has a perimeter of 2 meters. What is the length of one side? 4. The area of a triangle with base length 6 meters and height 3 meters equals what percent larger than that of a triangle with base and height 8 meters? 5. Two cars are traveling in opposite directions along parallel roads that are exactly kilometer apart. The first car drives at 30 kilometers per hour while the second travels at 40 km/h. Both cars travel for two hours before they pass each other. What was the average speed for both cars during this time?

A theorem is a mathematical statement that is demonstrated to be true by its proof. The proof of a theorem is usually very difficult, but it can be simplified by using another theorem as a basis for the proof. A lemma is a theorem that has been simplified in this way. This type of theorem has not yet been proven, but it has been shown to be true by its proof. A simple example of this would be the Pythagorean theorem: If we assume that the hypotenuse (the length of one side) is twice the length of the other two sides, then we can easily prove that the two sides are equal by showing that their sum is equal to the length of the hypotenuse. This is a lemma; however, it has not yet been proven to be true. Another example would be Euclid’s proposition: If you assume that a straight line can be divided into two parts so that each part is perpendicular to the line, and if you also assume that there are only two such parts, then you have enough information to show that they are equal. This proposition has been proved by Euclid’s proof; however, it still needs to be proved true by some other method.

Mathmatics is the study of numbers, geometry, and reasoning. It encompasses a wide range of skills, from basic arithmetic to advanced calculus and statistics. Mathmatics is a key part of many disciplines, including science, engineering, medicine, and economics. It helps us make sense of the world around us and can be used to solve a wide range of problems. When learning math, it's important to remember that math is not something you do quickly; it's something you do well. It takes time to develop an understanding of the subject. Math is like playing an instrument: You need to practice and spend time developing your skills before you can play well. The most important thing to keep in mind when learning math is that it’s all about taking steps forward. Don’t be afraid of mistakes or to try things out - that's how you get there! Always think in terms of moving forward; this will help you stick with the process and build your confidence as you go along.

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