## Questions and Answers

What is a triangle called when it has all sides of different lengths?

Scalene Triangle

Which type of triangle has at least two sides of equal length and two equal interior angles?

Isosceles Triangle

In an equilateral triangle, what are the angles measurement of each internal angle?

60 degrees

What type of triangle has all sides of equal length?

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Which type of triangle is based on the classification of side lengths and angles?

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What is the definition of an equilateral triangle?

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Which of the following is a polynomial expression?

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What is the general form of a linear equation?

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Which of the following is an algebraic expression?

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If $f(x) = x^2 - 4x + 4$, what is the value of $f(2)$?

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Which of the following is the solution to the linear equation $2x - 3 = 7$?

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What is the degree of the polynomial $3x^4 - 2x^2 + 5$?

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## Study Notes

## Mathematical Concepts

Mathematics is a broad field of study encompassing various concepts such as geometry, algebra, arithmetic, calculus, and statistics. These mathematical concepts form the foundation of many scientific, engineering, and technological applications. Let's delve into some of these important areas:

### Polynomials

A polynomial is a mathematical expression consisting of variables and coefficients combined using the operations of addition, subtraction, multiplication, and non-negative integer powers. For example, `x^2 - 4x + 4`

and `3x^2 - 2x + 1`

are polynomial expressions. Polynomials are often used in algebra, calculus, and various other mathematical fields.

### Linear Equations

A linear equation is a mathematical statement that describes a relationship between two quantities, where each term could involve only itself, one power of another variable, and constant terms. Linear equations typically have the general form `ax + b = c`

, where `a`

, `b`

, and `c`

are constants, and `x`

represents a variable. Solving linear equations involves finding the value of the variable `x`

that satisfies the equation.

### Algebraic Expressions

Algebraic expressions are mathematical combinations of numbers and symbols representing unknown values or variables. They can be used to represent relationships between different variables and perform operations on them. Examples of algebraic expressions include `3x - 7y`

, `(4x^2 + 5) / (2x - 1)`

, and `sqrt(x^2 + y^2)`

. These expressions can be simplified or manipulated using algebraic rules to solve problems involving numerical values.

### Triangles

In geometry, a triangle is a polygon with three edges and three vertices. It is one of the basic shapes in Euclidean geometry. Classification of triangles is based on their side lengths and angles. There are several types of triangles:

#### Scalene Triangle

A scalene triangle has all three sides of different lengths. In other words, there are no congruent sides. An example of a scalene triangle is shown below:

```
______________
| |
| A |
| |
| |
| B |
| |
|____________|
```

#### Isosceles Triangle

An isosceles triangle has at least two sides of equal length and at least two equal interior angles. An example of an isosceles triangle looks like this:

```
*
***
*****
*******
*********
```

#### Equilateral Triangle

Equilateral means all sides are of equal length. Thus, an equilateral triangle is one whose three sides are of equal length, and all internal angles are of 60 degrees. Here is an example of an equilateral triangle:

```
*
***
*****
******
*****
***
*
```

These mathematical concepts, including triangles, polynomials, linear equations, and algebraic expressions, provide fundamental building blocks for understanding more complex mathematical theories and applications.

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