In mathematics, inequalities are used **to compare the relative size of values**. They can be used to compare integers, variables, and various other algebraic expressions.

In Euclidean geometry: Similarity of triangles. The fundamental theorem of similarity states that **a line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side**.

square root

“At Most” in Probability

You can similarly say “**at most two**” or “at most three,” and so on. In each case, the outcome can only be less than or equal to the stated number.

symbol ∼

The bottom line is that “atleast” is **not a word**. The correct version is “at least.”

The special symbol ≠ It is used to show that **one value is not equal to another**. a ≠ b says that a is not equal to b. Example: 4 ≠ 9 shows that 4 is not equal to 9.

For the configurations known as angle-angle-side (AAS), angle-side-angle (ASA) or side-angle-angle (SAA), it doesn't matter how big the sides are; **the triangles will always be similar**. These configurations reduce to the angle-angle AA theorem, which means all three angles are the same and the triangles are similar.

In mathematics, inequalities are used **to compare the relative size of values**. They can be used to compare integers, variables, and various other algebraic expressions.

Whereas, At most in the probability means that **all the probabilities that are smaller than the given probability**. So, we can say that at most means maximum, whereas at least means minimum.

It's true that mathematics enables us to quantitatively describe the Universe, it's an incredibly useful tool when applied properly. But **the Universe is a physical, not mathematical entity**, and there's a big difference between the two.

Well, as it happens, there are others. Among physicists, it's not controversial. **Our universe is but one in an unimaginably massive ocean of universes called the multiverse**. If that concept isn't enough to get your head around, physics describes different kinds of multiverse.

Not only could mathematics be different on a different planet or in another universe; which are of course unprovable one way or the other; but **mathematics could and actually has been different at different eras on this planet.**

**Because math is a foundational part of computer systems**, every programmer and computer scientist needs to have basic mathematical knowledge. The type and level of math you need depends on what areas of computer science you want to work in. Some computer science career tracks require only minimal mathematical knowledge.

Algebraic expressions include at least one variable and at least one operation (addition, subtraction, multiplication, division). For example, **2(x + 8y)** is an algebraic expression.

Below are some of the examples of algebraic expressions.

For example.

1. | -5y+3=2(4y+12) |
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2. | 4 x 2 − 2 x − 2 x − 2 = − 1 2 |

3. | x√x=-x |

4. | |x-a|= a^{2}-x^{2} |

5. | 4 x 2 + 1 − 2 x 2 + 2 = 8 |

NCERT Solution for Class 9 Mathematics **Chapter 9** - Algebraic Expressions and Identities.

Constants are considered as **algebraic expressions which only involve numbers**. They have termed constants because their value is always the same. No variable can change the value of a constant. For instance, take the number 6.

**Algebraic expressions** are combinations of variables , numbers, and at least one arithmetic operation. For example, 2x+4y−9 is an algebraic expression. Term: Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables.

**You should already be familiar with algebra and geometry before learning trigonometry**. From algebra, you should be comfortable with manipulating algebraic expressions and solving equations. From geometry, you should know about similar triangles, the Pythagorean theorem, and a few other things, but not a great deal.

**Here are the basic steps to follow to simplify an algebraic expression:**

- remove parentheses by multiplying factors.
- use exponent rules to remove parentheses in terms with exponents.
- combine like terms by adding coefficients.
- combine the constants.

Dated : 18-May-2022

Category : Education