The topic we learned this week was how to solve word problems using math equations.
For example, we have a problem:
“We have two numbers whose sum is 46. If twice the first number is equal to three units less than three times the second number, what are these two numbers?

To solve this problem, we go through 4  steps:

1. Definition of variables: we assume that the first number and the second number are

2. Writing equations: according to the problem: The sum of two numbers:

• Twice the first number equals three units less than three times the second number:

3. Solving equations:
From the first equation, we find:

We put this in the second equation:

After simplifying, we arrive at and.

Result: The desired numbers are 27 and 19.
Using this method, we can solve many word problems and strengthen our equation solving skills

In the last week of school, to start the winter holidays, we had exercises about different types of slopes and we also learned a new lesson related to them. Our new topic was about solving and finding the two points of X and Y for two equations, the first method was graphing, which includes the ponit slope_slope y-intercept _general form of the slope. Determined and found y. The second step in this method is to convert the coffesient to 1 and the third step is to isolate them and finally insert them.

The last method, which is one of my favorite methods, is elimination. This method is one of the easiest and fastest methods. In this method, in the first step, one of our variables must be zero, and after that, the numbers that Collect them in a similar position. In the last step, we have to solve the obtained answer in the form of an equation, then when we get one of the problems, we replace them and find the other one.

The last stage that is common to all of these is that in the final stage of all of them, they should be checked by awarding them.

In this week, the topic we learned is the new formulas related to the slope, which is one of the formulas that was new and useful for me, and also interesting to me. The main formula of the slope is written as

m=
The characteristics of this formula are its letters, one of the main letters which indicates the slope is m, and the rest are letters y and x.

This formula is used to get the slope of the line segment with given endpoint

The slope has different formulas that are used to obtain a series of interviews. One of them was interesting to me and it was a bit useful. There is a formula for finding a point without using a graph.
(x1,y1)A
(x2,y2)B
The main formula of this calculation
For example

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Relation and function are important and fundamental concepts in mathematics that are used in many subjects such as algebra, geometry, and even computer science. In this article, we will discuss the definition, differences, and applications of these two concepts.

The topic of relations, in simple terms, if we have two sets and , the relation can include any possible combination of members of these two sets.

A function is a special type of relationship in which each element of the first set (the source set) is associated with exactly one element of the second set (the destination set).

In simpler terms, a relation can be said to be a relation when a line passes through a point or dimension twice, and if it is not the same and all the points and lines are in different places, then the graph is a function.

Functions can be represented in a variety of ways:
1. Table: Specifying inputs and outputs.
2. Graph: Plotting points on a coordinate system.
3. Formula: Expressing the relationship between inputs and outputs with an equation such as .

here is some examples of relation and function

These are the examples in the first one you can see the the up and down of the circle are in one line so this is the relation

The new things we learned this week are related to the x and y axis. The explanation is easy and to start this topic, it is about domain and range. We learned that domain is the relation between all possible sets for x, and range is also for possible relations for y. The possible states that we can check domain and range from are different (photo)

(need to complete)

• This week, the new topic we started is related to the pattern and the relationship between their data, which is almost similar to the lessons we have studied in previous years.
  In order to make it easier to explain

from examples such as

• the value of a computer is related to its age.
•  the price of a watermelon is related to its weight.
• it can even be said that the number of students in a school is related to the size of that school.
• In mathematics, these two things are called relation.

In the following, there are things related to this topic and quantities, including:

• table of value
• set of the ordered pairs
• a mapping diagram
• an equation
• a graph
• in words

Also, by considering this example, it can help to introduce and get familiar with the topic of relation
took
the cost, C (cents per km), of driving a car is related to the speed, S (km/h), at which it is driven.

Here C and S are our variables, the price depends on the speed

C is called dependent variable and the S is called independent variable

independent variable is the input and the dependent variable is the output value

We can use the above solutions to get c and s and find their relation and dependence

To get c and s, we can use the above solutions and find their relationship and dependence, which in the first step and using graph, we can show it in two ways, which are in the form of the following images.

Another way is ordered pairs, which is written like this:

(S,C)

• (20,10)
• (30,9.1)
• (40,8.4)
• (50,7.9)
• (60,7.6)
• (70,7.5)
• (80,7.6)
• (90,7.9)
• (100,8.4)
• etc…
• For ordered pairs, you can make a table and put the numbers in it by writing input and output above the numbers to show the table of value method.
  

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• Equation:  C=-0.14s+12.4

This week, for exercises and flashbacks, the exercises we did in class included factoring or simplifying and scientific numbers, as well as simplifying fractions with negative exponents. i
I want to explain about fraction and negative power and its function.

Negative exponents are written with a base and a negative exponent. In general, if $a$ is a non-zero number and $n$ is a positive number, the definition of a negative exponent is as follows:

=

n goes to the power of a in the denominator

One of the main functions of the exponent that we do with the number we have is to reverse or reverse that number, for example, one second to the negative power of one is equal to two one.

2=^{-1}$

Here the answer is equal to 2. That is, by putting the number

In the negative power of one, we actually reached the inverse of that number.

​Negative exponents allow us to easily calculate inverse values. This feature is especially useful in mathematics and various sciences.

In this week, the new topic we learned is factoring trionimial form +bx+c

for example

(x+2)(x+4)= +4x+2x+8 = +6x+8

(x+3)(x+3)= +3x+3x+9 = +6x+9

Here x is to the power of 2, the number of x’s are in parentheses,

the next binomial(bx) is the sum of the x’s

and the value of the multiplication of the numbers.

By looking at numbers without variables in parentheses, we can easily get the answer by doing math with our eyes. It is also possible to reject some questions that we only answer one of them, for example only the answer
We have the addition and multiplication of those two numbers and we need to find those two numbers.

Like the example below:

+8x+12

Here we have to choose the numbers whose sum is equal to 8 and whose denominator is equal to 12
In the first rank, we have to write all the numbers whose multiplication answer is 12
1.12
2.6
3.4
are
Then we have to check them to find which one’s answer is equal. 8
1+12=13
2+6=8
3+4=7
And we choose those two numbers

To make the answer more concise and correct, you can write Anhar once more and multiply it