Rational Expressions and Equations

For chapter 6, I learned solving rational expressions and equations which include addition, subtraction, multiplication, and division.

First, rational expressions are defined as a fraction in which the numerator and denominator are polynomials but one thing to note is that the denominator can’t be zero. It cannot contain roots and exponents of variables.

If there is a variable that makes the denominator zero, then it is considered as a non-permissible value.

e.g

x-3/x-5

x cannot be +5 as it will make changes to the denominator to (5-5=0). That’s why +5 is a non-permissible value.

here are the examples of dealing with addition, subtraction, multiplication, and division.

for addition, subtraction, the key point is to find the same denominator as normal fractions, as long as we’ve got the same denominator, then just focus on the upper part.

for multiplication and division, we can just simply apply the strategies for doing normal rational numbers.

One important thing is at the end, all the non-permissible value must be listed out

 

quadratic functions

Before Christmas, we have to go through chapter 4.

First,  there are 3 types quadratic function

  • 1) Standard form: y = ax^2 + bx + c where the a,b, and c are numbers.
  • 2) Factored form: y = (ax + c)(bx + d) again the a,b,c, and d are numbers.
  • 3) Vertex form: y = a(x + b)^2 + c again the a, b, and c are numbers.

My favorite part and I found it interesting is graphing quadratic function

features in a graph :

 

Vertex

the lowest and highest point of the parabola is called the vertex. If the parabola opens up, the vertex represents the lowest point on the graph or the minimum value of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph or the maximum value.

Axis of Symmetry

Parabolas also have an axis of symmetry, which is parallel to the y-axis. It’s is a vertical line drawn through the vertex.

y-intercept

The y-intercept is the point at which the parabola crosses the y-axis. There cannot be more than one such point, for the graph of a quadratic function. If there were, the curve would not be a function, as there would be two values.

x-intercepts

The x-intercepts are the points at which the parabola crosses the x-axis. If they exist, the x-intercepts represent the zeros, or roots, of the quadratic function, the values of at which . There may be zero, one, or two -intercepts. The number of x-intercepts varies depending upon the location of the graph.

here is an example of graphing, given a vertex form y= (x-1)^2+1

there is a hidden 1 before (x-1)^2, so it’s positive, the graph opens upwards, x-(+1) makes the graph shift right to (1), x=1. the +1 y= (x-1)^2+1 makes the graph goes upwards (y=1). This is how we graph.

solve quadratic equations

last week, we have learned two ways to solve quadratic equations

the first method is completing the squares

example 1: Solve the equation below using the method of completing the square.

Move the constant to the right side of the equation, while keeping the x-terms on the left. I can do that by subtracting both sides by 14.

Next, identify the coefficient of the linear term (just the x-term) which is

Take that number, divide by 2 and square it.

Add 814 to both sides of the equation, and then simplify.

Express the trinomial on the left side as a square of binomial.

Take the square roots of both sides of the equation to eliminate the power of 2 of the parenthesis. Make sure that you attach the plus or minus symbol to the constant term (right side of equation).

Solve for “x” by adding both sides by 9/2 .

Find the two values of “x” by considering the two cases: positive and negative.

Therefore, the final answers are x= and x. You may back-substitute these two values of from the original equation to check.

for the quadratic formula

substitute for a,b and c in

adding and subtracting radicals

In chapter 2, I have learned that Radicals can be simplified through adding and subtracting. The first thing to note is that radicals can only be added and subtracted if they have the same root number. If the radicals in a question are unlike, you won’t be able to combine them together. That’s one of the main rules for radicals that you should remember

How to subtract radicals

Our example will help you grasp the basics of what we mean when we say you have to find like radicals before combining them. The simplifying radicals problem below deals with how to subtract radicals.

Question 1:

√90−√

Solution:

We are going to first simplify this expression. We will perform a division analysis for the number 90 in order to identify its roots:

division analysis of number 90 for combining like radicals
the result of division analysis for 90

We learn that √90 can be re-written as:

√5⋅2⋅

Since we are dealing with square roots (which is what a radical sign stands for. There should be a tiny 2 next to the radical sign to indicate that we’re working with square roots, but it is generally accepted to simply write the sign without it), we are looking for numbers in pair. In this case, we can see that we have a pair of 3s

radical 5x2x3x3

Now, we can take the pair outside of the radical (square root), leaving us with:

3√5⋅2=

This means our question can be transformed into the following expression:

3√10

You can see that we’ve now identified the “like” radicals in the question: 3-radical-10-radical-10.

We can finally do the subtraction, and the result gives us:

2√

To add radicals, the method is the same as subraction  the radicand (the number that is under the radical) must be the same for each radical, so, a generic equation will have the form:

ab+cb=(a+c)b

Let’s plug some numbers in place of the variables:

 

 

math pre-cal 11

last week, I have get to know more about square roots. One of the skills that we learned is turning mixed radical to entire radical. In order to do this, we need to take the integer number in front of the root sign, which is called the index, and put it under a root sign. In other words, we replace the integer with a radical. Thus, we will end up with two radicals that need to be multiplied. We multiply the two numbers under the roots and place the product under a root sign.

Writing mixed radicals as entire radicals is useful in that in allows us to more easily to determine which radical in a set is largest. As long as the radicals have the same index, then they can be compared by comparing the radicands.

Also, I have learned to deal with a negative exponent. It means to divide by that number of factors instead of multiplying. So 4−3 is the same as 1/(43), and x−3 = 1/x3

 

new media 11 blog log 2

Things we should do during covid -19

For blog two, this time I have found an article that suits the situation right now and the new media lessons. Basically, this is a short and easy-understanding article. And the reason I chose it is that the content is really brought a positive and clear message about what we do during this pandemic.

First, the writer stated out that it is a fact that covid 19 has driven the whole world crazy, and it leads to many unexpected effects and worries. But it is normal that people feel anxiety and stress, daily routines and scheduled plans will be messed up.  The things we should do is trying to accept and to make changes such as limited our time spending on social media, as it may bring us negative and wrong information. We should also get access to new information from trusted sources and news. don’t believe everything from different internet sites, memes, try to seek help from a trustful person when encountering any difficulties. entertain ourselves more, such as reading a book you like, singing and dancing your favorite songs.

 

Anyway, I think we should stay connected go through these hard times together so that one day I believe we will be take off our masks together.

new media 11 challenge reflection

Making connections

During English class, we are given a challenge called the new media 11 challenge, we are given a partner randomly, with the groups of 2-3. Then, we are allowed to spread to the whole school to start our conversation. My partner was Jade, who was sitting at the corner of the classroom. For me, as an international student, I didn’t know anyone of the students in the class; everything has become so unfamiliar. I am stressed out and feeling scared. I find it nerve-racking to talk to strangers. But then I still move on and accepted the challenge. After I met her, we both agreed to head to the library, finding an empty and quiet room for us two.

At a later time, we started to introduce ourselves and I started to get to know more about my partner. The thing that surprised me is that I am not the only one who feels nervous and scared about this project.  But then Jade stated that she has the same feeling too. Before this project, I think that most Canadians are outgoing and sociable, which is the opposite of me.

In the conversation, I learn that she is realistic, a girl with a simple and clear mind. She is a self-aware person. Loyalty is the thing she values the most in a friendship. She thinks finding the passion for doing something is the most important in life as well as health and family. She wishes to fix the poverty problem in order to make the world a better place. Moreover, the person she admires is Cher, who is an American singer and actress and she wants to have a conversation with her. The best gift she has received is her necklace which her father gave her, she doesn’t receive a bad gift ever, as she thinks that people who do give gifts are in good intention.

Through this challenge, I have learned that although we are different in many different aspects, we still have something that is common and we can have the same opinions sometimes, this shows that human stills connect if they share their own thoughts and views, digging in each’s others story is important instead of just looking the surface with the ‘single story’. Besides, we should also take a step forward to approach different people but not staying quiet to make connections.

New media 11-blog log

Social media can be a weapon

Nowadays, people of different ages rely on technology, whenever we talk about technology. social media and networks are the topics that definitely remind me the most. The heading od the article   ”The Dark psychology of Social network” really drives me and so I am interested to go deeper to the article. Although social networks or app brings us many conveniences, such as Facebook, Instagram, Snapchat…etc. Thanks to these media, we can get connected to the word and others easily. However, various disadvantages also exist when committing to social networking. The author wrote this article to inform that human being’s conduct and behavior can be changed based on social media. Like for example, we would like to gossip or get interested in the private affairs of a celebrity. Social media can lead to human thinking ability declines when the crowd starting believing every comment or discussion. Moreover, because of the exists of social media optimism has faded and the list of known or misbelieve harms has grown such as online political discussions often among strangers are experienced as angrier and less civil than those in real life; networks of partisans co-create worldviews that can become more extreme; disinformation campaigns flourish; violent ideologies lure recruits. After reading the article, I have get to know how social media affect us and it can be destructive and toxic. Furthermore, it is dangerous as it’s a platform for us to expose our private thoughts and information to the public.

summartive assignment

One reason you should do empathy

In this course, English new media 11, we have discussed various topics about media and human connections. The topic which impresses me the most is the fish picture. The picture shows two young fish swimming in the same way, there is another old fish upon asked them how’s the water. But then the young fish just reply “what the heck is water”. After looking at the picture. Well, that really catches me. And I have done a bit of reflection based on it. In my opinion, I think the two young fish symbolizes teens and kids nowadays, they rely on technology so much. They just follow the trends on the internet the social norms. The technology already became their daily needs just like air. They are
focusing on social media and believing the truth saw on the internet instead of reality and the surroundings which are water. Technology and media can act as a tool which makes people’s relationship becoming indifferent, unconcern. While The old wise fish is representing the older generations and critical thinkers who are being aware of the surroundings and reality.

When an individual is in a group, the original severity of the crowd members is strengthened, and a viewpoint or attitude is strengthened from the original average level of the crowd to a dominant local phenomenon, which means they won’t
consider whether the thing is right or wrong before making a solution. Hitler is a very good example. The famous historic person from German who just took all the power and making people believing and supporting his idea, if not people will be sent jail or put to death As a result, it leads to Polarization and apathy among the crowd. most people just believe him blindly and take things that don’t exist as facts and have bad social effects.

Changes in the media environment of politics may also have had an important role in polarization, when a culture is polarized, the society will corrupt, many negative problems and outcomes such as the cold war or inequality will happen within the community. The relationships and connections between humans will be getting worse.

So in order to prevent Polarization, everyone should develop empathy, being a critical thinker, be able
to think from the other side’s position, experience other people’s emotions and thoughts in the process of interpersonal communication, understand the positions and feelings of others, and think and deal
with problems from the perspective of others. Its main manifestations include emotional self-control, listening ability, and expression of respect and other aspects related to emotional intelligence.

In fact, people can control their own thoughts. We can choose to look at the situation in different ways! The most important point is “empathy.” We can think, how do we think? and where should our thinking focus? You can choose to look at things in an empathetic way. Always remember! Try feeling instead of just seeing. If everyone takes a step forward to do so, we can definitely make the world more peaceful and beautiful!