We did a lot of practice on scale factoring and it can be very important to most of the problems we had to work with. Scale factoring is what you use to enlarge or decrease the measurements of the rectangles, or whatever you are working with. Scale factoring is used to show the way it is stretched.
- with this example I have the sides written as 2 and 4.
- 2 x 2= 4 and 4 x2 =8
- When using a scale factor of 2 you are stretching the sides. Therefor it would now become 4 and 8.
- This example using bigger numbers of 4, 8, 9. With the scale factor of 3.
- You do the same thing and make it three times bigger. 4 x 3 =12, 8 x 3= 24, and 9 x 3= 27. Therefor, I now have sides of 12, 24 and 27.
This blog post I chose to focus on finding angles with intersecting lines when it adds to 360 degrees. As well as understanding the different terms when choosing your reasonings.
complementary- Angles that add to 90 degrees
supplementary- Angles that add to 180 degrees
Vertical Opposite- an equal opposite
- The first step is I like to evaluate if It is a triangle and it adds to 360 degrees, or if it it goes all the way around and adds to 360 degrees. For this specific equation I have 104 degrees already written in for me.
2. The next step I like to take is to see how I can make a total of 360 degrees within my equation. I know that 104 + 104 = 208 which solves 2 of the angles.
3. To find the next two angels, I use the equation 360-208=152. Now that I have 152 I divide that by 2 to find the two angles that are equal. 152 divided by 2 = 76. therefor 76 is each angle.
To double check my work I use the long format to show my equation to check my answer:
104 + 104 + 76 +76 = 360
4. Now I have all my angles with all my work shown, I know can decide how to classify them with a reasoning:
For angle 5: Vertically opposite: This one I classified as vertically opposite because we are given the angle of 104 degrees on one side, and for this diagram both ends are equal. therefor, it is the same. So because it is straight across (opposites) it is vertically opp.
For angle 6: supplementary: this one I classify it as supplementary because the angle adds up to 360 degrees.
For angle 7: vertically opposite: this one I classified as vertically opposite as well, because it is right across vertically from angle 6 which is 76 degrees as well.
This week we learned mainly about how solving for a triangle and finding the missing angle. I found this important because it is the base line to all of the questions in this unit and understanding how to solve these are super important.
Things I ask myself before doing a question:
- Is there a 90 degree angle?
- Is there a 180 degree line?
- Can I solve another side without calculations beforehand?
- Starting with a very simple example: we have 65 degrees in one corner and 70 in another corner.
2. First I add together the 65 and the 70. where I get 65+70=135
- knowing I have 135, I now can figure out what to add in order to get 180.
- I like to subtract the sum of the two angles to figure out what the missing side is.
3. Therefor I would have 180-135 which is 45. So the angle would be equal to 45.
to check my work: 70+65+45+180
- This next example, I have this angle to solve. Starting off, I notice that it is a right angle which means that inner corner is 90 degrees.
2. now that we know it has to be equal to 90 degrees, we fill in the blanks.
3. So I have 16 degrees. 16+____=90?
4. You could do a few methods to find your answer, I like to use the angle given to find the missing angle. For this equation I did 90-16=74. Therefor, the missing angle is 74 degrees.
During this week I found some skills a little difficult, and wanted some extra practice on a few skills.
Some key points to remember:
general form: Y intercept/ Y= ax2 + bx +c = 0
Vertex: Vertex Point/ Y=a(x-b)2 +c
factored: X intercept y= a (x-b) (x-b)
For this example, I want to focus on general form quadratic equations, and converting these equations.
The function I chose to show is y=(x+3)2 – 9 which we put into general form which is y=ax2+bx+c.
I like to write out both equations again so I can cleary see them so I do not mix up a number or write it incorrectly.
You then re-write the equation in a longer form. So we square what is in the brackets so we can see it clearly.
Now I multiply where the arrows indicate, and write it out fully. Therefor, now I have 4 terms and the constant.
I now have to put the like terms together, so I take x2 with x2 which gives me 2×2. Same thing with 3x and 3x, therefor that gives me 6x.
Now my equation is in general form, and has all of the terms included.
Another step within quadratics that I found important was being able to identify the pattern and what direction you graph in.
For this example, i can already see that it is a negative so I know it will be a downwards angle instead of upwards. I can also tell it would start at zero on the graph because it has no vertex point within the function. These are a few ways I can identify and start to spot before doing any actual calculations.
For this week I found many things important while learning our lesson on quadratics. I found being able to solve the equation, put it into a table of values is extremely important because you need to be able to complete these steps in order to graph it. I found a few methods in solving for Y in the table of values but this way was the easiest for me.
Important Key things to remember:
- I found is very important to remember your negatives and positives because if you get the wrong number you cannot properly graph them. Watching for when you have two negatives, that creates a positive is very critical and sometimes hard to remember.
- When writing down your work, make sure you have it written out to show your work so you don’t get confused or miss a step.
Starting off I found an equation that I could use to solve and place into the table. I used the equation: Y=x2-x-6.
- First step I like to do is re-write the equation so I have it laid out in-front of me. Next you input all the numbers. For this equation I input -3 into the X slot. Therefor my equation would have no “X’s” involved and would be replaced with numbers.
2. Next, you re-write the equation with the new inputted numbers. Which for the first one would be -3^2+3-6. Which you would continue to solve/simplify in order to find Y.
3. next you solve the equation. You take-3 and times it to the power of 2. Which means -3 times -3 which would create positive 9 because a negative and a negative make a positive. Then moving to the next slot is now +3 which is positive as well, because a negative and a negative is a positive. Lastly, you keep the -6 on the end. This equation is now 9+3-6.
which is very easy to solve because 9+3=12 AND 12-6 =6. Therefor it =6.
4. Now that we have solved the equation and we know that the first plot point is 6 and we can then input it into our table.
Now you can repeat the same process until you have found Y for every X slot. Until you have filled your table up so you can then graph them.
This is another example on how you input the numbers: using the next X number which was -2.
These examples I found most crucial and important to learn because these steps are what guide you into being able to plot your points on a graph. If you were to continue to the next section to plot points you would simply take your X coordinate and your Y coordinate and match it up. So the point would sit on X’s Number and Y’s number where they intertwine.
One of the most important things we learned this week was solving an equation. I think this was one of the most important because it ties everything in this unit together and you have to start with solving an equation before anything else. I chose to talk about linear equations and the process of solving one.
- A few things I try to remember while solving is to make sure I use the correct steps in order. In this specific case brackets would come first.
- making sure you use negatives in the correct spots, and when a negative is used with another negative it becomes a positive.
- Flipping the signs when dealing with negative numbers can also be a factor.
- making sure you show your work to help you keep track and section off your calculations as you go.
Process for an example of an equation: First I chose the equation and looked into the steps I need to take because this equation makes it easier to understand the basic concept and steps for a more challenging equation.
- With this example with this equation they have brackets therefor I would do that first. In this equation you take the number outside the bracket and multiply the numbers in the brackets going from left to right.
2. After I multiplied the numbers I have now have a smaller equation without the brackets. Now I need to isolate the Y and create an equation. For this specific equation I moved the 5y to the left, and moved the 6 to the right side. Therefor my equation became 3y-5y=-30-6.
3. Next I simplify that equation, therefor it became 2y=-36. I first did 5y-3y which is 2y, and then -30 – 6 is -36. which this now means I can now divide by 2.
4. watching my negative numbers and dividing both sides by -2, I have my final answer below.
I found this important because it is one of the main things we learned. After some practice I found this much easier to do and understand.