1) The first thing I did was set up the problem which was 6y-2=5y+2. Next I subtracted-5y and added 2 on both sides. Y=10. Then i plugged in which became 6(10)-2. The answer is 58

2) The first thing I did was set up the problem which was 11x+8+8x+1=180. Then I combine like terms and it is 19x+9=180. Then subtract 9 on both sides and its going to be 19x=171. Then divide by 9 and then x =9. Plug 9 back in which will be 8(9)+1 and the answer is 73.

3) The first thing I did was set up the problem which was 2x+24=6x. Subtract-2x from both sides which is 24=4x then divide by 4. The answer is 6.

This week in class we learned about inscribed angles. An inscribed angle is the angle formed in the interior of a circle. Its to chords that share a common endpoint. The angle doesn’t change its vertex. There can be inscribed angles where one cord is a diameter. There can also be inscribed angles with the center of the circle as the interior and exterior. In conclusion, the common endpoints form the vertex of the inscribed angles.

This week in class I struggled with learning about arcs and chords. In the same or congruent circle the chords are congruent IFF they’re equal distance from the center. Two minor arcs are congruent IFF their responding chords are congruent. If a diameter of a circle is perpendicular to a chord then it bisects the chord and its arc. An arc is a part of a curve. A chord is a line joining two points on a curve. Two chords are congruent IFF their responding arcs are congruent.

1. For problem one the first thing I like to do is fill in all the angles. Then I do the first question which is mKL. Then for each question i just fill in the angle that the question is asking. The answer will be 23. The second question is mLON. I do the same thing and the answer is 203. The third question is mON=113. The forth question is mKNL= 337. The fifth question is mNL= 157.

2. For this problem we’re trying to find the length of PQS. The first thing i did was find what X and R equal. Then you plug in the numbers into the equation which will be l=128/360•2pie(9.5). The last thing i do is solve it. The answer will be 21.1793.

This week in class we learned about central angles, circumference, and diameters. I personally don’t understand this lesson well, but I have been studying. A diameter of a circle is a chord that passes through the center and has both ends of the circle made up of a collinear radi. If given a radius you can find the diameter by multiplying it by 2. Half of the diameter is the radius of the circle. The circumference is the boundary of the circle. You find the circumference by multiplying the diameter by pie which is 3.1415926535.

I enjoyed my winter break. I spent time with my family. I also got a car for christmas. However, I spent most of my time playing fortnite and shopping. I bought my family many gifts and they loved them. I also spent time with my boyfriend and his family. I had a good and well needed winter break.

1. The first question is a trig ratios problem. The first thing you do is draw and label the triangle because it isnt drawn for you. Next, you find the correct formula which is cos. You fill the numbers of your triangle into the formula. It will be cos(67)=18/x. After that you solve it. The answer will be x= 46.036.

2. This type of question is a pythagorean theorem problem. The first thing you do is label the triangle. After that you fill in the number into the formula which will be 17^2+13^2=c^2. Then, you multiply it by itself. Then, you add the numbers which will be 458=c^2. Then you do the square root. The answer is c=21.401

3. This type of question is a trig ratios problem. The first thing do is label the triangle. After that you find the correct formula which is tan. Then, you fill in the numbers into the formula which will be tan(15)=x/22. After that you solve for the variable. The answer will be x=5.896.

4. This type of question is a trig ratios problem also. The first step is to label the triangle. Next, you find the correct formula which is sin. Then, you put the numbers into the equation which is theta=18/25. Next, you solve it then do the inverse. The answer is theta=46.054.

5a. The first step is to find c using law of cosines. The first thing you do is label the triangle. The next thing is to find the correct formula which is c^2= a^2+b^2- 2abCosC. The next thing you do is fill in the formula with the correct numbers. After that you multiply what’s necessary which is 900+400-1200•.515. Then you do the square root then the answer will be c=26.115.

b. This step we’re finding A using law of sin. The first thing you do is label the triangle. The next thing is to fill in the correct numbers into the formula which is 26.115/sin(59)=a/sin(30). Then you do sin for both denominators which will be 26.115/.857=a/.5. Then you cross multiply which will be 13.058=.857a. Then you divide and the answer will be A= 15.237.

c. This step you take the answer you got for A and C then subtract it by 180 , which will be 180-59-15.237 and the answer will 105.763.

Law of cosines is used on non-right triangles when we can’t use law of sines. Its used when we dont have all of a letter. We use law of cosine for 2 types of triangles. The types of triangles are SAS and SSS. Both types of triangles have formulas. In order to solve it you fill in the formula.

Law of sins are only used in non-right triangles. Lower case letters are sines and Upper case letters are angles. You use the formula to solve for the sines and angles. For example, one formula is a/sin A = b/ sin B . You solve for the missing sine or angle.

I am thankful for many things. Im thankful for my family, weekends, and money. Im thankful for my family because they are my supporters and care givers. I enjoy weekends because its a time where i can relax and not have to worry about anything. Finally, i’m thankful for money because you need it to get anything you want.