41. Make it into two triangles. After splitting the shape into two equal parts, you need to divide 89 by two and divide 42 by two in order to come up with the angles of the triangle that you made. 89/2=44.5 and 42/2=21. After that just add both the angles, and subtract it from 180. When you add the angles you get 65.5 and when you subtract that from 180, you get the answer, which is 114.5.
42. Set both of the terms equal to each other. 1/2x+15=2x-15. Solve for x. subtract 15 from both sides, and then you have 1/2x=2x-30. Then subtract 2x from both sides. That gives you -3/2x=30. Then you divide both sides by -3/2, which gives you x=20.
43. This one is a square since all sides are congruent. All of the angles in a square must be 90 degrees, therefor you set 2x=90. This gives you x=45
45. Make 60+60+8x+8x=360. After that make solve for x. Combine like terms first. Do 60+60=120 and 8x+8x=16x. Now we have 120+16x=360. Subtract 120 from both sides. That gives you 16x=240, and then divide both sides by 16 and you get x=15.
46. Set one parallel side equal to the one it is parallel with to find x. We can start with 3x+12=18. First subtract 12 from both sides. You get 3x=6 and then divide both sides by 3 to get x=2. Plug x into both equations to see if the answer is correct.
47. Make two congruent triangles. After that, to find the angles of the triangles, divide 95 by 2and divide 35 by 2. Your new triangle has the angles 17.5 and 47.5. To find x, in other words, the missing angle, add the two together and subtract it from 180. By adding 47.5 and 17.5 you get 65. That means x is equal to 180-65 which equals 115.
49. Add all the sides and set them to 360. Do 3x+2x+44+86=360. Combine like terms and get 5x+130=360. Subtract 130 from 360 and get 5x=230. Then divide 5 from both side and get x=46. To find what the angles equal, just plug x into it. The one on the left is 138 and the one on the right is 92.
50. I am not sure what the terms are corresponding to. From what I am assuming, the answer would be x=29. This is from adding the two together and solving for x. You would do that if the terms were corresponding to angles that would add to be a total of 180. Don't take my word on this one. If you know what they are corresponding to, then please message me. I'd love to help you out (:
51. To find x, just use a^2+b^2=c^2. Basically square 2 and square 4 and add them together. By squaring them, you get 4+16=c^2. To solve you need to do 4+16=20, and then take the square root of 20, which is approximately 4.472
In most of these I was teaching you how to solve for x, if you need further help, please let me know.
For every function you need evaluate the function for every value in the domain D. And the collection of this values correspond to the range of the function.
Let G be a graph with n vertices. There are n possible degrees: 0,1,...,n-1.
Observe that a graph can not contain a vertice with degree n-1 and a vertice with degree 0 because if one of the vertices has degree n-1 means that this vertice is adjacent to all others vertices, then the other vertices has at least degree 1.
Then there are n vertices and n-1 possible degrees. By the pigeon principle there are two vertices that have the same degree.
