We are given with RM = SN, TM = TN and we are to prove that RN = SM. The steps that are followed for this proof are as follow:
1. RM = SN , TM = TN Given
2. ∠T = ∠T Reflexive
3. RM + TM = SN + TN Addition Property of Equality
4. RM + TM = RT, SN + TN = ST Betweeness
5. RT = ST Substitution
6. Triangle RTN congruent to Triangle STM SAS
7. RN = SM CPCTE
The slope is -4x and a he y intercept is 1/2.
A coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression I think it's A In algebra a term is either a single number or variable or numbers and variables multiplied together.Terms are separated by +or - signs hope this helps
Answer:
Step-by-step explanation:
Given that ||v|| = 2 and ||w|| = 3, and the angle between v and w is 120 degrees
We know by definition of dot product and properties that
where t is the angle between them
Using this we find
(a) v·w =![2(3) cos 120\\=-3](https://tex.z-dn.net/?f=2%283%29%20cos%20120%5C%5C%3D-3)
(b) ∥2v+w∥
![(2v+w).(2v+w) = 4 v.v +4 w.v +w.w= 4(2)^2+4(-3)+9 =13](https://tex.z-dn.net/?f=%282v%2Bw%29.%282v%2Bw%29%20%3D%204%20v.v%20%2B4%20w.v%20%2Bw.w%3D%204%282%29%5E2%2B4%28-3%29%2B9%20%3D13)
![||2v+w||^2 =13\\||2v+w||=\sqrt{13}](https://tex.z-dn.net/?f=%7C%7C2v%2Bw%7C%7C%5E2%20%3D13%5C%5C%7C%7C2v%2Bw%7C%7C%3D%5Csqrt%7B13%7D)
(c) ∥2v−3w∥
![(2v-3w).(2v-3w) = 4 v.v -12 w.v +9w.w= 4(2)^2-12(-3)+9(9) =133](https://tex.z-dn.net/?f=%282v-3w%29.%282v-3w%29%20%3D%204%20v.v%20-12%20w.v%20%2B9w.w%3D%204%282%29%5E2-12%28-3%29%2B9%289%29%20%3D133)
![||2v-3w||^2 =133\\||2v-3w||=\sqrt{133}](https://tex.z-dn.net/?f=%7C%7C2v-3w%7C%7C%5E2%20%3D133%5C%5C%7C%7C2v-3w%7C%7C%3D%5Csqrt%7B133%7D)