The Angle Angle Side postulate (often abbreviated as AAS) states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.
The Side Angle Side postulate (often abbreviated as SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.
SSS stands for "side, side, side" and means that we have two triangles with all three sides equal. For example: is congruent to: (See Solving SSS Triangles to find out more) If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal. If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
CPCTC is an acronym for corresponding parts of congruent triangles are congruent. CPCTC is commonly used at or near the end of a proof which asks the student to show that two angles or two sides are congruent. ... Corresponding means they're in the same position in the 2 triangles.
Answer:
m6 = 117 degrees
m7 = 63 degrees
Step-by-step explanation:
I just asked my friend 0_0
Given:
The function for size of a square frame is

where, x is the side length of the picture.
The function for the price in dollars for the frame is

To find:
The single function for the price of a picture with an edge length of x.
Solution:
We know that, for a picture with an edge length of x.
Size of a square frame = f(x)
Price in dollars for the frame = p(x)
Single function for the price of a picture with an edge length of x is

![[\because f(x)=x+2]](https://tex.z-dn.net/?f=%5B%5Cbecause%20f%28x%29%3Dx%2B2%5D)
![[\because p(x)=3x]](https://tex.z-dn.net/?f=%5B%5Cbecause%20p%28x%29%3D3x%5D)
Let the name of this function is c(x). So,

Therefore, the required function is
.
Answer:
Step-by-step explanation:
A. (b - 10)(b + 10) = 180
-100 = 180
= 280
b = 
b = 2
Your A is correct.
B. 2
- 10 = c
c = 6.733200531 = 6.73 Try rounding to 3 significant figures.
C. 2
+ 10 = d
d = 26.73320053 = 26.7
You are correct in all 3 answers. Perhaps you should try rounding to 3 significant figures for your c and d values.
I hope this helps!! ^-^
You could use perturbation method to calculate this sum. Let's start from:

On the other hand, we have:

So from (1) and (2) we have:

Now, let's try to calculate sum

, but this time we use perturbation method.

but:
![S_{n+1}=\sum\limits_{k=0}^{n+1}k\cdot k!=0\cdot0!+\sum\limits_{k=1}^{n+1}k\cdot k!=0+\sum\limits_{k=0}^{n}(k+1)(k+1)!=\\\\\\= \sum\limits_{k=0}^{n}(k+1)(k+1)k!=\sum\limits_{k=0}^{n}(k^2+2k+1)k!=\\\\\\= \sum\limits_{k=0}^{n}\left[(k^2+1)k!+2k\cdot k!\right]=\sum\limits_{k=0}^{n}(k^2+1)k!+\sum\limits_{k=0}^n2k\cdot k!=\\\\\\=\sum\limits_{k=0}^{n}(k^2+1)k!+2\sum\limits_{k=0}^nk\cdot k!=\sum\limits_{k=0}^{n}(k^2+1)k!+2S_n\\\\\\ \boxed{S_{n+1}=\sum\limits_{k=0}^{n}(k^2+1)k!+2S_n}](https://tex.z-dn.net/?f=S_%7Bn%2B1%7D%3D%5Csum%5Climits_%7Bk%3D0%7D%5E%7Bn%2B1%7Dk%5Ccdot%20k%21%3D0%5Ccdot0%21%2B%5Csum%5Climits_%7Bk%3D1%7D%5E%7Bn%2B1%7Dk%5Ccdot%20k%21%3D0%2B%5Csum%5Climits_%7Bk%3D0%7D%5E%7Bn%7D%28k%2B1%29%28k%2B1%29%21%3D%5C%5C%5C%5C%5C%5C%3D%0A%5Csum%5Climits_%7Bk%3D0%7D%5E%7Bn%7D%28k%2B1%29%28k%2B1%29k%21%3D%5Csum%5Climits_%7Bk%3D0%7D%5E%7Bn%7D%28k%5E2%2B2k%2B1%29k%21%3D%5C%5C%5C%5C%5C%5C%3D%0A%5Csum%5Climits_%7Bk%3D0%7D%5E%7Bn%7D%5Cleft%5B%28k%5E2%2B1%29k%21%2B2k%5Ccdot%20k%21%5Cright%5D%3D%5Csum%5Climits_%7Bk%3D0%7D%5E%7Bn%7D%28k%5E2%2B1%29k%21%2B%5Csum%5Climits_%7Bk%3D0%7D%5En2k%5Ccdot%20k%21%3D%5C%5C%5C%5C%5C%5C%3D%5Csum%5Climits_%7Bk%3D0%7D%5E%7Bn%7D%28k%5E2%2B1%29k%21%2B2%5Csum%5Climits_%7Bk%3D0%7D%5Enk%5Ccdot%20k%21%3D%5Csum%5Climits_%7Bk%3D0%7D%5E%7Bn%7D%28k%5E2%2B1%29k%21%2B2S_n%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BS_%7Bn%2B1%7D%3D%5Csum%5Climits_%7Bk%3D0%7D%5E%7Bn%7D%28k%5E2%2B1%29k%21%2B2S_n%7D)
When we join both equation there will be:
![\begin{cases}S_{n+1}=S_n+(n+1)(n+1)!\\\\S_{n+1}=\sum\limits_{k=0}^{n}(k^2+1)k!+2S_n\end{cases}\\\\\\ S_n+(n+1)(n+1)!=\sum\limits_{k=0}^{n}(k^2+1)k!+2S_n\\\\\\\\ \sum\limits_{k=0}^{n}(k^2+1)k!=S_n-2S_n+(n+1)(n+1)!=(n+1)(n+1)!-S_n=\\\\\\= (n+1)(n+1)!-\sum\limits_{k=0}^nk\cdot k!\stackrel{(\star)}{=}(n+1)(n+1)!-[(n+1)!-1]=\\\\\\=(n+1)(n+1)!-(n+1)!+1=(n+1)!\cdot[n+1-1]+1=\\\\\\= n(n+1)!+1](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7DS_%7Bn%2B1%7D%3DS_n%2B%28n%2B1%29%28n%2B1%29%21%5C%5C%5C%5CS_%7Bn%2B1%7D%3D%5Csum%5Climits_%7Bk%3D0%7D%5E%7Bn%7D%28k%5E2%2B1%29k%21%2B2S_n%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5C%0AS_n%2B%28n%2B1%29%28n%2B1%29%21%3D%5Csum%5Climits_%7Bk%3D0%7D%5E%7Bn%7D%28k%5E2%2B1%29k%21%2B2S_n%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Csum%5Climits_%7Bk%3D0%7D%5E%7Bn%7D%28k%5E2%2B1%29k%21%3DS_n-2S_n%2B%28n%2B1%29%28n%2B1%29%21%3D%28n%2B1%29%28n%2B1%29%21-S_n%3D%5C%5C%5C%5C%5C%5C%3D%0A%28n%2B1%29%28n%2B1%29%21-%5Csum%5Climits_%7Bk%3D0%7D%5Enk%5Ccdot%20k%21%5Cstackrel%7B%28%5Cstar%29%7D%7B%3D%7D%28n%2B1%29%28n%2B1%29%21-%5B%28n%2B1%29%21-1%5D%3D%5C%5C%5C%5C%5C%5C%3D%28n%2B1%29%28n%2B1%29%21-%28n%2B1%29%21%2B1%3D%28n%2B1%29%21%5Ccdot%5Bn%2B1-1%5D%2B1%3D%5C%5C%5C%5C%5C%5C%3D%0An%28n%2B1%29%21%2B1)
So the answer is:

Sorry for my bad english, but i hope it won't be a big problem :)