Answer:
∠ EAB = 85°
Step-by-step explanation:
∠ EBC and ∠ BCD are same- side interior angles and sum to 180° , so
∠ BCD = 180° - ∠ EBC = 180° - 148° = 32°
the sum of the 3 angles in Δ ADC = 180° , that is
∠ EDC + ∠ BCD + ∠ EAB = 180°
63° + 32° + ∠ EAB = 180°
95° + ∠ EAB = 180° ( subtract 95° from both sides )
∠ EAB = 85°
12(x-12)=18
x-12=18/12
x-12=3/2
x=3/2+12
x=3/2+24/2
x=27/2
64-12= 52
So, she ate 52 since I subtracted what she had eaten (12) from how many she started (64)
So the answer would be 52
Don’t get mad at me if I’m wrong
:)
Sum of the First n Terms of a Geometric Sequence
Given a geometric sequence (or series) with a first-term a1 and common ratio r, the sum of the first n terms is given by:
![S_n=a_1\cdot\frac{1-r^n}{1-r}](https://tex.z-dn.net/?f=S_n%3Da_1%5Ccdot%5Cfrac%7B1-r%5En%7D%7B1-r%7D)
We are given the series:
![120-80+\frac{160}{3}-\frac{320}{9}+\cdots](https://tex.z-dn.net/?f=120-80%2B%5Cfrac%7B160%7D%7B3%7D-%5Cfrac%7B320%7D%7B9%7D%2B%5Ccdots)
Before calculating the required sum, we need to find the common ratio. It's defined as the division of two consecutive terms. For example, using the first two terms:
![\begin{gathered} r=-\frac{80}{120} \\ Simplify\colon \\ r=-\frac{2}{3} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20r%3D-%5Cfrac%7B80%7D%7B120%7D%20%5C%5C%20Simplify%5Ccolon%20%5C%5C%20r%3D-%5Cfrac%7B2%7D%7B3%7D%20%5Cend%7Bgathered%7D)
The first term is a1 =120. Now apply the formula:
![S_8=120\cdot\frac{1-(-\frac{2}{3})^8}{1+\frac{2}{3}}](https://tex.z-dn.net/?f=S_8%3D120%5Ccdot%5Cfrac%7B1-%28-%5Cfrac%7B2%7D%7B3%7D%29%5E8%7D%7B1%2B%5Cfrac%7B2%7D%7B3%7D%7D)
Operating:
![\begin{gathered} S_8=120\cdot\frac{1-\frac{2^8}{3^8}}{\frac{5}{3}} \\ S_8=120\cdot\frac{1-\frac{256}{6561}}{\frac{5}{3}} \\ S_8=120\cdot\frac{\frac{6561-256}{6561}}{\frac{5}{3}} \\ S_8=120\cdot\frac{\frac{6305}{6561}}{\frac{5}{3}} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20S_8%3D120%5Ccdot%5Cfrac%7B1-%5Cfrac%7B2%5E8%7D%7B3%5E8%7D%7D%7B%5Cfrac%7B5%7D%7B3%7D%7D%20%5C%5C%20S_8%3D120%5Ccdot%5Cfrac%7B1-%5Cfrac%7B256%7D%7B6561%7D%7D%7B%5Cfrac%7B5%7D%7B3%7D%7D%20%5C%5C%20S_8%3D120%5Ccdot%5Cfrac%7B%5Cfrac%7B6561-256%7D%7B6561%7D%7D%7B%5Cfrac%7B5%7D%7B3%7D%7D%20%5C%5C%20S_8%3D120%5Ccdot%5Cfrac%7B%5Cfrac%7B6305%7D%7B6561%7D%7D%7B%5Cfrac%7B5%7D%7B3%7D%7D%20%5Cend%7Bgathered%7D)
Calculating: