To find the measure of the interior angles, we know that the sum of all the angles is 900 degrees (from above)... And there are seven angles... So, the measure of the interior angle of a regular heptagon is about 128.57 degrees.
Answer:
![k= \frac{-34}{3}](https://tex.z-dn.net/?f=k%3D%20%5Cfrac%7B-34%7D%7B3%7D)
Step-by-step explanation:
<u>Step 1 :</u>-
<u>Perpendicular condition :-</u>
<u>Step 1:-</u>
Two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.
![m_{2} = \frac{-1}{m_{1} }](https://tex.z-dn.net/?f=m_%7B2%7D%20%3D%20%5Cfrac%7B-1%7D%7Bm_%7B1%7D%20%7D)
![m_{1} m_{2} = -1](https://tex.z-dn.net/?f=m_%7B1%7D%20m_%7B2%7D%20%3D%20-1)
<u>Step 2:-</u>
The given points are (-8,k) and (-4,-8)
![m_{1} = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }](https://tex.z-dn.net/?f=m_%7B1%7D%20%3D%20%5Cfrac%7By_%7B2%7D-y_%7B1%7D%20%20%7D%7Bx_%7B2%7D-x_%7B1%7D%20%20%7D)
finding slope of the first line is ![m_{1}](https://tex.z-dn.net/?f=m_%7B1%7D)
using formula ![m_{1} = \frac{-8-k}{-4+8}](https://tex.z-dn.net/?f=m_%7B1%7D%20%3D%20%5Cfrac%7B-8-k%7D%7B-4%2B8%7D)
= ![\frac{-8-k}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B-8-k%7D%7B4%7D)
finding slope of the second line is ![m_{2}](https://tex.z-dn.net/?f=m_%7B2%7D)
using formula ![m_{2} = \frac{--5+11}{5-10}](https://tex.z-dn.net/?f=m_%7B2%7D%20%3D%20%5Cfrac%7B--5%2B11%7D%7B5-10%7D)
= ![\frac{6}{-5}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B-5%7D)
<u>Step 3:</u>-
using perpendicular condition
The two lines are perpendicular and their slopes are
![m_{1} m_{2} = -1](https://tex.z-dn.net/?f=m_%7B1%7D%20m_%7B2%7D%20%3D%20-1)
![(\frac{-k-8}{4} )(\frac{-6}{5} )= -1](https://tex.z-dn.net/?f=%28%5Cfrac%7B-k-8%7D%7B4%7D%20%29%28%5Cfrac%7B-6%7D%7B5%7D%20%29%3D%20-1)
simplification,we get solution is
![\frac{6(k+8)}{20} =-1](https://tex.z-dn.net/?f=%5Cfrac%7B6%28k%2B8%29%7D%7B20%7D%20%3D-1)
![6 k+48 =-20](https://tex.z-dn.net/?f=6%20k%2B48%20%3D-20)
![6 k = -20 -48](https://tex.z-dn.net/?f=6%20k%20%3D%20-20%20-48)
![6 k = -68](https://tex.z-dn.net/?f=6%20k%20%3D%20-68)
![\frac{-68}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B-68%7D%7B6%7D)
![k= \frac{-34}{3}](https://tex.z-dn.net/?f=k%3D%20%5Cfrac%7B-34%7D%7B3%7D)
<u>Final answer is </u>
![k= \frac{-34}{3}](https://tex.z-dn.net/?f=k%3D%20%5Cfrac%7B-34%7D%7B3%7D)
Answer: 1260 books
Step-by-step explanation:
2/5=0.4
19000x0.4=7600
12500x0.4=5000
7600+5000=12600
1/10=0.1
12600x0.1 = 1260
Answer:
Thx
Step-by-step explanation:
so its free points right?