Answer:
23ft approx
Step-by-step explanation:
Given data
Distance from tree= 10ft
Length of ladder= 25ft
We can find the height of the tree by applying the Pythagoras theorem
z^2= x^2+y^2
z= The height of the ladder
x= The distance from the tree
y= The height of the tree
25^2= 10^2+ y^2
625=100+y^2
625-100=y^2
525=y^2
y= √525
y= 22.91
Hence the height of the tree is 23ft approx
Answer:
Equations: ![x+y=80\,,\,2x+4y=216\,\,](https://tex.z-dn.net/?f=x%2By%3D80%5C%2C%2C%5C%2C2x%2B4y%3D216%5C%2C%5C%2C)
number of chickens = 52
number of goats = 28
Step-by-step explanation:
Given: A small ranch has chickens and goats
Total number of heads = 80
Total number of legs = 216
To find: number of chickens and goats
To draw: the graph
Solution:
Let x denotes number of chickens and y denotes number of goats.
According to the question,
![x+y=80\,\,(i)\\2x+4y=216\,\,(ii)](https://tex.z-dn.net/?f=x%2By%3D80%5C%2C%5C%2C%28i%29%5C%5C2x%2B4y%3D216%5C%2C%5C%2C%28ii%29)
From (i), put
in (ii)
![2(80-y)+4y=216\\160-2y+4y=216\\2y=216-180\\2y=56\\y=\frac{56}{2}=28](https://tex.z-dn.net/?f=2%2880-y%29%2B4y%3D216%5C%5C160-2y%2B4y%3D216%5C%5C2y%3D216-180%5C%5C2y%3D56%5C%5Cy%3D%5Cfrac%7B56%7D%7B2%7D%3D28)
Put
in equation (i)
![x+28=80\\x=80-28=52](https://tex.z-dn.net/?f=x%2B28%3D80%5C%5Cx%3D80-28%3D52)
So,
number of chickens = 52
number of goats = 28