Step-by-step explanation:
Pythagoras' theorem for the smallest one :
![c^2 = 4^2 + 6^2](https://tex.z-dn.net/?f=c%5E2%20%3D%204%5E2%20%2B%206%5E2)
![c^2 = 16 + 36](https://tex.z-dn.net/?f=c%5E2%20%3D%2016%20%2B%2036)
= 52
Pythagoras' theorem for the middle one :
=
+ ![a^{2}](https://tex.z-dn.net/?f=a%5E%7B2%7D)
Pythagoras' theorem for the biggest one :
![(4+a)^2 = c^2 + b^2](https://tex.z-dn.net/?f=%284%2Ba%29%5E2%20%3D%20c%5E2%20%2B%20b%5E2)
![16 + 8a + a^2 = 52 + b^2](https://tex.z-dn.net/?f=16%20%2B%208a%20%2B%20a%5E2%20%3D%2052%20%2B%20b%5E2)
Using the formula before (for
) it becomes :
![16 + 8a + a^2 = 52 + (6^2 + a^2)](https://tex.z-dn.net/?f=16%20%2B%208a%20%2B%20a%5E2%20%3D%2052%20%2B%20%286%5E2%20%2B%20a%5E2%29)
![16 + 8a + a^2 = 52 + 6^2 + a^2](https://tex.z-dn.net/?f=16%20%2B%208a%20%2B%20a%5E2%20%3D%2052%20%2B%206%5E2%20%2B%20a%5E2)
![16 + 8a = 52 + 6^2](https://tex.z-dn.net/?f=16%20%2B%208a%20%3D%2052%20%2B%206%5E2)
16 + 8a = 52 + 36
16+8a = 88
8a = 88-16
8a = 72
a = 9
Verifying :
![b^2 = 6^2 + a^2](https://tex.z-dn.net/?f=b%5E2%20%3D%206%5E2%20%2B%20a%5E2)
![b^2 = 36 + 81](https://tex.z-dn.net/?f=b%5E2%20%3D%2036%20%2B%2081)
![b^2 = 117](https://tex.z-dn.net/?f=b%5E2%20%3D%20117)
= 117
The biggest one :
![(4+a)^2 = c^2 + b^2](https://tex.z-dn.net/?f=%284%2Ba%29%5E2%20%3D%20c%5E2%20%2B%20b%5E2)
![(4+9)^2 = 52 + 117](https://tex.z-dn.net/?f=%284%2B9%29%5E2%20%3D%2052%20%2B%20117)
![13^2 = 169](https://tex.z-dn.net/?f=13%5E2%20%3D%20169)
True
The correct answer is 4> -3
Answer:
13
Step-by-step explanation:
substitute all the numbers in
6+3/6+3/6+6=13
Answer:
110%
Step-by-step explanation:
if each square is a whole, then when one is filled, it's 100% . 10% of the other square is filled so you just add the two.
Answer:
y = lnx / ln 7.
Step-by-step explanation:
x = 7^y
Take logarithms of both sides:
ln x = ln 7^y
ln x = y ln 7 ( because ln a^b = b ln a. One of the Laws of Logarithms).
y = lnx / ln 7.