Answer:
3.6 litres
Step-by-step explanation:
1 bottle = 450ml
8 bottles = 450 × 8
= 3600ml
1000ml = 1 litre
3600ml = 3.6 litres (3600÷1000)
Answer:
![\dfrac{1}{6561}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B6561%7D)
Step-by-step explanation:
Given the expression
, Using the laws of indices to simplify the expression. The following laws will be applicable;
![a^m*a^n = a^{m+n}\\(a^m)^n = a^{mn}\\](https://tex.z-dn.net/?f=a%5Em%2Aa%5En%20%3D%20a%5E%7Bm%2Bn%7D%5C%5C%28a%5Em%29%5En%20%3D%20a%5E%7Bmn%7D%5C%5C)
![a^{-m} = 1/a^m](https://tex.z-dn.net/?f=a%5E%7B-m%7D%20%3D%201%2Fa%5Em)
Given ![[(2^{-2})(3^{4})]^{-3} * [(2^{-3})(3^2)]^{2}](https://tex.z-dn.net/?f=%5B%282%5E%7B-2%7D%29%283%5E%7B4%7D%29%5D%5E%7B-3%7D%20%2A%20%5B%282%5E%7B-3%7D%29%283%5E2%29%5D%5E%7B2%7D)
open the parenthesis
![= (2^{-2})^{-3}(3^{4})^{-3}* (2^{-3})^2(3^2)^2\\\\= 2^{-2*-3}* 3^{4*-3} * 2^{-3*2} * 3^{2*2}\\\\= 2^6 * 3^{-12} * 2^{-6} * 3^4\\\\collecting \ like \ terms\\\\= 2^6 * 2^{-6} * 3^{-12} * 3^4\\\\= 2^{6-6} * 3^{-12+4}\\\\= 2^0 * 3^{-8}\\\\= 1 * \frac{1}{3^8}\\ \\= \frac{1}{6561}](https://tex.z-dn.net/?f=%3D%20%282%5E%7B-2%7D%29%5E%7B-3%7D%283%5E%7B4%7D%29%5E%7B-3%7D%2A%20%282%5E%7B-3%7D%29%5E2%283%5E2%29%5E2%5C%5C%5C%5C%3D%202%5E%7B-2%2A-3%7D%2A%203%5E%7B4%2A-3%7D%20%2A%202%5E%7B-3%2A2%7D%20%2A%203%5E%7B2%2A2%7D%5C%5C%5C%5C%3D%202%5E6%20%2A%203%5E%7B-12%7D%20%2A%202%5E%7B-6%7D%20%2A%203%5E4%5C%5C%5C%5Ccollecting%20%5C%20like%20%5C%20terms%5C%5C%5C%5C%3D%202%5E6%20%2A%202%5E%7B-6%7D%20%2A%203%5E%7B-12%7D%20%2A%203%5E4%5C%5C%5C%5C%3D%202%5E%7B6-6%7D%20%2A%203%5E%7B-12%2B4%7D%5C%5C%5C%5C%3D%202%5E0%20%2A%203%5E%7B-8%7D%5C%5C%5C%5C%3D%201%20%2A%20%5Cfrac%7B1%7D%7B3%5E8%7D%5C%5C%20%5C%5C%3D%20%5Cfrac%7B1%7D%7B6561%7D)
The numbers are "x" and "y"
Therefore, we can suggest this system of equations:
x+y=10 ⇒x=10-y
xy=-60
Solve this system of equations by substitution method.
(10-y)y=-60
10y-y²=-60
y²-10y-60=0
Solve this square equation:
y=[10⁺₋√(100+240)]/2=(10⁺₋2√85)/2=5⁺₋√85
We have two solutions:
y₁=5-√85 ⇒x₁=10-(5-√85)=5+√85
y₂=5+√85 ⇒x₂=10-(5+√85)=5-√85
Answer: the numbers are (5-√85) and (5+√85)
The answer is a , solve everything out and work it out you will see how i got it