Answer: cost of 1 pot of ivy = $12
Cost of 1 rose bush =$ 10
Step-by-step explanation:
Step 1
Let rose bushes be represented as r
and pot of ivy be represented as p
such that Amy who spent 82 dollars on 7 rose bushes and 1 pot of ivy can be expressed as
7 r + p = 82----- eqn 1
Rob who spent 74 on 5 rose bushes and 2 pots of ivy can be expressed as
5r +2 p = 74----- eqn 2
Step 2
Solving
7 r + p = 82----- eqn 1
5r +2 p = 74----- eqn 2
By elimination method Multiply eqn 1 by 5 and eqn 2 by 7
35r+ 5p= 410--- eqn 3
35r+ 14p =518--- eqn 4
Subtracting eqn 4 from eqn 3
9p = 108
p = 108/9
p=12
p = pot of ivy = $12
therefore rose bush wll be ( from equation 1)
7r+ p= 82
7r=82-12
7r= 70 r= 70/7
r= rose bush =$ 10
-9 I believe this is correct
Exponent properties help us to simplify the powers of expressions. The quotient of the given expression ![\dfrac{6 - 3(\sqrt[3]{6})}{\sqrt[3]{9}}](https://tex.z-dn.net/?f=%5Cdfrac%7B6%20-%203%28%5Csqrt%5B3%5D%7B6%7D%29%7D%7B%5Csqrt%5B3%5D%7B9%7D%7D)
is (2∛3 - ∛18).
<h3>What are the basic exponent properties?</h3>
![{a^m} \cdot {a^n} = a^{(m+n)}\\\\\dfrac{a^m}{a^n} = a^{(m-n)}\\\\\sqrt[m]{a^n} = a^{\frac{n}{m}}\\\\(a^m)^n = a^{m\times n}\\\\(m\times n)^a = m^a\times n^a\\\\](https://tex.z-dn.net/?f=%7Ba%5Em%7D%20%5Ccdot%20%7Ba%5En%7D%20%3D%20a%5E%7B%28m%2Bn%29%7D%5C%5C%5C%5C%5Cdfrac%7Ba%5Em%7D%7Ba%5En%7D%20%3D%20a%5E%7B%28m-n%29%7D%5C%5C%5C%5C%5Csqrt%5Bm%5D%7Ba%5En%7D%20%3D%20a%5E%7B%5Cfrac%7Bn%7D%7Bm%7D%7D%5C%5C%5C%5C%28a%5Em%29%5En%20%3D%20a%5E%7Bm%5Ctimes%20n%7D%5C%5C%5C%5C%28m%5Ctimes%20n%29%5Ea%20%3D%20m%5Ea%5Ctimes%20n%5Ea%5C%5C%5C%5C)
Given to us
We will solve the problem using the basic exponential properties,
![\dfrac{6 - 3(\sqrt[3]{6})}{\sqrt[3]{9}}\\\\ = \dfrac{6}{\sqrt[3]{9}} - \dfrac{3(\sqrt[3]{6})}{\sqrt[3]{9}}\\\\ = (6\cdot 3^{-\frac{2}{3}}) - [3 \cdot (2 \cdot 3)^{-\frac{2}{3}}3^{-\frac{2}{3}}]\\\\= (2 \cdot 3 \cdot 3^{-\frac{2}{3}}) - [3 \cdot 2^{-\frac{2}{3}} \cdot 3^{-\frac{2}{3}}3^{-\frac{2}{3}}]\\\\](https://tex.z-dn.net/?f=%5Cdfrac%7B6%20-%203%28%5Csqrt%5B3%5D%7B6%7D%29%7D%7B%5Csqrt%5B3%5D%7B9%7D%7D%5C%5C%5C%5C%20%3D%20%5Cdfrac%7B6%7D%7B%5Csqrt%5B3%5D%7B9%7D%7D%20-%20%5Cdfrac%7B3%28%5Csqrt%5B3%5D%7B6%7D%29%7D%7B%5Csqrt%5B3%5D%7B9%7D%7D%5C%5C%5C%5C%20%3D%20%286%5Ccdot%203%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%29%20-%20%5B3%20%5Ccdot%20%282%20%5Ccdot%203%29%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D3%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%5D%5C%5C%5C%5C%3D%20%282%20%5Ccdot%203%20%5Ccdot%203%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%29%20-%20%5B3%20%5Ccdot%202%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%20%5Ccdot%203%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D3%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%5D%5C%5C%5C%5C)
![= [2 \cdot 3^{(1-\frac{2}{3})}] - [2^{\frac{1}{3}}\cdot 3^{(1+\frac{1}{3} - \frac{2}{3})}]\\\\= [2 \cdot 3^{(\frac{1}{3})}] - [2^{\frac{1}{3}}\cdot 3^{(\frac{2}{3})}]\\\\= 2\sqrt[3]{3} - \sqrt[3]{2}\sqrt[3]{9}\\\\=2\sqrt[3]{3} - \sqrt[3]{18}](https://tex.z-dn.net/?f=%3D%20%5B2%20%5Ccdot%203%5E%7B%281-%5Cfrac%7B2%7D%7B3%7D%29%7D%5D%20-%20%5B2%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ccdot%203%5E%7B%281%2B%5Cfrac%7B1%7D%7B3%7D%20-%20%5Cfrac%7B2%7D%7B3%7D%29%7D%5D%5C%5C%5C%5C%3D%20%20%5B2%20%5Ccdot%203%5E%7B%28%5Cfrac%7B1%7D%7B3%7D%29%7D%5D%20-%20%5B2%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ccdot%203%5E%7B%28%5Cfrac%7B2%7D%7B3%7D%29%7D%5D%5C%5C%5C%5C%3D%202%5Csqrt%5B3%5D%7B3%7D%20-%20%5Csqrt%5B3%5D%7B2%7D%5Csqrt%5B3%5D%7B9%7D%5C%5C%5C%5C%3D2%5Csqrt%5B3%5D%7B3%7D%20-%20%5Csqrt%5B3%5D%7B18%7D)
Hence, the quotient of the given expression is (2∛3 - ∛18).
Learn more about Exponents:
brainly.com/question/5497425
Is it 0.5? if so, the answer is 0.25%
if it is supposed to be just a 5 then the answer would be 2.5%
