Answer:
![4 \sqrt{5}](https://tex.z-dn.net/?f=4%20%5Csqrt%7B5%7D)
Step-by-step explanation:
![\sqrt{80}](https://tex.z-dn.net/?f=%5Csqrt%7B80%7D)
80 can be written as a product of 16 and 5.
![\sqrt{16 \times 5}](https://tex.z-dn.net/?f=%5Csqrt%7B16%20%5Ctimes%205%7D)
Distribute the square root to both terms.
![\sqrt{16} \times \sqrt{5}](https://tex.z-dn.net/?f=%5Csqrt%7B16%7D%20%5Ctimes%20%5Csqrt%7B5%7D)
16 is a perfect square 4×4.
![4 \times \sqrt{5}](https://tex.z-dn.net/?f=4%20%5Ctimes%20%5Csqrt%7B5%7D)
Maybe 28kms in 1 hour
Or 2,8kms because 7/10 is 0,7km
Answer:
x = 1
y = 4
Step-by-step explanation:
9x + 5y = 29 eqn 1
3x + y = 7 eqn 2
Using the method of substitution,
"substituting y"
multiplying through eqn 2 by -5
-15x - 5y = -35 eqn 2
9x + 5y =29 eqn 1
adding eqn 1 and eqn 2
-6x = -6
x = 1
3x + y = 7
3 (1) + y = 7
3 + y = 7
y = 7 - 3
y = 4
Answer:
10.4
Step-by-step explanation:
If you add all of these up and divide by 5 you get 10.4 which is the average value.
Answer:
The solution is:
Part A.
which is sqrt(5)^7k/3[/tex]
Part B. k = 18/7
Step-by-step explanation:
Part A.
To solve this part, we're going two use THREE important properties of exponents:
1. ![(x^{n})^{m} = x^{nm}](https://tex.z-dn.net/?f=%28x%5E%7Bn%7D%29%5E%7Bm%7D%20%3D%20x%5E%7Bnm%7D)
2. ![\frac{x^{n}}{x^{m}} = x^{n-m}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7Bn%7D%7D%7Bx%5E%7Bm%7D%7D%20%3D%20x%5E%7Bn-m%7D)
3. ![\sqrt[n]{x^{m}} = x^{\frac{m}{n} }](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%5E%7Bm%7D%7D%20%3D%20x%5E%7B%5Cfrac%7Bm%7D%7Bn%7D%20%7D)
Let's work the numerator using the properties 1, 2 and 3:
![(\sqrt{5}^{3} )^{\frac{k}{9} } } = (\sqrt{5}^{3\frac{k}{9}}) = (\sqrt{5}^{\frac{k}{3}})](https://tex.z-dn.net/?f=%28%5Csqrt%7B5%7D%5E%7B3%7D%20%29%5E%7B%5Cfrac%7Bk%7D%7B9%7D%20%7D%20%7D%20%20%3D%20%28%5Csqrt%7B5%7D%5E%7B3%5Cfrac%7Bk%7D%7B9%7D%7D%29%20%3D%20%28%5Csqrt%7B5%7D%5E%7B%5Cfrac%7Bk%7D%7B3%7D%7D%29)
Let's work the denominator using the properties 1, 2 and 3:
![(\sqrt{5}^{6} )^{-\frac{k}{3} } } = (\sqrt{5}^{6\frac{k}{3}}) = (\sqrt{5}^(2k))](https://tex.z-dn.net/?f=%28%5Csqrt%7B5%7D%5E%7B6%7D%20%29%5E%7B-%5Cfrac%7Bk%7D%7B3%7D%20%7D%20%7D%20%20%3D%20%28%5Csqrt%7B5%7D%5E%7B6%5Cfrac%7Bk%7D%7B3%7D%7D%29%20%3D%20%28%5Csqrt%7B5%7D%5E%282k%29%29)
Now dividing the numerator by the denominator:
![\sqrt{5}^{\frac{k}{3}-(-2k)})=\sqrt{5}^{\frac{7k}{3}})](https://tex.z-dn.net/?f=%5Csqrt%7B5%7D%5E%7B%5Cfrac%7Bk%7D%7B3%7D-%28-2k%29%7D%29%3D%5Csqrt%7B5%7D%5E%7B%5Cfrac%7B7k%7D%7B3%7D%7D%29)
Part B
if ![5^{\frac{3}{2} } 5^{\frac{3}{2}} = \sqrt{5}^{\frac{7k}{3}})](https://tex.z-dn.net/?f=5%5E%7B%5Cfrac%7B3%7D%7B2%7D%20%7D%205%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%20%3D%20%5Csqrt%7B5%7D%5E%7B%5Cfrac%7B7k%7D%7B3%7D%7D%29)
Then:
![5^{3} = 5^{\frac{7k}{6}})](https://tex.z-dn.net/?f=5%5E%7B3%7D%20%3D%205%5E%7B%5Cfrac%7B7k%7D%7B6%7D%7D%29)
So ![\frac{7k}{6}} = 3](https://tex.z-dn.net/?f=%5Cfrac%7B7k%7D%7B6%7D%7D%20%3D%203)
Solving for k, we have:
k = 18/7