<h2>
Hello!</h2>
The answer is:
The simplified form of the given expression is 7.
![49^{\frac{1}{2}}=\sqrt[2]{49^{1}}=\sqrt[2]{49}=7](https://tex.z-dn.net/?f=49%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D%5Csqrt%5B2%5D%7B49%5E%7B1%7D%7D%3D%5Csqrt%5B2%5D%7B49%7D%3D7)
<h2>Why?</h2>
To simplify the given expression, we must remember the following property of roots:
![a^{\frac{m}{n}}=\sqrt[n]{a^{m} }](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7Bm%7D%7Bn%7D%7D%3D%5Csqrt%5Bn%5D%7Ba%5E%7Bm%7D%20%7D)
We are given the expression:
![49^{\frac{1}{2}}](https://tex.z-dn.net/?f=49%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)
Which can be also written as:
![49^{\frac{1}{2}}=\sqrt[2]{49^{1}}=\sqrt[2]{49}](https://tex.z-dn.net/?f=49%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D%5Csqrt%5B2%5D%7B49%5E%7B1%7D%7D%3D%5Csqrt%5B2%5D%7B49%7D)
Then, simplifying we have:
![\sqrt[2]{49}=7](https://tex.z-dn.net/?f=%5Csqrt%5B2%5D%7B49%7D%3D7)
Hence, the simplified form of the given expression is 7.
Have a nice day!
12 green beads
60 red beads
30 yellow beads.
102 beads in all.
I hope this helped:)
Answer:
25 rounds
Step-by-step explanation:
Let
x -----> the number of rounds of golf
y ---> total charges to play
The linear equation in slope intercept form is equal to
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where
m is the slope or unit rate
b is the y-intercept or initial value
<em>Membership</em>
----> equation A
The slope is m=$35 per round
The y-intercept b=$500 (annual membership fee)
<em>Non-Membership</em>
----> equation B
The slope is m=$55 per round
The y-intercept b=$0
Equate equation A and equation B
![55x=35x+500](https://tex.z-dn.net/?f=55x%3D35x%2B500)
solve for x
![55x-35x=500](https://tex.z-dn.net/?f=55x-35x%3D500)
![20x=500](https://tex.z-dn.net/?f=20x%3D500)
![x=25\ rounds](https://tex.z-dn.net/?f=x%3D25%5C%20rounds)
For x=25 rounds the cost to be the same with and without a membership
5(20) + 4y = 216
100 + 4y = 216
4y = 216 - 100
4y = 116
y = 116/4
y = 29.....so they sold 29 four-dollar yogurts + 20 five-dollar yogurts....for a total of 49 yogurts sold <==