<u>The concept:</u>
We are given the equation:
![5^{x(x-1)} = 1](https://tex.z-dn.net/?f=5%5E%7Bx%28x-1%29%7D%20%3D%201)
Which can be simplified as:
![5^{x^{2} - x} = 1^{1}](https://tex.z-dn.net/?f=5%5E%7Bx%5E%7B2%7D%20-%20x%7D%20%3D%201%5E%7B1%7D)
Since any number to the power '0' is 1
x² - x must be equal to 0 for the given equation to be true
<u></u>
<u>Solving for x:</u>
x² - x = 0
x(x-1) = 0
now, we can divide both sides by either x OR x-1
So we will see what we get for either choice:
x = 0/(x-1) x-1 = 0/x
x = 0 x = 1
Hence, the value of x is either 0 or 1
Answer:
C
Step-by-step explanation:
Key in the expression is "s" that represents students going to the trip
The first part shows what the adventure park is going to charge, a group day charge of $300 and $30 more for the students taking the ropes course
300+30*s
The second being the amount the class can get, $500 the have in the account and $25 per student in tickets they have to sell
500+25s
The result of this subtraction is the money they need to raise to complete
C: The expression shows how much money the freshman class may need to raise in order to afford the event
Answer:
f(x) = ![x = \frac{y^{2} - 1}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7By%5E%7B2%7D%20-%201%7D%7B2%7D)
g(x) = 1
Step-by-step explanation:
y = (2x + 1)^1/2
![y^{2} = 2x + 1](https://tex.z-dn.net/?f=y%5E%7B2%7D%20%3D%202x%20%2B%201)
![y^{2} - 1 = 2x](https://tex.z-dn.net/?f=y%5E%7B2%7D%20-%201%20%3D%202x)
![\frac{y^{2} - 1}{2} = x](https://tex.z-dn.net/?f=%5Cfrac%7By%5E%7B2%7D%20-%201%7D%7B2%7D%20%3D%20x)
y = x - 1
y + 1 = x
Answer:
264
Step-by-step explanation: