<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
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<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
P has a y intercept of 6 and a slope of 1 up for every two to the right, 1/2
y = (1/2) x + 6
Q has a y intercept of -3 and a slope of 4 down from every one to the right, -4.
y = -4x - 3
For the solution we equate the two ys,
(1/2)x + 6 = -4x - 3
x + 12 = -8x - 6
9x = -18
x = -2
y = (1/2) (-2) + 6 = 5
Solution: (x,y)=(-2, 5)
Answer: 42
Step-by-step explanation:
12+6=18 5+5=10
18+10=28 4+4=8
28+8= 36 3+3=6
36+6=42