Exponential form: F(x)= 3/125^x+1
Original voltage: 3/125 of a volt
Answer:
![x=0.75 \pm 2.47067i](https://tex.z-dn.net/?f=x%3D0.75%20%5Cpm%202.47067i)
Step-by-step explanation:
Quadratic Formula: ![x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D)
√-1 is imaginary number i
Step 1: Define
y = -3x² + 4.5x - 20
a = -3
b = 4.5
c = -20
Step 2: Substitute and Evaluate
![x=\frac{-4.5 \pm \sqrt{4.5^2-4(-3)(-20)} }{2(-3)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-4.5%20%5Cpm%20%5Csqrt%7B4.5%5E2-4%28-3%29%28-20%29%7D%20%7D%7B2%28-3%29%7D)
![x=\frac{-4.5 \pm \sqrt{20.25-240} }{-6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-4.5%20%5Cpm%20%5Csqrt%7B20.25-240%7D%20%7D%7B-6%7D)
![x=\frac{-4.5 \pm \sqrt{-219.75} }{-6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-4.5%20%5Cpm%20%5Csqrt%7B-219.75%7D%20%7D%7B-6%7D)
![x=\frac{-4.5 \pm \sqrt{219.75}(\sqrt{-1} ) }{-6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-4.5%20%5Cpm%20%5Csqrt%7B219.75%7D%28%5Csqrt%7B-1%7D%20%29%20%7D%7B-6%7D)
![x=\frac{-4.5 \pm i\sqrt{219.75} }{-6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-4.5%20%5Cpm%20i%5Csqrt%7B219.75%7D%20%7D%7B-6%7D)
![x=\frac{4.5 \pm i14.824 }{6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4.5%20%5Cpm%20i14.824%20%7D%7B6%7D)
![x=0.75 \pm 2.47067i](https://tex.z-dn.net/?f=x%3D0.75%20%5Cpm%202.47067i)
For this case we have the following functions:
h (x) = 2x - 5
t (x) = 6x + 4
Part A: (h + t) (x)
(h + t) (x) = h (x) + t (x)
(h + t) (x) = (2x - 5) + (6x + 4)
(h + t) (x) = 8x - 1
Part B: (h ⋅ t) (x)
(h ⋅ t) (x) = h (x) * t (x)
(h ⋅ t) (x) = (2x - 5) * (6x + 4)
(h ⋅ t) (x) = 12x ^ 2 + 8x - 30x - 20
(h ⋅ t) (x) = 12x ^ 2 - 22x - 20
Part C: h [t (x)]
h [t (x)] = 2 (6x + 4) - 5
h [t (x)] = 12x + 8 - 5
h [t (x)] = 12x + 3
This shape is a Rectangle because the sides aren’t even