The table represents a multiplicative relationship
For this case we have the following quadratic equation:
![x ^ 2-4x + 23 = 0](https://tex.z-dn.net/?f=x%20%5E%202-4x%20%2B%2023%20%3D%200)
The solutions will be given by:
![x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B-b%20%5Cpm%20%5Csqrt%20%7Bb%20%5E%202-4%20%28a%29%20%28c%29%7D%7D%20%7B2a%7D)
Where:
![a = 1\\b = -4\\c = 23](https://tex.z-dn.net/?f=a%20%3D%201%5C%5Cb%20%3D%20-4%5C%5Cc%20%3D%2023)
Substituting the values we have:
![x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (1) (23)}} {2 (1)}\\x = \frac {4 \pm \sqrt {16-92}} {2}\\x = \frac {4 \pm \sqrt {-76}} {2}\\x = \frac {4 \pm \sqrt {76i ^ 2}} {2}\\x = \frac {4 \pmi \sqrt {76}} {2}\\x = \frac {4 \pmi \sqrt {2 ^ 2 * 19}} {2}\\x = \frac {4 \pm2i \sqrt {19}} {2}\\x = 2 \pm i\sqrt {19}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B-%20%28-%204%29%20%5Cpm%20%5Csqrt%20%7B%28-%204%29%20%5E%202-4%20%281%29%20%2823%29%7D%7D%20%7B2%20%281%29%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B4%20%5Cpm%20%5Csqrt%20%7B16-92%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B4%20%5Cpm%20%5Csqrt%20%7B-76%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B4%20%5Cpm%20%5Csqrt%20%7B76i%20%5E%202%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B4%20%5Cpmi%20%5Csqrt%20%7B76%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B4%20%5Cpmi%20%5Csqrt%20%7B2%20%5E%202%20%2A%2019%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B4%20%5Cpm2i%20%5Csqrt%20%7B19%7D%7D%20%7B2%7D%5C%5Cx%20%3D%202%20%5Cpm%20i%5Csqrt%20%7B19%7D)
We have two roots:
![x_ {1} = 2-i \sqrt {19}\\x_ {2} = 2 + i \sqrt {19}](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%202-i%20%5Csqrt%20%7B19%7D%5C%5Cx_%20%7B2%7D%20%3D%202%20%2B%20i%20%5Csqrt%20%7B19%7D)
ANswer:
![x_ {1} = 2-i\sqrt {19}\\x_ {2} = 2 + i\sqrt {19}](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%202-i%5Csqrt%20%7B19%7D%5C%5Cx_%20%7B2%7D%20%3D%202%20%2B%20i%5Csqrt%20%7B19%7D)
Answer:
She has an initiall amount of 6 hours, so if T is the amount of time that passed since she rented the boat, the inequality that describes this system is:
0≤ T ≤ 6
This means that she can use the boat from 0 hours to 6 hours, here we are allowing the intermediate values because, of course, she can return the boat earlier than in the given time.
From this we have that the maximum time left that she has can be written as:
x + T = 6
so if T = 3h, meaning that 3 hours passed, she has:
X + 3 = 6
x = 6 - 3 = 3
3 hours left.
Factor
0.0625
0.25 * 0.25
Square root is a 2nd root which is even so there can be negative solutions.
Sqrt(0.0625) = 0.25 or -0.25
Since FA || BE, then angle 1 must equal angle 2 since they are corresponding angles along parallel lines where the transverse line cuts.
Thus, if angle 1 is 59, then angle 2 must also be 59 (ie D)