Answer: 3.033
Step-by-step explanation:
Since it's using the word faster, you know Jana wants to remove time from her total. So, you'd subtract however many minutes she wants to be faster by from the current total.
3.058 - 0.025 = 3.033
![1\text{ and }\frac{\text{-1 }}{2}\pm\text{ }\frac{i\sqrt[]{3^{}}}{2}\text{ (option C)}](https://tex.z-dn.net/?f=1%5Ctext%7B%20and%20%7D%5Cfrac%7B%5Ctext%7B-1%20%7D%7D%7B2%7D%5Cpm%5Ctext%7B%20%7D%5Cfrac%7Bi%5Csqrt%5B%5D%7B3%5E%7B%7D%7D%7D%7B2%7D%5Ctext%7B%20%28option%20C%29%7D)
Explanation:
![\begin{gathered} x^3-\text{ 1 = 0} \\ x^3-\text{ 1 has a root of 1} \\ x^3-1=(x-1)(x^2\text{ + x + 1)} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5E3-%5Ctext%7B%201%20%3D%200%7D%20%5C%5C%20x%5E3-%5Ctext%7B%201%20has%20a%20root%20of%201%7D%20%5C%5C%20x%5E3-1%3D%28x-1%29%28x%5E2%5Ctext%7B%20%2B%20x%20%2B%201%29%7D%20%5Cend%7Bgathered%7D)
we find the root of x² + x + 1 has it can't be factorized
Using quadratic formula:
![x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%5Ctext%7B%20%3D%20%7D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D)
for a² + bx + c = 0
comparing: x² + x + 1
where a = 1, b = 1, c = 1
![\begin{gathered} x\text{ = }\frac{-1\pm\sqrt[]{(1)^2^{}-4(1)(1)}}{2(1)} \\ x\text{ = }\frac{-1\pm\sqrt[]{1^{}-4}}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5Ctext%7B%20%3D%20%7D%5Cfrac%7B-1%5Cpm%5Csqrt%5B%5D%7B%281%29%5E2%5E%7B%7D-4%281%29%281%29%7D%7D%7B2%281%29%7D%20%5C%5C%20x%5Ctext%7B%20%3D%20%7D%5Cfrac%7B-1%5Cpm%5Csqrt%5B%5D%7B1%5E%7B%7D-4%7D%7D%7B2%7D%20%5Cend%7Bgathered%7D)
![\begin{gathered} x\text{ = }\frac{-1\pm\sqrt[]{-3}}{2}\text{= }\frac{-1\pm\sqrt[]{-1(3)}}{2} \\ Since\text{ we can't find the square root of a negative number, we apply complex root} \\ \text{let i}^2\text{ = -1} \\ x\text{ = }\frac{-1\pm\sqrt[]{3i^2}}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5Ctext%7B%20%3D%20%7D%5Cfrac%7B-1%5Cpm%5Csqrt%5B%5D%7B-3%7D%7D%7B2%7D%5Ctext%7B%3D%20%7D%5Cfrac%7B-1%5Cpm%5Csqrt%5B%5D%7B-1%283%29%7D%7D%7B2%7D%20%5C%5C%20Since%5Ctext%7B%20we%20can%27t%20find%20the%20square%20root%20of%20a%20negative%20number%2C%20we%20apply%20complex%20root%7D%20%5C%5C%20%5Ctext%7Blet%20i%7D%5E2%5Ctext%7B%20%3D%20-1%7D%20%5C%5C%20x%5Ctext%7B%20%3D%20%7D%5Cfrac%7B-1%5Cpm%5Csqrt%5B%5D%7B3i%5E2%7D%7D%7B2%7D%20%5Cend%7Bgathered%7D)
![\begin{gathered} x\text{ = }\frac{-1\pm\sqrt[]{3i^2}}{2}\text{ = }\frac{-1\pm i\sqrt[]{3^{}}}{2} \\ x\text{ = }\frac{-1+i\sqrt[]{3^{}}}{2}or\text{ }\frac{-1-i\sqrt[]{3^{}}}{2} \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5Ctext%7B%20%3D%20%7D%5Cfrac%7B-1%5Cpm%5Csqrt%5B%5D%7B3i%5E2%7D%7D%7B2%7D%5Ctext%7B%20%3D%20%7D%5Cfrac%7B-1%5Cpm%20i%5Csqrt%5B%5D%7B3%5E%7B%7D%7D%7D%7B2%7D%20%5C%5C%20x%5Ctext%7B%20%3D%20%7D%5Cfrac%7B-1%2Bi%5Csqrt%5B%5D%7B3%5E%7B%7D%7D%7D%7B2%7Dor%5Ctext%7B%20%7D%5Cfrac%7B-1-i%5Csqrt%5B%5D%7B3%5E%7B%7D%7D%7D%7B2%7D%20%5C%5C%20%20%5Cend%7Bgathered%7D)
I’m not sure if you need to find the coordinates, but I’ll leave them here for you.
The upper left corner is at 10, 20.
The bottom left corner is at 10, 5.
The bottom right is 20, 5.
Hope this helps you.
Y = 3x
How to solve:
y2 - y1/x2-x1
27-15/9-5
= 12/4 = 3
Looks like you got it already :)