Answer:
0.6
Step-by-step explanation:
0.6 is extremely high
1 over 7 to the 2nd power
Step-by-step explanation:
![6 {v}^{2} + 24 = 0 \\ \\ \therefore \: 6 {v}^{2} = - 24 \\ \\ \therefore \: {v}^{2} = \frac{ - 24}{6} \\ \\ \therefore \: {v}^{2} = - 4\\ \\ \therefore \: {v}^{2} = 4\times - 1\\ \\ \therefore \: {v} =\pm \sqrt {4} \times \sqrt{- 1} \\ \\ \therefore \: {v} =\pm 2 \times i\\ \\ \therefore \: {v} = \pm \sqrt{2} i](https://tex.z-dn.net/?f=6%20%7Bv%7D%5E%7B2%7D%20%20%2B%2024%20%3D%200%20%5C%5C%20%20%5C%5C%20%20%5Ctherefore%20%5C%3A%206%20%7Bv%7D%5E%7B2%7D%20%20%3D%20%20-%2024%20%20%5C%5C%20%20%5C%5C%20%5Ctherefore%20%5C%3A%20%7Bv%7D%5E%7B2%7D%20%20%3D%20%20%20%5Cfrac%7B%20-%2024%7D%7B6%7D%20%5C%5C%20%20%5C%5C%20%5Ctherefore%20%5C%3A%20%7Bv%7D%5E%7B2%7D%20%20%3D%20%20%20%20-%204%3C%2Fp%3E%3Cp%3E%5C%5C%20%20%5C%5C%20%5Ctherefore%20%5C%3A%20%7Bv%7D%5E%7B2%7D%20%20%3D%20%20%20%204%5Ctimes%20-%201%3C%2Fp%3E%3Cp%3E%5C%5C%20%20%5C%5C%20%5Ctherefore%20%5C%3A%20%7Bv%7D%20%20%3D%5Cpm%20%20%20%20%5Csqrt%20%7B4%7D%20%5Ctimes%20%5Csqrt%7B-%201%7D%20%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%5C%5C%20%20%5C%5C%20%5Ctherefore%20%5C%3A%20%7Bv%7D%20%20%3D%5Cpm%20%20%20%202%20%5Ctimes%20i%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%5C%5C%20%20%5C%5C%20%5Ctherefore%20%5C%3A%20%7Bv%7D%20%3D%20%20%20%20%20%5Cpm%20%5Csqrt%7B2%7D%20i)
Answer:
The slope is 3.
Step-by-step explanation:
y=-1+3x
y=3x-1
y=mx+b where m=slope and b=y-intercept
![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)