Answer:
6*10^-7
Step-by-step explanation:
Step-by-step explanation:
(x−1)²−9=0
(x-1)²= 9
x-1 = ±√9
x-1 = ±3
x = 1-3=-2 or x=1+3=4
the solution = {-2,4}
Answer:
Solving the given linear system, we get x = 1 and y = -3.
The solution set is: (1,-3)
Step-by-step explanation:
We need to solve the linear system of equations.
![3x-y=6 \\y=x-4](https://tex.z-dn.net/?f=3x-y%3D6%20%5C%5Cy%3Dx-4)
We can write second equation y=x-4 as: ![-x+y=-4](https://tex.z-dn.net/?f=-x%2By%3D-4)
Let:
![3x-y=6--eq(1)\\ -x+y=-4--eq(2)](https://tex.z-dn.net/?f=3x-y%3D6--eq%281%29%5C%5C%20-x%2By%3D-4--eq%282%29)
Now, Adding equation 1 and 2
![3x-y=6\\ -x+y=-4\\--------\\2x+0y=2\\2x=2\\x=\frac{2}{2}\\x=1](https://tex.z-dn.net/?f=3x-y%3D6%5C%5C%20-x%2By%3D-4%5C%5C--------%5C%5C2x%2B0y%3D2%5C%5C2x%3D2%5C%5Cx%3D%5Cfrac%7B2%7D%7B2%7D%5C%5Cx%3D1)
So, we get x = 1
Now, put value of x in second equation to find value of y:
![y=x-4\\Put\:x=1\\y=1-4\\y=-3](https://tex.z-dn.net/?f=y%3Dx-4%5C%5CPut%5C%3Ax%3D1%5C%5Cy%3D1-4%5C%5Cy%3D-3)
So, we get y = -3
Solving the given linear system, we get x = 1 and y = -3.
The solution set is: (1,-3)
9514 1404 393
Answer:
x^2 -4x +2 = 0
Step-by-step explanation:
The other root is the conjugate of the given one, so is 2-√2. The quadratic equation in factored form is then ...
(x -2-√2)(x -2+√2) = 0
Expanding this, we get ...
(x -2)^2 -(√2)^2 = 0
x^2 -4x +4 -2 = 0
x^2 -4x +2 = 0 . . . . the equation you're looking for
By applying Pythagorean theorem, we have proven that the point (-1/2, -√3/2) lies on the unit circle.
<h3>How to prove this point lies on the unit circle?</h3>
In Trigonometry, an angle with a magnitude of -120° is found in the third quarter and as such, both x and y would be negative. Also, we would calculate the reference angle for θ in third quarter as follows:
Reference angle = 180 - θ
Reference angle = 180 - 120
Reference angle = 60°.
For the coordinates, we have:
sin(-120) = -sin(60) = -1/2.
cos(-120) = -cos(60) = -√3/2.
By applying Pythagorean theorem, we have:
z² = x² + y²
z = √((-1/2)² + (-√3/2)²)
z = √(1/4 + 3/4)
z = √1
z = 1.
Read more on unit circle here: brainly.com/question/9797740
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