The solution to the equation x(x+4) = 6 is x = -2 + √10 or x = -2 - √10 after solving with the quadratic formula.
<h3>What is a quadratic equation?</h3>
Any equation of the form
where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
![\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%5Crm%20x%20%3D%20%5Cdfrac%7B-b%20%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
We have an equation:
x(x + 4) = 6
By distributive property:
x² + 4x = 6
x² + 4x - 6 = 0
a = 1, b = 4, c = -6
Plugging all the values in the formula:
![\rm x = \dfrac{-4 \pm\sqrt{4^2-4(1)(-6)}}{2(1)}](https://tex.z-dn.net/?f=%5Crm%20x%20%3D%20%5Cdfrac%7B-4%20%5Cpm%5Csqrt%7B4%5E2-4%281%29%28-6%29%7D%7D%7B2%281%29%7D)
After calculating:
![\rm x = \dfrac{-4 \pm\sqrt{40}}{2}](https://tex.z-dn.net/?f=%5Crm%20x%20%3D%20%5Cdfrac%7B-4%20%5Cpm%5Csqrt%7B40%7D%7D%7B2%7D)
![\rm x=-2+\sqrt{10},\ \ \ or \ \ \ x=-2-\sqrt{10}](https://tex.z-dn.net/?f=%5Crm%20x%3D-2%2B%5Csqrt%7B10%7D%2C%5C%20%5C%20%5C%20or%20%5C%20%5C%20%5C%20x%3D-2-%5Csqrt%7B10%7D)
Thus, the solution to the equation x(x+4) = 6 is x = -2 + √10 or x = -2 - √10 after solving with the quadratic formula.
Learn more about quadratic equations here:
brainly.com/question/2263981
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No, the graph fails the vertical line test. In a function, each x value only has one y value. The y value can have more than one x value in a function
Answer:
Domain- the set of possible values of the independent variable or variables of a function.
Range- the set of values that a given function can take as its argument varies.
The equation of the line passing through
and
is
. Here
is the slope of the line.
Substituting numerical values, the equation of the line is
![\frac{x-0}{y-5} =\frac{-2-0}{11-5} \\ \frac{x}{y-5} =-\frac{1}{3} \\ 3x=5-y\\ 3x+y=5](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx-0%7D%7By-5%7D%20%3D%5Cfrac%7B-2-0%7D%7B11-5%7D%20%5C%5C%20%5Cfrac%7Bx%7D%7By-5%7D%20%3D-%5Cfrac%7B1%7D%7B3%7D%20%5C%5C%203x%3D5-y%5C%5C%203x%2By%3D5%20)
The equation of the line is ![3x+y=5](https://tex.z-dn.net/?f=%203x%2By%3D5%20)
Answer:
The slope is -2
Step-by-step explanation:
(-4,6) (3,-8)
(y₂ - y₁) / (x₂ - x₁)
((-8) - (6)) / ((3) - (-4))
(-8 - 6) / (3 + 4)
-14/7 = -2