Answer:
![x = \frac{ -3 - \sqrt{5} }{2} \: or \: x = \frac{ -3 + \sqrt{5} }{2}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%20-3%20-%20%20%5Csqrt%7B5%7D%20%7D%7B2%7D%20%20%5C%3A%20or%20%20%5C%3A%20x%20%20%3D%20%20%5Cfrac%7B%20-3%20%2B%20%5Csqrt%7B5%7D%20%7D%7B2%7D)
Step-by-step explanation:
The given function is
![f(x) = - {x}^{2} - 3x - 1](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20-%20%20%7Bx%7D%5E%7B2%7D%20%20-%203x%20-%201)
To find the roots, we solve:
![- {x}^{2} - 3x - 1 = 0](https://tex.z-dn.net/?f=%20-%20%20%7Bx%7D%5E%7B2%7D%20%20-%203x%20-%201%20%3D%200)
Multiply through by -1 to get:
![{x}^{2} + 3x + 1 = 0](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%2B%203x%20%2B%201%20%3D%200)
We compare to the general quadratic equation
![a {x}^{2} + bx + c = 0](https://tex.z-dn.net/?f=a%20%7Bx%7D%5E%7B2%7D%20%20%2B%20bx%20%20%2B%20c%20%3D%200)
Then we have a=1,b=3, c=1.
The solution is given by:
![x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac } }{2a}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%20-%20b%5Cpm%20%5Csqrt%7B%20%7Bb%7D%5E%7B2%7D%20-%204ac%20%7D%20%7D%7B2a%7D%20)
![x = \frac{ - 3\pm \sqrt{ { (- 3)}^{2} - 4 \times1 \times 1 } }{2 \times 1}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%20-%20%20%203%5Cpm%20%5Csqrt%7B%20%7B%20%28-%203%29%7D%5E%7B2%7D%20-%204%20%5Ctimes1%20%5Ctimes%201%20%7D%20%7D%7B2%20%5Ctimes%201%7D%20)
![x = \frac{ - 3\pm \sqrt{ 9 - 4 } }{2}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%20-%20%20%203%5Cpm%20%5Csqrt%7B%209%20-%204%20%7D%20%7D%7B2%7D%20)
![x = \frac{ -3\pm \sqrt{5} }{2}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%20-3%5Cpm%20%5Csqrt%7B5%7D%20%7D%7B2%7D%20)
![x = \frac{ -3 - \sqrt{5} }{2} \: or \: x = \frac{ -3 + \sqrt{5} }{2}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%20-3%20-%20%20%5Csqrt%7B5%7D%20%7D%7B2%7D%20%20%5C%3A%20or%20%20%5C%3A%20x%20%20%3D%20%20%5Cfrac%7B%20-3%20%2B%20%5Csqrt%7B5%7D%20%7D%7B2%7D%20)
Answer: Choice B) -4
The lower quartile, also known as Q1 or the first quartile, is the left edge of the box. In this case, that is at -4. We can drop a vertical line from the left edge of the box until we hit -4 on the number line.
Side Note: 25% of the data values are below Q1, while 75% of the data values are above Q1
Answer:
It equals 420.
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
12×5=60 60÷1/2=30
srry if I was wrong