The correct answer would be C.)-3
Answer:
![\displaystyle n_1 = \frac{-2 + \sqrt{34}}{2} \approx 1.9155 \text{ or } n_2 = \frac{-2-\sqrt{34}}{2} \approx -3.9155](https://tex.z-dn.net/?f=%5Cdisplaystyle%20n_1%20%3D%20%5Cfrac%7B-2%20%2B%20%5Csqrt%7B34%7D%7D%7B2%7D%20%5Capprox%201.9155%20%5Ctext%7B%20or%20%7D%20n_2%20%3D%20%5Cfrac%7B-2-%5Csqrt%7B34%7D%7D%7B2%7D%20%5Capprox%20-3.9155)
Step-by-step explanation:
We are given the equation:
![\displaystyle 2n^2 - 15 = -4n](https://tex.z-dn.net/?f=%5Cdisplaystyle%202n%5E2%20-%2015%20%3D%20-4n)
And we want to solve using the quadratic formula.
First, isolate the equation:
![\displaystyle 2n^2 + 4n - 15 = 0](https://tex.z-dn.net/?f=%5Cdisplaystyle%202n%5E2%20%2B%204n%20-%2015%20%3D%200)
Recall that for equations in the form <em>ax</em>² + <em>bx</em> + <em>c</em> = 0, the solutions are given by:
![\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%20%3D%20%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
In this case, <em>a</em> = 2, <em>b</em> = 4, and <em>c</em> = -15.
Substitute and evaluate:
![\displaystyle \begin{aligned} n&= \frac{-(4)\pm\sqrt{(4)^2-4(2)(-15)}}{2(2)} \\ \\ &= \frac{-4\pm\sqrt{136}}{4} \\ \\ &= \frac{-4\pm2\sqrt{34}}{4} \\ \\ &= \frac{-2\pm\sqrt{34}}{2} \end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%20n%26%3D%20%5Cfrac%7B-%284%29%5Cpm%5Csqrt%7B%284%29%5E2-4%282%29%28-15%29%7D%7D%7B2%282%29%7D%20%5C%5C%20%5C%5C%20%26%3D%20%5Cfrac%7B-4%5Cpm%5Csqrt%7B136%7D%7D%7B4%7D%20%5C%5C%20%5C%5C%20%26%3D%20%5Cfrac%7B-4%5Cpm2%5Csqrt%7B34%7D%7D%7B4%7D%20%5C%5C%20%5C%5C%20%26%3D%20%5Cfrac%7B-2%5Cpm%5Csqrt%7B34%7D%7D%7B2%7D%20%5Cend%7Baligned%7D)
In conclusion, our two solutions are:
![\displaystyle n_1 = \frac{-2 + \sqrt{34}}{2} \approx 1.9155 \text{ or } n_2 = \frac{-2-\sqrt{34}}{2} \approx -3.9155](https://tex.z-dn.net/?f=%5Cdisplaystyle%20n_1%20%3D%20%5Cfrac%7B-2%20%2B%20%5Csqrt%7B34%7D%7D%7B2%7D%20%5Capprox%201.9155%20%5Ctext%7B%20or%20%7D%20n_2%20%3D%20%5Cfrac%7B-2-%5Csqrt%7B34%7D%7D%7B2%7D%20%5Capprox%20-3.9155)
M < 2 = 27...and because < GBC is vertical from < 2, they are equal because vertical angles are equal. Supplementary angles are two angles when added together = 180. So the supplement for < GBC is 180 - 27 = 153
50 /50 I think it is the answer. i think there will be 50 non fiction and 50 fiction books in the library
Answer:
$70.80
Step-by-step explanation:
60 x 18% = 10.80
$60.00 + $10.80 = $70.80