Hi there!
![\large\boxed{x = -1 \pm \sqrt{5}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Bx%20%3D%20-1%20%5Cpm%20%5Csqrt%7B5%7D%7D)
We can solve by setting both equations equal to each other:
.5x + 4 = -.25x² + 5
Move everything to one side:
0 = -.25x² - .5x + 1
Multiply both sides by 4 to cancel out the decimals:
0 = -x² - 2x + 4
Factor out negative from both sides:
0 = x² + 2x - 4
Use the quadratic formula:
![\frac{-b \pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Plug in the corresponding terms:
![x = \frac{-2 \pm \sqrt{4-4(-4)(1)}}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-2%20%5Cpm%20%5Csqrt%7B4-4%28-4%29%281%29%7D%7D%7B2%7D)
Simplify:
![x = \frac{-2 \pm \sqrt{4 + 16}}{2}\\\\x = \frac{-2 \pm \sqrt{20}}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-2%20%5Cpm%20%5Csqrt%7B4%20%2B%2016%7D%7D%7B2%7D%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B-2%20%5Cpm%20%5Csqrt%7B20%7D%7D%7B2%7D)
Simplify the radical to reduce:
![x = \frac{-2 \pm 2\sqrt{5}}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-2%20%5Cpm%202%5Csqrt%7B5%7D%7D%7B2%7D)
Divide all terms by 2:
![x = -1 \pm \sqrt{5}](https://tex.z-dn.net/?f=x%20%3D%20-1%20%5Cpm%20%5Csqrt%7B5%7D)
Answer:
Step-by-step explanation:
Ok so the beaker is 200 water:800 acid
So she drains 100 from the acid and 100 from the water which equals
100:700
Then she adds 200 water:
300:700
there is 300 mL water in da beaker now
i might got it wrong tho
20 ounces of juice because u take 9.5+1.75 . 6 times and get 20 that is how it is 20 ounces of juice
According to the diagram the answer should be C. ∠BEA ≈ ∠BEC. Hope this helps :)