Answer:
![x=\frac{27+\sqrt143i}{8}{} ,\frac{27-\sqrt{143i} }{8}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B27%2B%5Csqrt143i%7D%7B8%7D%7B%7D%20%2C%5Cfrac%7B27-%5Csqrt%7B143i%7D%20%7D%7B8%7D)
![y=-9+\frac{27+\sqrt{143} i}{4} ,-9+\frac{27-\sqrt{143} i}{4}](https://tex.z-dn.net/?f=y%3D-9%2B%5Cfrac%7B27%2B%5Csqrt%7B143%7D%20i%7D%7B4%7D%20%2C-9%2B%5Cfrac%7B27-%5Csqrt%7B143%7D%20i%7D%7B4%7D)
Step-by-step explanation:
1) Solve for 2x - y = 9
A. Solve for y.
2x - y = 9
B. Subtract 2x from both sides.
-y = 9 - 2x
C. Multiply both sides by -1.
y = -9 + 2x
D. Regroup terms.
y = 2x - 9
2) Substitute y = 2x- 9 into 4x² + 3y² - 2x + y = 16
A. Start with the original equation.
4x² + 3y² - 2x + y = 16
B. Let y = 2x - 9.
4x² + 3(2x - 9)² - 2x + 2x - 9 = 16
C. Simplify.
16x² - 108x + 234 = 16
3) Solve for x in 16x² - 108x + 234 = 16
A. Solve for x.
16x² - 108x + 234 -= 16
B. Move all terms to one side.
16x² - 108x + 234 - 16 = 0
C. Simplify 16x² - 108x + 234 - 16 to 16 x² - 108x + 218
16 x² - 108x + 218 = 0
D. Use the Quadratic Formula.
, ![\frac{108-4\sqrt{143} i}{32}](https://tex.z-dn.net/?f=%5Cfrac%7B108-4%5Csqrt%7B143%7D%20i%7D%7B32%7D)
E. Simplify solutions.
![x=\frac{27+\sqrt{143} i}{8} ,\frac{27-\sqrt{143} i}{8}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B27%2B%5Csqrt%7B143%7D%20i%7D%7B8%7D%20%2C%5Cfrac%7B27-%5Csqrt%7B143%7D%20i%7D%7B8%7D)
4) Substitute
into y = 2x - 9.
1) Start with the original equation.
y = 2x - 9
2) Let x = ![\frac{27+\sqrt{143} i}{8} ,\frac{27-\sqrt{143}i }{8} .](https://tex.z-dn.net/?f=%5Cfrac%7B27%2B%5Csqrt%7B143%7D%20i%7D%7B8%7D%20%2C%5Cfrac%7B27-%5Csqrt%7B143%7Di%20%7D%7B8%7D%20.)
![y=2*\frac{27+\sqrt{143} i}{8} -9,2*\frac{27-\sqrt{143}i }{8} -9](https://tex.z-dn.net/?f=y%3D2%2A%5Cfrac%7B27%2B%5Csqrt%7B143%7D%20i%7D%7B8%7D%20-9%2C2%2A%5Cfrac%7B27-%5Csqrt%7B143%7Di%20%7D%7B8%7D%20-9)
3) Simplify
![y=-9+\frac{27+\sqrt{143}i }{4} ,-9+\frac{27-\sqrt{143i} }{4}](https://tex.z-dn.net/?f=y%3D-9%2B%5Cfrac%7B27%2B%5Csqrt%7B143%7Di%20%7D%7B4%7D%20%2C-9%2B%5Cfrac%7B27-%5Csqrt%7B143i%7D%20%7D%7B4%7D)
The first answer is “B” and the second one is “D”. Attached below is my work.
I hoped this helped!! ^w^
From the given data set, the get the IQR we rearrange the set in ascending order first.
11,12,14,14,16,16.5,18,18,20
the first quartile =14
The upper quartile=18
then
IQR=Q1-Q3
=18-14=4