ANSWER
![y \leqslant - 2x - 2](https://tex.z-dn.net/?f=y%20%5Cleqslant%20%20%20-%202x%20-%202)
EXPLANATION
The boundary line passes through (-2,2) and (0,-2).
The slope of this line is
![m = \frac{ - 2 - 2}{0 - - 2}](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7B%20-%202%20-%202%7D%7B0%20-%20%20-%202%7D%20)
![m = \frac{ - 4}{2} = - 2](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7B%20-%204%7D%7B2%7D%20%20%3D%20%20-%202)
The y-intercept is , c=-2.
The slope-intercept form of this line is given by;
![y = mx + c](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20c)
We substitute values to obtain;
![y = - 2x - 2](https://tex.z-dn.net/?f=y%20%3D%20%20-%202x%20-%202)
Since the lower half-plane is shaded the required inequality is
![y \leqslant - 2x - 2](https://tex.z-dn.net/?f=y%20%5Cleqslant%20%20%20-%202x%20-%202)
So, values of x are: ![x=2\sqrt{15},\,\,x=-2\sqrt{15}](https://tex.z-dn.net/?f=x%3D2%5Csqrt%7B15%7D%2C%5C%2C%5C%2Cx%3D-2%5Csqrt%7B15%7D)
Step-by-step explanation:
We need to find the square root of 5x^2 = 300
Writing in mathematical form:
![5x^2=300](https://tex.z-dn.net/?f=5x%5E2%3D300)
Divide both sides by 5
![\frac{5x^2}{5}=\frac{300}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B5x%5E2%7D%7B5%7D%3D%5Cfrac%7B300%7D%7B5%7D)
![x^2=60](https://tex.z-dn.net/?f=x%5E2%3D60)
Taking square root on both sides
![\sqrt{x^2}=\sqrt{60}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2%7D%3D%5Csqrt%7B60%7D)
![x=\pm (\sqrt{2\times 2\times 3\times 5})](https://tex.z-dn.net/?f=x%3D%5Cpm%20%28%5Csqrt%7B2%5Ctimes%202%5Ctimes%203%5Ctimes%205%7D%29)
![x=\pm (\sqrt{2^2 \times 3\times 5})](https://tex.z-dn.net/?f=x%3D%5Cpm%20%28%5Csqrt%7B2%5E2%20%5Ctimes%203%5Ctimes%205%7D%29)
![x=\pm (2\sqrt{3\times 5})](https://tex.z-dn.net/?f=x%3D%5Cpm%20%282%5Csqrt%7B3%5Ctimes%205%7D%29)
![x=\pm (2\sqrt{15})](https://tex.z-dn.net/?f=x%3D%5Cpm%20%282%5Csqrt%7B15%7D%29)
![x=2\sqrt{15},\,\,x=-2\sqrt{15}](https://tex.z-dn.net/?f=x%3D2%5Csqrt%7B15%7D%2C%5C%2C%5C%2Cx%3D-2%5Csqrt%7B15%7D)
So, values of x are: ![x=2\sqrt{15},\,\,x=-2\sqrt{15}](https://tex.z-dn.net/?f=x%3D2%5Csqrt%7B15%7D%2C%5C%2C%5C%2Cx%3D-2%5Csqrt%7B15%7D)
Keywords: Square root
Learn more about square root at:
#learnwithBrainly
Answer:
1/2
Step-by-step explanation:
A^2+b^2=c^2
Is the Pythagorean theorem
Answer:
The average rate of change in that space would be 12.
Step-by-step explanation:
To find this, use the two ordered pairs (-1, 3) and (1, 27) in the slope formula.
m(slope) = (y2 - y1)/(x2 - x1)
m = (27 - 3)/(1 - -1)
m = 24/2
m = 12