Answer:
![\{-\frac{1}{2} \} \cup \{\frac{2}{5}\}](https://tex.z-dn.net/?f=%5C%7B-%5Cfrac%7B1%7D%7B2%7D%20%5C%7D%20%5Ccup%20%5C%7B%5Cfrac%7B2%7D%7B5%7D%5C%7D)
Step-by-step explanation:
![10x^2 + x - 2 = 0; \\ a = 10, b = 1, c = -2; \\ D = b^2 - 4ac = 1^2 - 4 * 10 * (-2) = 1 + 80 = 81 = 9^2, > 0; \\ x_{1, 2} = \frac{-b \pm \sqrt{D}}{2a} = \frac{-1 \pm \sqrt{9^2}}{2 * 10} = \frac{-1 \pm 9}{20} = \left \ [ {{\frac{-1 - 9}{20} = -\frac{10}{20} = -\frac{1}{2} } \atop {\frac{-1 + 9}{20} = \frac{8}{20} = \frac{2}{5}}} \right.](https://tex.z-dn.net/?f=10x%5E2%20%2B%20x%20-%202%20%3D%200%3B%20%5C%5C%20a%20%3D%2010%2C%20b%20%3D%201%2C%20c%20%3D%20-2%3B%20%5C%5C%20D%20%3D%20b%5E2%20-%204ac%20%3D%201%5E2%20-%204%20%2A%2010%20%2A%20%28-2%29%20%3D%201%20%2B%2080%20%3D%2081%20%3D%209%5E2%2C%20%3E%200%3B%20%5C%5C%20x_%7B1%2C%202%7D%20%3D%20%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7BD%7D%7D%7B2a%7D%20%3D%20%5Cfrac%7B-1%20%5Cpm%20%5Csqrt%7B9%5E2%7D%7D%7B2%20%2A%2010%7D%20%3D%20%5Cfrac%7B-1%20%5Cpm%209%7D%7B20%7D%20%3D%20%5Cleft%20%5C%20%5B%20%7B%7B%5Cfrac%7B-1%20-%209%7D%7B20%7D%20%3D%20-%5Cfrac%7B10%7D%7B20%7D%20%3D%20-%5Cfrac%7B1%7D%7B2%7D%20%20%7D%20%5Catop%20%7B%5Cfrac%7B-1%20%2B%209%7D%7B20%7D%20%3D%20%5Cfrac%7B8%7D%7B20%7D%20%3D%20%5Cfrac%7B2%7D%7B5%7D%7D%7D%20%5Cright.)
Answer: x ≥ 11
Step-by-step explanation: We wrote an inequality to represent this situation.
Answer:
y = -x+3
Step-by-step explanation:
We have two points so we can find the slope
m =(y2-y1)/(x2-x1)
(1-2)/(2-1)
-1/1
The slope is -1
We can use the slope intercept form of the equation
y = mx+b where m is the slope and b is the y intercept
y = -x+b
Substitute a point into the equation to find b
2 = -1 +b
Add 1 to each side
2+1 =-1+1 +b
3 =b
y = -x+3
Answer:
3.5 square cm
Step-by-step explanation:
![Area \: of \: both \: squares \\ = {2}^{2} + {3}^{2} \\ = 4 + 9 \\ = 13 \: {cm}^{2} \\ \\ Area \: of \: both \: right \: \triangle s \\ = \frac{1}{2} \times (2 + 3) \times 2 + \frac{1}{2} \times3 \times 3 \\ = 5 \times 1+ 1.5 \times 3 \\ = 5 + 4.5 \\ = 9.5 \: {cm}^{2} \\ \\ Area \: of \:shaded \: region \\ = Area \: of \: both \: squares\\ - Area \: of \: both \: right \: \triangle s \\ = 13 - 9.5 \\ \purple { \boxed{ \bold{Area \: of \:shaded \: region = 3.5 \: {cm}^{2} }}}](https://tex.z-dn.net/?f=Area%20%5C%3A%20of%20%5C%3A%20both%20%5C%3A%20squares%20%20%5C%5C%20%3D%20%20%7B2%7D%5E%7B2%7D%20%20%2B%20%20%7B3%7D%5E%7B2%7D%20%20%5C%5C%20%20%3D%204%20%2B%209%20%5C%5C%20%20%3D%2013%20%5C%3A%20%20%7Bcm%7D%5E%7B2%7D%20%20%5C%5C%20%20%5C%5C%20Area%20%5C%3A%20of%20%5C%3A%20both%20%5C%3A%20right%20%5C%3A%20%20%5Ctriangle%20s%20%5C%5C%20%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%5Ctimes%20%282%20%2B%203%29%20%5Ctimes%202%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%20%5Ctimes3%20%5Ctimes%203%20%5C%5C%20%20%3D%205%20%5Ctimes%201%2B%201.5%20%5Ctimes%203%20%5C%5C%20%20%3D%205%20%2B%204.5%20%5C%5C%20%20%3D%209.5%20%5C%3A%20%20%7Bcm%7D%5E%7B2%7D%20%20%5C%5C%20%20%5C%5C%20Area%20%5C%3A%20of%20%5C%3Ashaded%20%5C%3A%20region%20%5C%5C%20%20%3D%20Area%20%5C%3A%20of%20%5C%3A%20both%20%5C%3A%20squares%5C%5C%20-%20Area%20%5C%3A%20of%20%5C%3A%20both%20%5C%3A%20right%20%5C%3A%20%20%5Ctriangle%20s%20%5C%5C%20%20%3D%2013%20-%209.5%20%5C%5C%20%20%20%5Cpurple%20%7B%20%5Cboxed%7B%20%5Cbold%7BArea%20%5C%3A%20of%20%5C%3Ashaded%20%5C%3A%20region%20%3D%203.5%20%5C%3A%20%20%7Bcm%7D%5E%7B2%7D%20%7D%7D%7D)