the solution of inequality
is ![x>-9](https://tex.z-dn.net/?f=x%3E-9)
Step-by-step explanation:
We need to draw graph of the solution to inequality ![-3x-7](https://tex.z-dn.net/?f=-3x-7%3C20)
First we will solve the inequality to find value of x
Solving the inequality:
![-3x-7](https://tex.z-dn.net/?f=-3x-7%3C20)
Adding 7 on both sides
![-3x-7+7](https://tex.z-dn.net/?f=-3x-7%2B7%3C20%2B7)
![-3x](https://tex.z-dn.net/?f=-3x%3C27)
Divide both sides by -3 and reverse the inequality
![x>-9](https://tex.z-dn.net/?f=x%3E-9)
The graph is attached in the figure below.
So, the solution of inequality
is ![x>-9](https://tex.z-dn.net/?f=x%3E-9)
Keywords: Graph the inequality
Learn more about graph the inequality at:
#learnwithBrainly
![9x^2 - 18 x + 93= -6](https://tex.z-dn.net/?f=9x%5E2%20-%2018%20x%20%2B%2093%3D%20-6)
take away 93 from both sides
![9x^2 - 18 x = - 99](https://tex.z-dn.net/?f=9x%5E2%20-%2018%20x%20%3D%20-%2099)
Divide by 9 through
![x^2 - 2 x = - 11](https://tex.z-dn.net/?f=x%5E2%20-%202%20x%20%3D%20-%2011)
Add (b/2)^2 to form perfect square
![x^2 - 2 x + ( \frac{2}{2} )^2 = - 11 + ( \frac{2}{2} )^2](https://tex.z-dn.net/?f=x%5E2%20-%202%20x%20%2B%20%28%20%5Cfrac%7B2%7D%7B2%7D%20%29%5E2%20%3D%20-%2011%20%2B%20%28%20%5Cfrac%7B2%7D%7B2%7D%20%29%5E2%20)
Form perfect square
![(x - 1)^2 = - 10](https://tex.z-dn.net/?f=%28x%20-%201%29%5E2%20%3D%20-%2010%20)
Square root both sides to find x
![x - 1 = \pm \sqrt{-10}](https://tex.z-dn.net/?f=x%20-%201%20%3D%20%5Cpm%20%20%5Csqrt%7B-10%7D%20)
add 1 on both sides
The answer is 6 11/12
4 1/6 = 4 2/12
2 3/4 = 2 9/12
4 2/12 + 2 9/12 = 6 11/12
Answer:
Absolute minimum = 1.414
Absolute maximum = 2.828
Step-by-step explanation:
![g(x,y)=\sqrt {x^2+y^2} \ constraints: 1\leq x\leq 2 ,\ 1\leq y\leq2](https://tex.z-dn.net/?f=g%28x%2Cy%29%3D%5Csqrt%20%7Bx%5E2%2By%5E2%7D%20%5C%20constraints%3A%201%5Cleq%20x%5Cleq%202%20%2C%5C%201%5Cleq%20y%5Cleq2)
For absolute minimum we take the minimum values of
and
.
![x_{minimum} =1\\y_{minimum}=1\\](https://tex.z-dn.net/?f=x_%7Bminimum%7D%20%3D1%5C%5Cy_%7Bminimum%7D%3D1%5C%5C)
Plugging in the minimum values in the function.
![g(1,1)=\sqrt {1^2+1^2}\\g(1,1) = \sqrt{1+1}\\g(1,1)=\sqrt {2}\\g(1,1)=\pm 1.414\\](https://tex.z-dn.net/?f=g%281%2C1%29%3D%5Csqrt%20%7B1%5E2%2B1%5E2%7D%5C%5Cg%281%2C1%29%20%3D%20%5Csqrt%7B1%2B1%7D%5C%5Cg%281%2C1%29%3D%5Csqrt%20%7B2%7D%5C%5Cg%281%2C1%29%3D%5Cpm%201.414%5C%5C)
Absolute minimum value will be always positive.
∴ Absolute minimum = 1.414
For absolute maximum we take the maximum values of
and
.
![x_{maximum} =2\\y_{maximum}=2\\](https://tex.z-dn.net/?f=x_%7Bmaximum%7D%20%3D2%5C%5Cy_%7Bmaximum%7D%3D2%5C%5C)
Plugging in the maximum values in the function.
![g(2,2)=\sqrt {2^2+2^2}\\g(2,2) = \sqrt{4+4}\\g(2,2)=\sqrt {8}\\g(2,2)=\pm 2.828\\](https://tex.z-dn.net/?f=g%282%2C2%29%3D%5Csqrt%20%7B2%5E2%2B2%5E2%7D%5C%5Cg%282%2C2%29%20%3D%20%5Csqrt%7B4%2B4%7D%5C%5Cg%282%2C2%29%3D%5Csqrt%20%7B8%7D%5C%5Cg%282%2C2%29%3D%5Cpm%202.828%5C%5C)
Absolute maximum value will be always positive.
∴ Absolute maximum = 2.828
5 would be an answer.<span />