Answer:
Step-by-step explanation:
![x^2+3x=10^{1\frac{1}{2}}\\\\x^2+3x=10^{1+\frac{1}{2}}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\x^2+3x=10\cdot10^\frac{1}{2}\qquad\text{use}\ \sqrt[n]{a}=a^\frac{1}{n}\\\\x^2+3x=10\sqrt{10}\qquad\text{subtract}\ 10\sqrt{10}\ \text{from both sides}\\\\x^2+3x-10\sqrt{10}=0\\\\\text{Use the quadratic formula}\\\\ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\a=1,\ b=3,\ c=-10\sqrt{10}\\\\b^2-4ac=3^2-4(1)(-10\sqrt{10})=9+40\sqrt{10}\\\\x=\dfrac{-3\pm\sqrt{40+10\sqrt{10}}}{2(1)}=\dfrac{-3\pm\sqrt{40+10\sqrt{10}}}{2}\\\\x=\dfrac{-3-\sqrt{10+10\sqrt{10}}}{2}\notin D](https://tex.z-dn.net/?f=x%5E2%2B3x%3D10%5E%7B1%5Cfrac%7B1%7D%7B2%7D%7D%5C%5C%5C%5Cx%5E2%2B3x%3D10%5E%7B1%2B%5Cfrac%7B1%7D%7B2%7D%7D%5Cqquad%5Ctext%7Buse%7D%5C%20a%5En%5Ccdot%20a%5Em%3Da%5E%7Bn%2Bm%7D%5C%5C%5C%5Cx%5E2%2B3x%3D10%5Ccdot10%5E%5Cfrac%7B1%7D%7B2%7D%5Cqquad%5Ctext%7Buse%7D%5C%20%5Csqrt%5Bn%5D%7Ba%7D%3Da%5E%5Cfrac%7B1%7D%7Bn%7D%5C%5C%5C%5Cx%5E2%2B3x%3D10%5Csqrt%7B10%7D%5Cqquad%5Ctext%7Bsubtract%7D%5C%2010%5Csqrt%7B10%7D%5C%20%5Ctext%7Bfrom%20both%20sides%7D%5C%5C%5C%5Cx%5E2%2B3x-10%5Csqrt%7B10%7D%3D0%5C%5C%5C%5C%5Ctext%7BUse%20the%20quadratic%20formula%7D%5C%5C%5C%5Cax%5E2%2Bbx%2Bc%3D0%5C%5C%5C%5Cx%3D%5Cdfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%5C%5C%5C%5Ca%3D1%2C%5C%20b%3D3%2C%5C%20c%3D-10%5Csqrt%7B10%7D%5C%5C%5C%5Cb%5E2-4ac%3D3%5E2-4%281%29%28-10%5Csqrt%7B10%7D%29%3D9%2B40%5Csqrt%7B10%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7B-3%5Cpm%5Csqrt%7B40%2B10%5Csqrt%7B10%7D%7D%7D%7B2%281%29%7D%3D%5Cdfrac%7B-3%5Cpm%5Csqrt%7B40%2B10%5Csqrt%7B10%7D%7D%7D%7B2%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7B-3-%5Csqrt%7B10%2B10%5Csqrt%7B10%7D%7D%7D%7B2%7D%5Cnotin%20D)
Answer:
Step-by-step explanation:
For each equation choose a value for x and then solve to find the corresponding y value that makes that equation true.
Answer:
-2
Step-by-step explanation:
f(1)=3(1)-5 = 3-5= -2
Answer: C. No solution. ( top shaded. Middle not. Bottom shaded.
Step-by-step explanation:
Given inequalities
y< -1/3x+5 and
y> -1/3x-1.
If we draw graph for y< -1/3x+5 equation, it would be a dotted line and we would shade down the dotted line because we have less than < symbol there.
Now, if we draw graph for second inequality y> -1/3x-1, it would also be a dotted line and we would shade up of dotted line because we have greater than > symbol there.
Now, we can see that slopes of both dotted lines are same that is -1/3.
So, there would not be any common shaded region.
Therefore, there would not by any solution of the system of inequalities.
And correct option is C option.
C. No solution. ( top shaded. Middle not. Bottom shaded.
Answer:
-2120x
Step-by-step explanation:
