![f(x)= \frac{x-4}{x^2-16}](https://tex.z-dn.net/?f=f%28x%29%3D%20%5Cfrac%7Bx-4%7D%7Bx%5E2-16%7D%20)
some things true about it
there is a vertical assymtote at x=-4
horizontal assymtote is at x=0
no zeroes
answer is C
X - a leg (x > 6);
x - 6 - a leg;
x + 1 - a <span>hypotenuse;</span>
Use the Pythagorean theorem
![(x+1)^2=x^2+(x-6)^2](https://tex.z-dn.net/?f=%28x%2B1%29%5E2%3Dx%5E2%2B%28x-6%29%5E2)
Use:
![(a\pm b)^2=a^2\pm2ab+b^2](https://tex.z-dn.net/?f=%28a%5Cpm%20b%29%5E2%3Da%5E2%5Cpm2ab%2Bb%5E2)
![x^2+2x+1=x^2+x^2-12x+36\ \ \ |-x^2-2x-1\\\\x^2-14x+35=0\ \ \ |-35\\\\x^2-14x=-35\\\\x^2-2\cdot x\cdot7=-35\ \ \ |+7^2\\\\x^2-2\cdot x\cdot7+7^2=-35+7^2\\\\(x-7)^2=14\iff x-7=\pm\sqrt{14}\ \ \ |+7\\\\x=7-\sqrt{14} < 6;\ x=7+\sqrt{14}](https://tex.z-dn.net/?f=x%5E2%2B2x%2B1%3Dx%5E2%2Bx%5E2-12x%2B36%5C%20%5C%20%5C%20%7C-x%5E2-2x-1%5C%5C%5C%5Cx%5E2-14x%2B35%3D0%5C%20%5C%20%5C%20%7C-35%5C%5C%5C%5Cx%5E2-14x%3D-35%5C%5C%5C%5Cx%5E2-2%5Ccdot%20x%5Ccdot7%3D-35%5C%20%5C%20%5C%20%7C%2B7%5E2%5C%5C%5C%5Cx%5E2-2%5Ccdot%20x%5Ccdot7%2B7%5E2%3D-35%2B7%5E2%5C%5C%5C%5C%28x-7%29%5E2%3D14%5Ciff%20x-7%3D%5Cpm%5Csqrt%7B14%7D%5C%20%5C%20%5C%20%7C%2B7%5C%5C%5C%5Cx%3D7-%5Csqrt%7B14%7D%20%3C%206%3B%5C%20x%3D7%2B%5Csqrt%7B14%7D)
![x=7+\sqrt{14}\\x-6=1+\sqrt{14}\\x+1=8+\sqrt{14}](https://tex.z-dn.net/?f=x%3D7%2B%5Csqrt%7B14%7D%5C%5Cx-6%3D1%2B%5Csqrt%7B14%7D%5C%5Cx%2B1%3D8%2B%5Csqrt%7B14%7D)
The perimeter:
Answer:
always true I think hope it helps
Answer:
Option B
Step-by-step explanation:
Only lines which are parallel to the line which connects the given two points will neve r intersect,
parallel line has same slope
the slope of the line which connects the given two points is, 5/2
and the line is option B also has the same slope, so those two lines will never intersect each other.
Answered by GAUTHMATH