Step-by-step explanation:
Since both terms are perfect squares, factor using the difference of squares formula, a 2 − b 2 = ( a + b ) ( a − b ) where a = 7 and b = a + x . − ( 7 + a + x ) ( a + x − 7 )
Answer:
![DC=\frac{8}{3}\ units](https://tex.z-dn.net/?f=DC%3D%5Cfrac%7B8%7D%7B3%7D%5C%20units)
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The triangle ABD is an isosceles triangle
because
AB=BD
The segment BM is a perpendicular bisector segment AD
so
<em>In the right triangle ABM</em>
Applying the Pythagorean Theorem
![BM^2=AB^2-AM^2](https://tex.z-dn.net/?f=BM%5E2%3DAB%5E2-AM%5E2)
we have
![AB=5\ units\\AM=x\ units](https://tex.z-dn.net/?f=AB%3D5%5C%20units%5C%5CAM%3Dx%5C%20units)
substitute
![BM^2=5^2-x^2](https://tex.z-dn.net/?f=BM%5E2%3D5%5E2-x%5E2)
-----> equation A
<em>In the right triangle BMC</em>
Applying the Pythagorean Theorem
![BM^2=BC^2-MC^2](https://tex.z-dn.net/?f=BM%5E2%3DBC%5E2-MC%5E2)
we have
![BC=7\ units\\MC=AC-AM=(9-x)\ units](https://tex.z-dn.net/?f=BC%3D7%5C%20units%5C%5CMC%3DAC-AM%3D%289-x%29%5C%20units)
substitute
![BM^2=7^2-(9-x)^2](https://tex.z-dn.net/?f=BM%5E2%3D7%5E2-%289-x%29%5E2)
![BM^2=49-81+18x-x^2](https://tex.z-dn.net/?f=BM%5E2%3D49-81%2B18x-x%5E2)
----> equation B
equate equation A and equation B
![-x^2+18x-32=25-x^2](https://tex.z-dn.net/?f=-x%5E2%2B18x-32%3D25-x%5E2)
solve for x
![18x=25+32\\18x=57\\\\x=\frac{57}{18}](https://tex.z-dn.net/?f=18x%3D25%2B32%5C%5C18x%3D57%5C%5C%5C%5Cx%3D%5Cfrac%7B57%7D%7B18%7D)
Simplify
![x=\frac{19}{6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B19%7D%7B6%7D)
<em>Find the length of DC</em>
![DC=AC-2x](https://tex.z-dn.net/?f=DC%3DAC-2x)
substitute the given values
![DC=9-2(\frac{19}{6})](https://tex.z-dn.net/?f=DC%3D9-2%28%5Cfrac%7B19%7D%7B6%7D%29)
![DC=9-\frac{19}{3}\\\\DC=\frac{8}{3}\ units](https://tex.z-dn.net/?f=DC%3D9-%5Cfrac%7B19%7D%7B3%7D%5C%5C%5C%5CDC%3D%5Cfrac%7B8%7D%7B3%7D%5C%20units)
The answer is 2.1 US dollars,
Answer: the slope intercept form of 2x+y=6 is y=-2+6
Step-by-step explanation:
2x+y=6 (subtract 2x from both sides)
-2x -2x (the -2x and the 2x cancel leaving...)
<u><em>y=-2x+6</em></u> →( y equals negative two x plus six)