Answer:
see explanation
Step-by-step explanation:
Simplify the radical
= 
= 
Square both sides
T² = ( multiply both sides by (g + f) )
T²(g + f) = Ufg ( distribute left side )
T²g + T²f = Ufg ← subtract Ufg from both sides
T²g - Ufg + T²f = 0 ← subtract T²f from both sides
T²g - Ufg = - T²f ← factor out g from each term on the left side
g(T² - Uf) = - T²f ← divide both sides by (T² - Uf)
g = - 
= 
The first equation can be simplified down to 3 and -\frac{3}{2}[/tex]. Therefore, ">" is correct.
The second equation can be simplified down to 12 and 6.25. Therefore, "<" is incorrect. It should be ">".
Are you just looking for the green space or more
The line segment HI has length 3<em>x</em> - 5, and IJ has length <em>x</em> - 1.
We're told that HJ has length 7<em>x</em> - 27.
The segment HJ is made up by connecting the segments HI and IJ, so the length of HJ is equal to the sum of the lengths of HI and IJ.
This means we have
7<em>x</em> - 27 = (3<em>x</em> - 5) + (<em>x</em> - 1)
Solve for <em>x</em> :
7<em>x</em> - 27 = (3<em>x</em> + <em>x</em>) + (-5 - 1)
7<em>x</em> - 27 = 4<em>x</em> - 6
7<em>x</em> - 4<em>x</em> = 27 - 6
3<em>x</em> = 21
<em>x</em> = 21/3
<em>x</em> = 7
