Answer
(a) The graph is as shown.
(b) The $x$-intercepts are $(5,0)$ and $(6,0)$.
(c) The solution is $x=5,6$.
(d) The result in part (c) is the same with the $x$-intercepts of the graph.
Work Step by Step
(a) The graph is as shown.
(b) The $x$-intercepts are $(5,0)$ and $(6,0)$.
(c) Setting $y=0$:
$$0=\sqrt{11x-30}-x$$
$$x=\sqrt{11x-30}$$
Squaring both sides:
$$x^2=11x-30$$
$$x^2-11x+30=0$$
$$(x+5)(x-6)=0$$
$$x+5=0$$
$$x=-5$$
$$x-6=0$$
$$x=6$$
Thus, the solution is $x=5,6$.
(d) The result in part (c) is the same with the $x$-intercepts of the graph.
