#### Answer

$-\frac{55}{64}$

#### Work Step by Step

When $x=\frac{3}{4}$ and $y=-\frac{4}{7}$:
$x^{2}+7y$
$=(\frac{3}{4})^{2}+7(-\frac{4}{7})$
$=(\frac{3}{4}\times\frac{3}{4})-(\frac{7}{1}\times\frac{4}{7})$
$=(\frac{3}{4}\times\frac{3}{4})-(\frac{1}{1}\times\frac{4}{1})$
$=\frac{9}{16}-\frac{4}{1}$
$=\frac{9}{16}-\frac{64}{16}$
$=-\frac{55}{64}$