Chapter 4 - Section 4.6 - Complex Fractions and Review of Order of Operations - Exercise Set - Page 286: 83

$-\frac{55}{64}$

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