(2,0 điểm) Thực hiện phép tính (tính hợp lí nếu có thể).

(a) \(\frac{4}{3}:\frac{{ - 5}}{6} + \frac{{11}}{2}\);

(b) \(\frac{3}{4}\,\,.\,\,\frac{{ - 4}}{7} + \frac{{ - 4}}{7}\,\,.\,\,\frac{5}{4}\);

(c) \[\sqrt {0,81} \,\,.\,\,{\left( {\frac{{ - 1}}{3}} \right)^2} - \sqrt {\frac{1}{{196}}} \,\,.\,\,{( - 7)^3}.\]

b) Vì \(AB\parallel xy\) nên \(\widehat {BAI} = \widehat {AIx} = 45^\circ \) (hai góc so le trong).

Ta có \(\widehat {AIF} = \widehat {AIx} + \widehat {FIx}\).

Suy ra \(\widehat {FIx} = \widehat {AIF} - \widehat {AIx} = 105^\circ - 45^\circ = 60^\circ \).

Vì \(\widehat {FIx}\) và \(\widehat {FIy}\) là hai góc kề bù nên \(\widehat {FIx} + \widehat {FIy} = 180^\circ \).

Suy ra \(\widehat {FIy} = 180^\circ - \widehat {FIx} = 180^\circ - 60^\circ = 120^\circ \).

Vậy \(\widehat {FIx} = 60^\circ \); \(\widehat {FIy} = 120^\circ \).

c) Ta thấy \(\widehat {FIy} = \widehat {EFI} = 120^\circ \) mà \(\widehat {FIy}\) và \(\widehat {EFI}\) ở vị trí so le trong.

Do đó\[AB\parallel EF\].

a) \(\frac{4}{5}x + \frac{5}{6} = \frac{{41}}{{30}}\)

\(\frac{4}{5}x = \frac{{41}}{{30}} - \frac{5}{6}\)

\(\frac{4}{5}x = \frac{8}{{15}}\)

\(x = \frac{2}{3}\)

Vậy \(x = \frac{2}{3}\).

b) \(\left| {2x + \frac{4}{3}} \right| = {\left( {0,45} \right)^{2023}}:{\left( {0,45} \right)^{2022}}\)

\(\left| {2x + \frac{4}{3}} \right| = {\left( {0,45} \right)^1}\)

\(\left| {2x + \frac{4}{3}} \right| = \frac{3}{{20}}\)

TH1: \(2x + \frac{4}{3} = \frac{3}{{20}}\)

\(2x = \frac{3}{{20}} - \frac{4}{3}\)

\(2x = \frac{{ - 71}}{{60}}\)

\(x = \frac{{ - 71}}{{120}}\).

Vậy \(x = \frac{{ - 71}}{{120}}\).

TH2: \(2x + \frac{4}{3} = \frac{{ - 3}}{{20}}\)

\(2x = \frac{{ - 3}}{{20}} - \frac{4}{3}\)

\(2x = \frac{{ - 89}}{{60}}\)

\(x = \frac{{ - 89}}{{120}}\).

Vậy \(x \in \left\{ {\frac{{ - 71}}{{120}};\,\,\frac{{ - 89}}{{120}}} \right\}\).

c) \(5 + \sqrt x = \frac{5}{2} + \frac{{27}}{8}\)

\(5 + \sqrt x = \frac{{47}}{8}\)

\(\sqrt x = \frac{{47}}{8} - 5\)

\(\sqrt x = \frac{7}{8}\)

\(x = \frac{{49}}{{64}}\).

Vậy \(x = \frac{{49}}{{64}}\).