(a) Evaluate : \(2 \div (\frac{64}{125})^{-\frac{2}{3}}\) (b) The lines \(y = 3x + 5\) and

Explanation

(a) \((\frac{64}{125})^{-\frac{2}{3}} = (\frac{125}{64})^{\frac{2}{3}}\)

= \((\frac{5}{4})^{3})^{\frac{2}{3}} \)

= \((\frac{5}{4})^{2}\)

= \(\frac{25}{16}\)

\(\therefore 2 \div (\frac{64}{125})^{-\frac{2}{3}} = 2 \div \frac{25}{16}\)

= \(2 \times \frac{16}{25}\)

= \(\frac{32}{25}\)

(b) \(3x + 5 = - 4x - 1\)

\(3x + 4x = - 1 - 5\)

\(7x = - 6\)

\(x = -\frac{6}{7}\)

\(y = 3x + 5\) ( You can use any of the given equations to get y)

\(y = 3(-\frac{6}{7}) + 5 = -\frac{18}{7} + \frac{35}{7}\)

= \(\frac{17}{7}\)

\(k = (x, y) = (-\frac{6}{7}, \frac{17}{7})\)