(a) Evaluate : \(2 \div (\frac{64}{125})^{-\frac{2}{3}}\)
(b) The lines \(y = 3x + 5\) and \(y = - 4x - 1\) intersect at a point k. Find the coordinates of k.
(b) The lines \(y = 3x + 5\) and \(y = - 4x - 1\) intersect at a point k. Find the coordinates of k.
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Correct Answer: Option n
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)
\(y = 3(-\frac{6}{7}) + 5 = -\frac{18}{7} + \frac{35}{7}\)
= \(\frac{17}{7}\)
\(k = (x, y) = (-\frac{6}{7}, \frac{17}{7})\)
(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)
\(y = 3(-\frac{6}{7}) + 5 = -\frac{18}{7} + \frac{35}{7}\)
= \(\frac{17}{7}\)
\(k = (x, y) = (-\frac{6}{7}, \frac{17}{7})\)