m2 + n2 = 29
m + n = 7
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If two graphs y = px\(^2\) + q and y = 2x\(^2\) -1 intersect at x = 2, find the value of p in terms q.
Divide: \(a^{3x} - 26a^{2x} + 156a^{x} - 216\) by \(a^{2x} - 24a^{x} + 108\).
Evaluate \(\frac{(0.14^2 \times 0.275)}{7(0.02)}\) to 3 decimal places.
If \(x = \frac{y}{2}\),evaluate\(\left(\frac{x^{3}}{y^{3}}+\frac{1}{2}\right) \div \left(\frac{1}{2} - \frac{x^{2}}{y^{2}}\right)\)
Given that \(p = 1 + \sqrt{2}\) and \(q = 1 - \sqrt{2}\), evaluate \(\frac{p^{2} - q^{2}}{2pq}\).
Simplify \((\sqrt[3]{64a^{3}})^{-1}\)
If the simple interest on N2000 after 9 months is N60, at what rate per annum is the interest charged?
Solve the equation 3 + 5x - 2x\(^2\) = 0
Find the volume (in cm\(^3\)) of the solid shown above
The area of a circle is 38.5cm2. Find its diameter [take \(\pi = \frac{22}{7}\)]
In the diagram, |PQ| = |PS| Which of the following statements is true?
The arc of a circle 50 cm long, subtends angle of 75° at the center of the circle. Find correct to 3 significant figures, the radius of the circle. Take \(\pi = \frac{22}{7}\)
The length of the parallel sides of a trapezium are 5cm and 7cm. If its area is 120cm\(^2\), find the perpendicular distance between the parallel sides
A tap leaks at the rate of 2cm\(^3\) per seconds. How long will it take the tap to fill a container of 45 liters capacity? (1 liters = 1000cm\(^3\))
The height of a pyramid on square base is 15cm. if the volume is 80cm^3, find the area of the square base.
A bicycle wheel of radius 42cm is rolled over a distance 66 meters. How many revolutions does it make?[Take \(\pi = \frac{22}{7}\)]