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If I is a 2 × 2 identity matrix, find the determinant of the matrix.
A varies directly as b\(^2\) when A = 4, b = 1. Find A when b = 2
Find the sum of the entries in the inverse of \(\begin{bmatrix} 1 & 2 \\ 3 & 5 \end{bmatrix}\)
The average weight of 15 iron bars is 1000 kg. If the heaviest iron bar is removed, the average weight is reduced by 5 kg. Find the weight in kg of the heaviest iron bar.
Y is partly constant and partly varies as x. When x = 3, y = 7 and when x = 5, y = 11. Find the constants of variation.
Find the number of permutations of the letters of the word SCHOOL.
Which of the following angles cannot be constructed using a protractor, a compass, and a sharpened pencil?
Given that Cos A = \(\frac{12}{13}\) for 0 ≤ A ≤ 90º, find Tan A.
Find the coordinates of the midpoint of line PQ given P(-3, 4) and Q(5, 6).
Simplify 125\(^{−\frac{1}{3}}\) × 49\(^{−\frac{1}{2}}\) × 10\(^0\)
Given that a * b = \(\frac{a + b}{\text{ab}}\) + (a - b). Find the value of 3 * 2
Solve the inequality 2x + 3 > 5x + 8
Solve the simultaneous equation \(\frac{\text{x}}{2}\) - \(\frac{\text{y}}{5}\) = 1 and y - \(\frac{\text{x}}{3}\) = 8
The set {1,2,3,4,5} is equivalent to
From the diagram above, find the area of the triangle PQR
(\(\sqrt{a} +\sqrt{8a})^2\) = 54 + b\(\sqrt{2}\), a and b are positive integers. Find the value of a and the value of b.
Make q the subject of the relation t = \(\sqrt{(\frac{pq}{r} - r^2q)}\)
The number of 144 students who registered for mathematics, physics, and chemistry in an examination are shown in the Venn diagram. How many registered for physics and mathematics?
The weights of 15 students in a class are given as 25, 30, 32, 30, 42, 45, 48, 50, 52, 51, 42, 38, 40, and 42. What is the mode of the given data?
A binary operation * is defined on a set of real numbers by x*y = x\(^y\) for all values of x and y, if x * 2 = x, find the possible values of x.