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To find the solutions of the equation 2x² + 3x + 5 = 0, we can use the quadratic formula: x = (-b ± √(b² – 4ac)) / (2a) In this equation: a = 2 b = 3 c = 5 First, we’ll calculate the discriminant (b² – 4ac): Discriminant = (3)² – 4(2)(5) This … Read more

Calculating the deviation from the mean for each item in a dataset involves a few steps, but don’t worry, it’s quite straightforward! Let’s break it down: Calculate the Mean: First, you need to find the mean (average) of your data items. To do this, add all the data items together and then divide that sum … Read more

To find the standard form of the equation of an ellipse given its foci and vertices, we can follow these steps: Step 1: Identify the Foci and Vertices The foci of the ellipse are located at (0, 2) and (0, -2). The vertices are at (0, 8) and (0, -8). The foci are vertical and … Read more

The orthocentre of a triangle is the point where all three of its altitudes intersect. An altitude in a triangle is a perpendicular line segment drawn from a vertex to the line that contains the opposite side. This point of concurrency is unique for each triangle, regardless of whether it is acute, right, or obtuse. … Read more

To find the value of tan(8), we start with the given information: sec(8) = \( \frac{\sqrt{37}}{6} \) sin(8) = 0 Firstly, we recall the relationship between the secant, cosine, and sine functions: sec(θ) = \( \frac{1}{cos(θ)} \) Therefore, if we know that sec(8) = \( \frac{\sqrt{37}}{6} \), we can express this in terms of the … Read more

The statement ‘the sun rises in the east’ is true. This phenomenon occurs due to the Earth’s rotation on its axis. As the Earth rotates, different parts of the planet are exposed to sunlight, creating the cycle of day and night. Specifically, the Earth spins from west to east, which is why the sun appears … Read more

To solve for fg(x) given the functions f(x) = x^4 and g(x) = 2x + 3, we need to follow a few steps: First, substitute x = 2 into the function g(x). Then, take the result from g(2) and substitute it into the function f(x) to find fg(2). Step 1: Evaluate g(2) Substituting x = … Read more

To solve the quadratic equation x² + 10x + 25 = 35, we will first simplify the equation by moving all terms to one side. 1. Subtract 35 from both sides: x² + 10x + 25 – 35 = 0 This simplifies to: x² + 10x – 10 = 0 2. Next, we can use … Read more

To find the equation of the line that passes through the points (0, 2) and (4, 6), we can follow these steps: Identify the points: We have two points: (x1, y1) = (0, 2) and (x2, y2) = (4, 6). Calculate the slope (m): The slope of a line through two points is given by … Read more

To find the terminal point (px, y) on the unit circle corresponding to the angle t = \frac{7\pi}{6}, we follow these steps: 1. Understanding the Unit Circle The unit circle is a circle with a radius of 1 centered at the origin (0, 0) of a coordinate plane. Any point on the unit circle can … Read more