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To find the equation of a line that passes through two points, you can follow these steps: Identify the points: Let’s say the two points are (x_1, y_1) and (x_2, y_2). Calculate the slope: The slope m of the line that passes through these points is calculated using the formula: m = (y_2 – y_1) … Read more

To find the surface area of a cylinder, you can use the formula: Surface Area = 2πr² + 2πrh Where: r is the radius of the cylinder. h is the height of the cylinder. In your case, the radius (r) is 3 feet and the height (h) is 4 feet. Let’s break this down step … Read more

Let’s assume Ramesh bought two boxes for a total of Rs 1300. We can denote the cost price of the first box as x and the cost price of the second box as y. According to the problem: The total cost of both boxes is: x + y = 1300 (1) The first box is … Read more

To find the height of a square pyramid given its volume and the length of its base side, we can use the formula for the volume of a pyramid: Volume = (1/3) × Base Area × Height For a square pyramid, the base area can be calculated as: Base Area = side × side = … Read more

To find the midpoint of a line segment defined by two endpoints in a coordinate plane, you can use the midpoint formula, which is quite simple and effective. The formula for the midpoint M of a segment with endpoints (x1, y1) and (x2, y2) is given by: M = ( (x1 + x2) / 2 … Read more

To find the product of two numbers a and b when their highest common factor (HCF) is 5 and their least common multiple (LCM) is 200, we can use the relationship between these three values. The product of the two numbers can be determined using the formula: Product of a and b = HCF(a, b) … Read more

When we modify the parent function f(x) = x^4 to f(2x), we are essentially applying a transformation that affects the shape and behavior of the graph. Specifically, this transformation is a horizontal compression or “squeezing” of the function’s graph. To understand this effect, let’s break it down: Original Function: The graph of f(x) = x^4 … Read more

To convert the phrase “nine crore five lakh forty one” into its numerical representation, we need to break down the components: One Crore is equal to 10,000,000 (ten million). Five Lakh refers to 500,000 (five hundred thousand). Forty One is simply 41. Now, let’s add them together: Nine Crore = 9 x 10,000,000 = 90,000,000 … Read more

To write the quadratic function f(x) = x² + 8x + 20 in the form f(x) = a(x – h)² + k, we’ll follow a process called completing the square. This technique allows us to express the quadratic in vertex form, making it easier to identify its vertex. 1. **Starting with the equation**: We have … Read more

To find the product of the expression x2 * 2x * 3 * 4 * x2 * 5x * 6, you should follow a step-by-step approach to combine the terms properly. Below is a detailed breakdown of the process. 1. **Identify and group the like terms:** In the expression, we have terms involving ‘x’ and … Read more