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To solve the absolute value inequality |2x – 4| < 8, we need to break it down into two separate inequalities. The absolute value expression |A| < B indicates that the value of A lies between -B and B. In this case, our A is 2x – 4 and our B is 8. We can ... Read more

To solve for the value of y when x = 0 in the equation xy + 5ey + 5e = 0, we start by substituting x with 0 in the equation. Substituting gives us: 0*y + 5ey + 5e = 0 Since 0*y is equal to 0, the equation simplifies to: 5ey + 5e = … Read more

A borrows Rs. 800 at a simple interest rate of 12% per annum, while B borrows Rs. 910 at a simple interest rate of 10% per annum. To find the total interest paid by each borrower, we use the formula for simple interest: Simple Interest (SI) = (Principal × Rate × Time) / 100 Assuming … Read more

Finding Missing Side Lengths in a Triangle When working with triangles, it’s often necessary to determine the lengths of missing sides. There are various methods to achieve this, depending on the information provided. Here’s a concise guide to help you through the process: 1. Using the Pythagorean Theorem If you’re dealing with a right triangle … Read more

To convert the length from meters to centimeters, you can use the conversion factor that 1 meter is equal to 100 centimeters. Therefore, to convert 0.564 meters to centimeters, you simply multiply it by 100: Calculation: 0.564 meters × 100 = 56.4 centimeters So, Jim’s measurement of 0.564 meters is equivalent to 56.4 centimeters.

Finding the Side Lengths of Two Squares To solve the problem, let’s denote the side lengths of the two squares as s1 and s2. We know from the problem: The sum of their areas: s12 + s22 = 468 The difference of their perimeters: 4s1 – 4s2 = 24 From the perimeter equation, we can … Read more

To calculate the total cash received from the issuance of bonds, we can follow a simple formula: Total Cash Received = Number of Bonds x Price per Bond In this case, you have: Number of Bonds: 1,000,000 Price per Bond: 101 Now, plugging the numbers into the formula: Total Cash Received = 1,000,000 x 101 … Read more

To find the area of a regular hexagon, you can use the formula: Area = (3√3 / 2) × s² Here, s is the length of a side of the hexagon. Since the side length of your regular hexagon is 10 units, you will substitute s with 10: Area = (3√3 / 2) × 10² … Read more

Graphing the Solution of y = x² – 2x To graph the equation y = x² – 2x, you can follow these steps: 1. Understand the Equation This equation is a quadratic equation in the standard form of y = ax² + bx + c, where: a = 1 (the coefficient of x²) b = … Read more