Questions

The smallest two-digit composite number is 10

Understanding the Difference Between Two Polynomials When comparing two polynomials, we need to perform subtraction to find the difference between them. In this case, we are looking at: Polynomial A: 9x² + 8x Polynomial B: 2x² + 3x Step-by-Step Subtraction The difference can be calculated as: (9x² + 8x) – (2x² + 3x) Distributing the … Read more

Transformations from f(x) to g(x) The graphs of the two functions, f(x) = 7x² and g(x) = 35x² + 5, can be understood in terms of several key transformations: 1. Vertical Stretch The first transformation involves a vertical stretch of the graph. The coefficient of x² in f(x) is 7, while in g(x) it is … Read more

To determine the value of x for the triangle with sides 3x, 5x, and 12 (assuming there’s a typo in the original question about sides that can also be interpreted as x and 20), we need to satisfy the condition for the triangle to be isosceles. An isosceles triangle has at least two sides that … Read more

To prove that if n is an integer and 3n² is even, then n must be even, we can use a direct proof by contradiction. 1. **Understanding Even and Odd Numbers:** An integer is considered even if it can be expressed as 2k, where k is an integer. An integer is odd if it can … Read more

To solve the question ’15 is 30 of what number?’, we can start by setting up a simple equation based on the relationship described. The question implies we’re looking for a number (let’s call it X) such that 30% of that number equals 15. We can express this mathematically as: 0.30 * X = 15 … Read more

To express the relationship where y varies directly as x and inversely as the square of z, we can use the concept of proportionality in mathematics. When we say that y varies directly as x, it means that as x increases, y also increases. This can be expressed as: y = k * x where … Read more

The decimal equivalent of the fraction 1/3 can be determined by performing the division of 1 by 3. When you divide, you get: 0.3333… (and so on) This decimal is a repeating decimal, meaning that the digit 3 continues infinitely. In mathematical notation, it is often represented as: 0.3 To write this in a more … Read more

To solve the equation 2cos(2x) * cos(x) = 1, we will follow a series of steps: Start by simplifying the equation: We begin with: 2cos(2x) * cos(x) – 1 = 0 Next, we can use the double angle identity: cos(2x) = 2cos²(x) – 1 By substituting this into our equation, we have: 2(2cos²(x) – 1) … Read more