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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

To find the value of x when given the numbers 14, 15, 16, and 17, we first need to clarify the context in which x relates to these numbers. Let’s analyze different scenarios: Statistical Average: If you want to determine the average (mean) of these numbers, you would add them together and divide by the … Read more

To find another factor of the expression y² + 10y + 24, we can start by using the given information that one of the factors is (y + 4). We can perform polynomial division to divide y² + 10y + 24 by (y + 4). Here’s how it works: Set up the division: y + … Read more