To find a rational number equivalent to 5/7, we can simply multiply both the numerator and the denominator of the fraction by the same non-zero integer. This process will create an equivalent fraction because it maintains the same ratio. For example, if we multiply both the numerator (5) and the denominator (7) by 2, we … Read more
The property of real numbers demonstrated in the sequence 3, 5, 6, 3, 5, 6 is known as the Identity Property of Addition. This property states that when you add a number to zero, the result is the original number. However, in this context, the focus is not solely on the addition of zero but … Read more
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