Understanding Common Factors To determine the common factors of the numbers 15, 45, and 90, we first need to identify the factors of each individual number. Factors of Each Number Factors of 15: 1, 3, 5, 15 Factors of 45: 1, 3, 5, 9, 15, 45 Factors of 90: 1, 2, 3, 5, 6, 9, … Read more
To classify the expressions x³y and 5xyz, we need to consider two key aspects: their degree and the number of terms they contain. 1. Classifying the Expression x³y The expression x³y consists of: Terms: It is a single term. Degree: The degree of a term is calculated by summing the exponents of all its variables. … Read more
The area under the standard normal curve between z = 0 and z = 3 can be found using statistical tools and properties of the normal distribution. The standard normal distribution is a symmetrical bell-shaped curve centered at a mean of 0 and a standard deviation of 1. To find the area between the z-scores … Read more
Prime numbers are numbers greater than 1 that cannot be formed by multiplying two smaller natural numbers. They have exactly two distinct positive divisors: 1 and themselves. Let’s identify the prime numbers between 12 and 15: 12: Not a prime number (divisors: 1, 2, 3, 4, 6, 12) 13: Prime number (divisors: 1, 13) 14: … Read more
The average rate of change of a function over a specified interval provides a measure of how much the function’s output value changes, on average, for each unit increase in the input value over that interval. To find the average rate of change of the function f(x) = 42x + 1 from x = 0 … Read more
To find the roots of the polynomial equation 4×5 + 12×4 + 5×3 + 6x + 2 = 0, we can set up a system of equations based on the context of finding its zeros using numerical methods or algebraic manipulation. Firstly, the given polynomial can be rearranged as: f(x) = 4×5 + 12×4 + … Read more
Finding the Equation of a Line To find the equation of a line that passes through two given points, we can use the point-slope form or the slope-intercept form of a line. In this case, we will first determine the slope of the line using the two points provided: (0, 1) and (2, 5). Step … Read more
To prove that if the sum of the digits of a number is divisible by 3, then the number itself is also divisible by 3, we can utilize modular arithmetic and the properties of numbers in base 10. Let’s denote a number as N. We can express N in terms of its digits. For a … Read more
The leading coefficient of a quadratic function is the coefficient of the term with the highest degree. In the case of the quadratic function f(x) = 2x² + 5x + 4, the term with the highest degree is 2x². To identify the leading coefficient, we look at the coefficient in front of the x² term. … Read more
To determine which expression is a polynomial with given roots, we can use the fact that if a polynomial has roots, then the polynomial can be formed by multiplying factors corresponding to those roots. In this case, we have the roots as √3, √3, and 2. This means the polynomial can be represented as: (x … Read more