No, the ratios of 3 to 4 and 4 to 3 are not the same. Let’s break it down to understand why. A ratio expresses the relationship between two quantities. When we say the ratio of 3 to 4, we can express this mathematically as: Ratio of 3 to 4: 3:4 or 3 ÷ 4 … Read more
Finding the Composition of Functions gf Given the functions: f(x) = 3x + 6 g(x) = x + 2 We want to find the composition gf, which means we need to substitute f(x) into g(x). Step 1: Substitute f(x) into g(x) First, let’s identify the function g with f(x) as input: g(f(x)) = g(3x + … Read more
A number that has more than two distinct factors is called a composite number. In simple terms, a composite number can be divided evenly by numbers other than just 1 and itself, meaning it has multiple positive divisors. To understand this better, let’s consider the definition of the two primary types of numbers in terms … Read more
Solving the Quadratic Equation: 5x + 6x² + 3 = 0 To solve the quadratic equation 5x + 6x² + 3 = 0, we first need to rearrange it in the standard form: 6x² + 5x + 3 = 0 The quadratic formula is given by: x = (-b ± √(b² – 4ac)) / 2a … Read more
To solve the system of equations y = 3x + 7 and y = x + 9, we will set the two equations equal to each other since both are equal to y. Thus, we can write: 3x + 7 = x + 9 Next, we’ll isolate the variable x. Start by subtracting x from … Read more
When we talk about numbers that have 5 as a factor, we are referring to numbers that are divisible by 5. One important characteristic of such numbers is their ones place digit. A number is divisibly specifically by 5 if its last digit (the ones place) is either 0 or 5. This is due to … Read more
To find the value of x in the equation 8x + 2y = 48 when y = 4, we start by substituting the value of y into the equation. 1. Substitute y in the equation: Original Equation: 8x + 2y = 48 Substituted Equation: 8x + 2(4) = 48 2. Now, simplify the equation: Calculate … Read more
Naming segments and lines might seem similar, but there are important distinctions to consider. When naming a line, you typically focus on a single continuous path or direction. Lines are often referenced in the context of geometry, programming, or art to denote a straight or curved connection between two points. On the other hand, a … Read more
To determine if Isiah is correct that 5a² is the greatest common factor (GCF) of the polynomial a³ + 25a²b⁵ + 35b⁴, we need to examine each term of the polynomial and identify the common factors. The polynomial consists of three terms: a³ 25a²b⁵ 35b⁴ Now, let’s break down each term to find their factors: … Read more
To simplify the complex number 134i into standard form, we need to express it as a + bi, where a is the real part and b is the imaginary part. In this case, the number 134i consists only of an imaginary part, which means: a = 0 (since there is no real component) b = … Read more