To find the equation of a line that passes through the points (3, 4) and (2, 1), we will follow a systematic approach that involves determining the slope and then using it to find the y-intercept. Step 1: Calculate the Slope (m) The slope (m) of a line passing through two points (x1, y1) and … Read more
Finding the Sum of Polynomials To find the sum of the polynomials 4x³ + 2x² + 4x + 3 and 7x³ + 4x² + 7x + 8, you need to combine like terms. This involves adding the coefficients of the terms that have the same degree. Step 1: Identify Like Terms Let’s break down both … Read more
To find the value of f(x) given the function f(x) = 6x + 4, we can substitute each value of x into the equation and calculate the resulting f(x). Let’s break it down: When x = 8: f(8) = 6(8) + 4 f(8) = 48 + 4 f(8) = 52 When x = 2: f(2) … Read more
The function h(x) = 5x + 9 is a linear function, which means we can easily determine its domain, range, and asymptotes. Domain: The domain of a linear function is all real numbers. This means that you can input any value of x into the function without any restrictions. Mathematically, this can be expressed as: … Read more
To simplify the expression 1 + 3i – 2 + 5i, we need to combine like terms, specifically the real parts and the imaginary parts separately. 1. Start by identifying the real parts and imaginary parts of the expression: Real parts: 1 and -2 Imaginary parts: 3i and 5i 2. Combine the real parts: 1 … Read more
To find the measures of two complementary angles that are in the ratio of 1 to 5, we first need to understand what complementary angles are. Complementary angles are two angles whose sum is 90 degrees. Let’s denote the smaller angle as x. Because the angles are in the ratio of 1 to 5, the … Read more
Finding the Roots of the Function f(x) = x³ + 3x² + x + 3 The Remainder Theorem states that for any polynomial f(x), if you divide it by (x – c), the remainder is f(c). This theorem not only helps in finding the remainder but also indicates if c is a root of the … Read more
To find the prime factorization of the number 18, we start by identifying the prime numbers that can multiply together to produce this number. Prime numbers are those greater than 1 that have no divisors other than 1 and themselves. 1. **Start with the smallest prime number, which is 2.** Since 18 is an even … Read more
To determine the probability of rolling a sum of 5 or lower with two six-sided dice, we first need to consider the possible outcomes when two dice are rolled. Each die has 6 sides, so when rolling two dice, there are a total of 6 x 6 = 36 possible outcomes. Next, let’s identify the … Read more
In the realm of mathematics, the term used to describe something that cannot be divided is indivisible. An indivisible item is one that remains whole and cannot be separated into smaller parts without losing its fundamental identity. To elaborate, in mathematics, the concept of indivisibility pertains primarily to integers. For instance, prime numbers are often … Read more