The sum of an arithmetic sequence can be found using the formula: Sn = (n/2) * (a + l) Where: Sn = Sum of the first n terms n = Number of terms a = First term l = Last term In this case, we have the following: a = 3 (the first term) l … Read more
To prove that the product of √2 and √5 is irrational, we can use a proof by contradiction. This method helps us show that assuming the opposite leads to an impossible situation. 1. **Assumption**: First, let’s suppose that √2 * √5 is rational. This means we can express it as a fraction of two integers … Read more
Creating a graph for the linear equation y = 2x + 6 involves a few straightforward steps. Here’s a detailed guide: 1. Understand the Equation This equation is in the slope-intercept form, which is generally written as y = mx + b. In this equation: m (the slope) is 2, which indicates that for every … Read more
When we talk about an expression like x0, we’re delving into a fundamental rule of exponents in mathematics. This rule states that any non-zero number raised to the power of 0 is equal to 1. So, regardless of what x represents (as long as it is not zero), the expression x0 will always equal 1. … Read more
The x-intercept of a graph is the point where the line crosses the x-axis. This occurs when the value of y is zero. To find the x-intercept for the equation 4x + 5y = 40, you can follow these steps: Substitute y = 0 into the equation: 4x + 5(0) = 40 This simplifies to: … Read more
To determine the most precise name for the quadrilateral ABCD with vertices A(3, 2), B(1, 4), C(4, 4), and D(2, 2), we follow a systematic approach involving basic geometry principles. First, let’s plot the points to visualize the shape: A(3, 2) B(1, 4) C(4, 4) D(2, 2) Next, we calculate the lengths of the sides … Read more
The sequence given is 2, 8, 14, 20, 26. To find the common difference between successive terms, we need to subtract each term from the one that follows it. Let’s calculate the differences: 8 – 2 = 6 14 – 8 = 6 20 – 14 = 6 26 – 20 = 6 From our … Read more
To prove the identity cot(a) – cot(b) = (1 – cota * cotb) / (cota * cotb), we can start by manipulating the left side of the equation. Recall that the cotangent function is defined as: cot(x) = cos(x) / sin(x) Thus, we can express cot(a) and cot(b) as: cot(a) = cos(a) / sin(a) cot(b) … Read more
To find the slope of a line that passes through two points, you can use the slope formula, which is: Slope (m) = (y2 – y1) / (x2 – x1) In this case, you have the points (1, 4) and (0, 1). We can label these points as follows: (x1, y1) = (1, 4) (x2, … Read more
To compute the least common multiple (LCM) of √2 and √3, we need to understand how the LCM works with irrational numbers. The LCM of two numbers is the smallest number that is a multiple of both. For our irrational numbers, we can express them in terms of their square roots: √2 = 21/2 √3 … Read more