To simplify the expression i^(233) * (1 + i), let’s break it down into parts. Understanding the Powers of i The imaginary unit i is defined as the square root of -1. The powers of i follow a cyclic pattern: i^1 = i i^2 = -1 i^3 = -i i^4 = 1 This cycle repeats … Read more
The given sequence is 3, 6, 12, 24. To find the 12th term, we first need to identify the pattern in the sequence. Looking at the sequence, we can observe the following: The first term is 3. The second term (6) is obtained by multiplying the first term (3) by 2. The third term (12) … Read more
To find the ordered pairs that solve the equation 2xy = 9, we first need to express one variable in terms of the other. Let’s solve for y. Starting with the equation: 2xy = 9 We can isolate y by dividing both sides by 2x (assuming x is not zero): y = 9 / (2x) … Read more
To find the slope of a line that is perpendicular to another line, we can use a simple rule from geometry regarding slopes. If the slope of the original line is denoted as m, then the slope of a line that is perpendicular (at a right angle) to it is given by the negative reciprocal … Read more
To determine if a number is divisible by 3, you can follow a couple of simple methods that are easy to use and understand. Here’s a detailed explanation of these methods: 1. The Rule of Sum of Digits The most common method to check for divisibility by 3 is to add up all the digits … Read more
Finding the Vertex of the Quadratic Function The vertex of a quadratic function is a crucial point that represents either the maximum or minimum value of the function. In the case of the quadratic function, it can be expressed in the standard form as: f(x) = ax2 + bx + c In your question, however, … Read more
Determining whether a graph is symmetric with respect to the origin involves a straightforward examination of the function represented by the graph. A function exhibits origin symmetry if, for every point (x, y) on the graph, the point (-x, -y) is also on the graph. Here’s a step-by-step method to check for this symmetry: Identify … Read more
If A is related to B and B is related to C, we can infer that there is a transitive relationship between A and C. This means that the connection that A has with B does not just end there; it extends to C as well. To illustrate this, consider A, B, and C as … Read more
To calculate the slope of a line that passes through two points, you can use the formula: slope (m) = (y2 – y1) / (x2 – x1) In this case, the two points are (3, 4) and (4, 1). Here, we designate: (x1, y1) = (3, 4) (x2, y2) = (4, 1) Now, we can … Read more
The area of a rectangle can be determined using the formula: Area = Length × Width In this case, the width is 12 feet and the length is 10 feet. Plugging these values into the formula gives: Area = 10 feet × 12 feet Now, calculating that: Area = 120 square feet Therefore, the area … Read more