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The equation you provided, x + y = 0, represents an interesting property of addition known as the Inverse Property of Addition. In this specific situation, you have: x = 1 + 2i y = -1 – 2i When you add these two complex numbers together: x + y = (1 + 2i) + (-1 … Read more

The area of a triangle can be calculated using the formula: Area = 0.5 × base × height. However, when two sides of a triangle are known, we can also use another formula that incorporates the sine of the angle between those two sides. The formula for the area when two sides and the included … Read more

Solving the System of Equations To solve the given system of equations: Equation 1: x² + y² = 25 Equation 2: y² = x² + 7 We’ll start by substituting Equation 2 into Equation 1. From Equation 2, we can express y² in terms of x²: y² = x² + 7 Now let’s substitute this … Read more

To demonstrate that if events A and B are independent, then A and B are also independent, we first need to define what it means for two events to be independent. Two events A and B are said to be independent if the occurrence of one does not affect the occurrence of the other. Mathematically, … Read more

To solve the problem, let’s define the two-digit number as 10a + b, where a is the tens digit and b is the units digit. According to the first part of the problem, the sum of the digits is five. We can represent this with the equation: a + b = 5 Next, when the … Read more

To simplify the expression 8 × 9 × 16 × 7, we can break it down step by step. First, let’s perform the multiplications in pairs: 8 × 9 = 72 16 × 7 = 112 Now, we can take the results from the pairs and multiply them together: 72 × 112 Next, we’ll calculate … Read more

To determine how many subsets of a set with 100 elements contain more than one element, we can begin by understanding some foundational principles of set theory. A set with n elements has a total of 2n subsets. This is because for each element in the set, you can choose to either include it in … Read more

To determine the range of the function f(x) = 12 – 3x, we need to evaluate this function for each value in the specified domain: -4, -2, 0, 2, and 4. Now let’s calculate the function for each domain value: For x = -4: f(-4) = 12 – 3(-4) = 12 + 12 = 24 … Read more

To understand the relationship between the rate at which the altitude of a triangle is increasing and the rate at which the area is increasing, we need to consider the formula for the area of a triangle: Area = (1/2) × base × height In this scenario, we are given: The altitude (height) of the … Read more

To find a unit vector that has the same direction as a given vector, you need to first understand what a unit vector is. A unit vector is a vector with a magnitude (length) of one. The process of finding a unit vector involves two key steps: determining the magnitude of the original vector and … Read more