devyy 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
The slope-intercept form of a line is expressed with the equation: y = mx + b Where: y is the dependent variable (the value of y for given x) m represents the slope of the line x is the independent variable b is the y-intercept (the value of y when x is 0) In this … Read more
To solve the equation x² + 8x + 3 = 0 by completing the square, we first need to rewrite the equation in a more manageable form. 1. Start with the original equation: x² + 8x + 3 = 0 2. To complete the square, we want to focus on the quadratic and linear terms, … Read more
To determine the measure of angle ABD in trapezoid ABCD, we need to understand the properties of trapezoids and the relationships between their angles. A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. In our case, let’s assume that sides AB and CD are the parallel sides. 1. **Identify … Read more