When we have an angle measuring 130 degrees, there are several geometric relationships we can explore in relation to angle 3, especially depending on the context in which both angles are presented. Let’s break this down: Supplementary Angles: If angle 3 is located in such a way that it is adjacent to the 130-degree angle, … Read more
The average rate of change of a function between two points is calculated using the formula: Average Rate of Change = \( \frac{f(b) – f(a)}{b – a} \) In this case, we are looking at the function: f(x) = 2x + 1 And we want to find the average rate of change from \(x = … Read more
To convert the exponential equation 2x = 8 into its logarithmic form, we need to understand the relationship between the two forms. An exponential equation is typically represented as ab = c, which can be rewritten in logarithmic form as loga(c) = b. In this case, we have the following: 1. Identify the base (a), … Read more
To find the x-coordinate of the vertex of the parabola given by the equation y = 3x² + 9x, we can use the vertex formula, which is derived from the standard form of a quadratic equation y = ax² + bx + c. In this equation, a is the coefficient of x², b is the … Read more
To simplify the expression 5×2 + 3x + 4 + 5×2 + 5x + 1, we will follow these steps: Identify like terms: We will group the terms that are similar. The expression consists of: Quadratic terms: 5×2 and 5×2 Linear terms: 3x and 5x Constant terms: 4 and 1 Combine the like terms: For … Read more
To simplify the expression (x² + 12x + 35) / (3x + 15), we will follow these steps: Factor the Numerator: We need to factor the quadratic expression in the numerator: Look for two numbers that multiply to the constant term, 35, and add up to the linear coefficient, 12. The numbers 5 and 7 … Read more
To solve for the measure of angle EBC in circle O, where AC and BE are diameters, we need to follow a few steps based on the properties of circles and the relationships between arcs and angles. 1. **Understanding Diameters and Arcs**: Since AC and BE are diameters of circle O, this means they divide … Read more
To solve the problem of finding all possible values of x where the difference between x and 9 is 6, we can represent this mathematically. The statement ‘the difference between x and 9 is 6’ can be translated into the following equation: |x – 9| = 6 This absolute value equation implies two separate cases: … Read more
To find the area of a circle, you can use the formula: A = πr², where: A is the area of the circle r is the radius of the circle In this case, the radius (r) is 9 yards. So, we plug that value into the formula: A = π(9)² Calculating the square of the … Read more
An ellipse centered at the origin (0,0) can be represented by the standard form of its equation. The general equation of an ellipse in standard form is: 1. For a horizontally oriented ellipse: \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) 2. For a vertically oriented ellipse: \( \frac{x^2}{b^2} + \frac{y^2}{a^2} = 1 \) In this … Read more