In an isosceles triangle, at least two sides are of equal length, and the angles opposite those sides are equal. Given that angle B measures 130 degrees, we can deduce important information about angles A and C. Since the sum of all angles in any triangle is always 180 degrees, we can first calculate the … Read more
To find the range of the function f(x) = 2x + 5 for the specific domain values of 2, 4, and 7, we will first calculate the output values by substituting each of the domain values into the function. For x = 2: f(2) = 2(2) + 5 = 4 + 5 = 9 For … Read more
To solve the quadratic equation 3x² + 5x + 1 = 0 using the quadratic formula, we start by identifying the coefficients in the standard form of a quadratic equation: ax² + bx + c = 0. In this equation: a = 3 b = 5 c = 1 The quadratic formula is given by: … Read more
Finding the Closest Point on a Line to the Origin To find the point on the line given by the equation y = 5x – 2 that is closest to the origin (0, 0), we can use the distance formula. The goal is to minimize the distance from any point (x, y) on the line … Read more
To find the inverse of the equation 2x + 22 = 87y, we need to solve for y in terms of x, and then interchange the roles of x and y. Here’s how we can proceed step-by-step: Start with the original equation: 2x + 22 = 87y Isolate y: Subtract 22 from both sides: 2x … Read more
To solve the equation 3×4 + 5×2 = 0, we can start by factoring out the common term. First, notice that both terms on the left side contain a factor of x2. We can factor this out: 3×4 + 5×2 = x2(3×2 + 5) = 0 Next, we set each factor equal to zero: x2 … Read more
To find the 42nd term of an arithmetic sequence where the first term a1 = 12 and the 27th term a27 = 66, we can follow these steps: 1. **Determine the common difference**: In an arithmetic sequence, the nth term can be calculated with the formula: an = a1 + (n – 1) * d … Read more
To find the two numbers, let’s denote them as x and y. According to the problem, we have the following two equations: The sum of the two numbers: x + y = 12 The difference of the two numbers: x – y = 4 We can solve this system of equations step by step. Step … Read more
A scalene triangle is a type of triangle in which all three sides and all three angles are different. This means that each angle is unique and no two sides are of equal length. Because of this, scalene triangles can take on a variety of shapes, producing figures that may look quite irregular compared to … Read more