To solve for the value of x in an isosceles trapezoid, we first need to understand what an isosceles trapezoid is. An isosceles trapezoid has one pair of parallel sides (the bases), and the non-parallel sides (the legs) are of equal length. Let’s denote the lengths of the two bases as a and b, and … Read more
To find the nth term of the sequence 4, 16, 64, 256, we first need to observe the pattern in the sequence. At first glance, we can notice that each term appears to be a power of 4: The first term is 4, which is equal to 41 The second term is 16, equal to … Read more
To solve the system of equations given by y = x² and y = 2x + 7, we can use substitution. 1. Since both equations equal y, we can set them equal to each other: x² = 2x + 7 2. Next, rearrange the equation to form a standard quadratic equation: x² – 2x – … Read more
A vertical line has the same x-coordinate for every point on the line. This means that no matter what the y-coordinate is, the x-coordinate will remain constant. For a vertical line passing through the point (5, 2), the x-coordinate is 5. Therefore, the equation of the vertical line can be expressed as: x = 5 … Read more
To solve the problem, we need to find both the greatest and the least numbers that can be formed using the digits 6, 2, 7, 4, and 3, each used only once. Step 1: Finding the Greatest Number To form the greatest number, we should arrange the digits in descending order. The digits in descending … Read more
Definition of Exponential Function An exponential function is a mathematical function of the form: f(x) = a * bx, where: f(x) represents the output of the function. x is the exponent or input variable. a is a constant, known as the initial value, which is not equal to zero. b is the base of the … Read more
To express the area A of a rectangle as a function of the width w, given that the width is twice the length, we start with some basic definitions. Let the length of the rectangle be denoted as l and the width as w. According to the problem statement, the width is twice the length, … Read more
To name the angles in a geometric figure, you generally follow a few simple steps that help ensure clarity and precision. Here’s how you can do it: Identify the vertices: The points where two sides of the angle meet are called vertices. In a triangle, for example, each corner represents a vertex. Use letters to … Read more
To prove that tan(75°) = cot(75°) * 4, we start by recalling a fundamental relationship between tangent and cotangent along with the angle sum identities from trigonometry. First, let’s express tan(75°). We can rewrite it as: tan(75°) = tan(45° + 30°) Using the tangent angle sum identity, we have: tan(A + B) = (tanA + … Read more
The given sequence is 12, 6, 3. To find the explicit formula for this geometric sequence, we first need to identify the common ratio between the terms. In a geometric sequence, each term is obtained by multiplying the previous term by a constant, known as the common ratio. Let’s determine the common ratio (r): From … Read more