devyy To find the value of the product of the complex numbers 3 + 2i and 3 + 2i, we will use the distributive property (also known as the FOIL method when dealing with binomials). First, we rewrite the expression: (3 + 2i) × (3 + 2i) Now, we apply the distributive property: First terms: 3 … Read more
To find the area of a circle using its diameter, you can follow these simple steps: Understand the formula: The area A of a circle is calculated using the formula: A = πr², where r is the radius of the circle. The radius is half the diameter. Determine the radius: If you have the diameter … Read more
Finding the Vertex, Axis of Symmetry, and Intercepts of the Quadratic Equation The quadratic equation we have is y = x² + 6x + 5. To analyze this quadratic function, we will determine its vertex, axis of symmetry, and intercepts systematically. 1. Finding the Vertex The vertex of a parabola given in standard form y … Read more
To determine the number that completes the pattern, we first need to analyze the given sequence: 66, 73, 13, 21, 52, 10, 20. Let’s break down the pairs in the sequence: 66 to 73: The difference is +7. 73 to 13: The difference is -60. 13 to 21: The difference is +8. 21 to 52: … Read more
To calculate the total number of hours you would work in a year, you can use a simple formula. Since you work 40 hours each week and there are 52 weeks in a year, you can multiply these two numbers together: Number of hours per week: 40 hours Number of weeks in a year: 52 … Read more
The standard form of the equation of a circle is expressed as: (x – h)² + (y – k)² = r² In this equation: (h, k) represents the center of the circle. r denotes the radius of the circle. To write the standard form, you need to determine the center and radius of the circle. … Read more
A regular pentagon has several interesting properties, particularly when it comes to its lines of symmetry. Here are the true statements regarding the lines of symmetry of a regular pentagon: A regular pentagon has exactly five lines of symmetry. Each line of symmetry passes through one vertex and the midpoint of the opposite side. The … Read more
To find the inverse of the function f(x) = 4x + 12, we follow a series of steps: Replace f(x) with y: Start by rewriting the function as: y = 4x + 12 Swap x and y: To find the inverse, interchange x and y: x = 4y + 12 Solve for y: Now, solve … Read more
To solve the equation 53b3 + 2b2 + 5 = 2b3 + 2, we first need to rearrange the equation so that all terms are on one side. This is a standard practice in solving polynomial equations. Let’s start by moving all terms to one side: 53b3 + 2b2 + 5 – 2b3 – 2 … Read more
The discriminant of a quadratic equation provides valuable information about the nature of its roots. For the general form of a quadratic equation, ax² + bx + c = 0, the discriminant (D) is calculated using the formula: D = b² – 4ac. In the case of the quadratic equation 2x² + 3x + 5 … Read more