To find the next number in the sequence 3, 6, 4, 8, 6, 12, 10, we first need to analyze the pattern of the sequence. Looking at the numbers, let’s break them down: 3 to 6: This is an increase of 3. 6 to 4: This is a decrease of 2. 4 to 8: This … Read more
To solve the equation x4 + 5×2 – 36 = 0 using factoring, we start by making a substitution to simplify our approach. Let’s set y = x2. This transforms our equation into a quadratic form: y2 + 5y – 36 = 0 Next, we will factor the quadratic equation. We need to find two … Read more
To find the sum of a geometric sequence, we need to use the formula: Sn = a (1 – rn) / (1 – r) Where: Sn is the sum of the first n terms. a is the first term of the sequence. r is the common ratio of the sequence. n is the number of … Read more
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