To factor the expression 1331×3 + 8y3, we can recognize that this is a sum of cubes. The general formula to factor a sum of cubes a3 + b3 is: (a + b)(a2 – ab + b2) In this case, we can identify: a = (11x) (since 1331 = 113) b = (2y) (since 8 … Read more
To find the slope of the line that passes through two points, you can use the slope formula: Slope (m) = (y2 – y1) / (x2 – x1) In this case, we have two points: (1, 2) and (3, 8). Let’s identify the coordinates: (x1, y1) = (1, 2) (x2, y2) = (3, 8) Now, … Read more
The given sequence is defined with the first term as a1 = 3 and follows the recurrence relation an = 2an-1 – 12 for n > 1. To determine the first three terms, we can calculate them step by step: Term 1 (a1): The first term is given: a1 = 3. Term 2 (a2): Using … Read more
To find the zeros of the polynomial function f(x) = x³ – 9x² – 20x, we need to determine the values of x for which f(x) = 0. Step 1: Factor the polynomial. We can start by factoring out the common term from the expression: f(x) = x(x² – 9x – 20) Step 2: Now, … Read more
The equation of the circle, x² + y² = 5625, describes the broadcast area of a radio station, indicating that the station reaches listeners within a circular region. To interpret this equation clearly, we can relate it to the standard form of a circle’s equation, which is (x – h)² + (y – k)² = … Read more
To determine the diameter of a cylinder when you know its volume and height, you can use the formula for the volume of a cylinder: Volume (V) = π × r² × h Where: V = Volume of the cylinder (in cubic units) r = Radius of the cylinder (in units) h = Height of … Read more
To solve the quadratic equation x² + 12x + 49 = 0 by completing the square, follow these steps: First, rewrite the equation: x² + 12x + 49 = 0 Next, we want to isolate the constant term on one side to focus on completing the square. To do this, we can move the constant … Read more
To convert the expression 6x^2 + 54x + 4x + 52 + 6 = 0 into a standard quadratic form, we need to first combine like terms. Let’s break it down step by step: Combine the linear terms: 54x + 4x gives us 58x. Now, rewrite the equation as: 6x^2 + 58x + 52 + … Read more
To find the lateral area of a cylinder, you can use the formula: Lateral Area = 2 × π × r × h Where: r = radius of the cylinder h = height of the cylinder π (Pi) is approximately equal to 3.14159 Given that the radius (r) is 4 and the height (h) is … Read more
To find the zeros of the polynomial function f(x) = x³ – 9x² – 20x, we need to set the function equal to zero: x³ – 9x² – 20x = 0 Next, we can factor out the common term, which in this case is x: x(x² – 9x – 20) = 0 This gives us … Read more