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To find the equation of a parabola with a specific vertex, we can use the vertex form of a quadratic equation. The vertex form of a parabola is given by: y = a(x – h)^2 + k In this equation, (h, k) represents the vertex of the parabola, and ‘a’ determines the direction and width … Read more

Finding the Polynomial To find the polynomial we need, let’s denote the polynomial as P(x). According to the information provided, we have the expression: Q(x) = 4x^5 + 3x^3 + 15 Given that the quotient of Q(x) and another polynomial P(x) equals x^3 + 3, we can set up the equation: Q(x) = P(x) * … Read more

To solve the quadratic equation 2x² + 4x + 7 = 0, we will utilize the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / (2a) In our equation, we identify the coefficients as follows: a = 2 b = 4 c = 7 Now, we will substitute these values … Read more

To express the sum 2 + 2 + 2 + 2 as a product, we first need to recognize that we are adding the number 2 four times. This can be mathematically represented as: 2 + 2 + 2 + 2 = 2 × 4 Here, we are essentially saying that the sum of four … Read more

To calculate the monthly interest rate from an annual interest rate, you can use a simple formula. The annual interest rate is divided by 12, which represents the 12 months in a year. In Cameron’s case, with an annual interest rate of 21%, the calculation would look like this: Monthly Interest Rate = Annual Interest … Read more

To find the slope of the line that passes through the given points, we can use the slope formula, which is defined as: slope (m) = (y2 – y1) / (x2 – x1) In this case, we have two points: Point 1: (0, 32) where x1 = 0 and y1 = 32 Point 2: (100, … Read more

In the realm of geometry, the concept of complementary angles is crucial and often comes into play when trying to solve various problems. By definition, two angles are considered complementary if the sum of their measures equals 90 degrees. Now, let’s explore the scenario presented: if two angles, let’s call them A and B, are … Read more

To find the first six terms of the sequence defined by the relation an = 7an-1 – 4, we first need to know the initial term of the sequence. Let’s assume the first term, a1, is defined as: a1 = 1 (you could choose another value, but for this example, we’ll start with 1). Now, … Read more

To solve the expression 91y³ ÷ (21y² + 35y + 7y), we will first simplify the denominator and then perform the division. 1. **Combine like terms in the denominator**:     The expression in the denominator is 21y² + 35y + 7y. Let’s combine the terms with y:         21y² + (35y + 7y) = 21y² + 42y … Read more

Square numbers and triangle numbers are two different categories of figurate numbers that arise in mathematics, each representing a distinct pattern of counting and arrangement. Square Numbers A square number is an integer that can be expressed as the square of another integer. In simpler terms, if you can arrange a certain number of objects … Read more