devyy The vertex of a graph typically refers to the highest or lowest point of a parabola, which is not applicable for cubic functions like the one described in the function f(x) = x³ + 7. Instead of a vertex, cubic functions have an inflection point where the curve changes direction. The function you provided, f(x) … Read more
The equation we want to solve is: cos(2x) + 2 cos(x) + 1 = 0 First, we can use the double angle identity for cosine, which states: cos(2x) = 2cos²(x) – 1 Substituting this into our equation gives: 2cos²(x) – 1 + 2cos(x) + 1 = 0 Simplifying this, we have: 2cos²(x) + 2cos(x) = … Read more
To find the value of ‘a’ when the least common multiple (LCM) of ‘a’ and 18 is 36 and the highest common factor (HCF) is 2, we can utilize the relationship between LCM and HCF. The formula that connects these two values is: LCM(a, b) × HCF(a, b) = a × b In our case, … Read more
The area of a square can be easily calculated using a simple mathematical formula: Area = side × side or Area = side2. In the case of a square computer screen with each side measuring 21 inches, you would proceed as follows: 1. Start with the length of one side of the square, which is … Read more
The slope of a line is a measure of its steepness and is calculated using the formula: Slope (m) = (y2 – y1) / (x2 – x1) In this case, we have two points: (2, 5) and (1, 4). We can assign: (x1, y1) = (2, 5) (x2, y2) = (1, 4) Now, plug the … Read more
To find the composition of the functions f and g, denoted as f(g(x)), we will substitute the expression of g(x) into the function f(x). Given the functions: f(x) = 4x + 7 g(x) = 10x + 6 We will start by calculating the value of g(x): g(x) = 10x + 6 Now, we need to … Read more
Understanding the Relationship Between Area and Perimeter of a Square A square is a special type of quadrilateral where all four sides are equal in length. When we talk about the area and perimeter of a square, we can derive a function that links these two important measurements. Formulas to Remember Side length (s): The … Read more
To find the value of s in the equation 3r + 10 = 5s when r = 10, we can follow these steps: First, substitute the value of r into the equation: 3(10) + 10 = 5s This simplifies to: 30 + 10 = 5s Now, simplify further: 40 = 5s Next, to isolate s, … Read more
Determining whether a number is prime or composite is a fundamental aspect of number theory, and it’s quite simple once you understand the basic definitions. A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. This means that a prime number can only … Read more
The quadratic formula is used to find the solutions (or roots) of a quadratic equation of the form ax² + bx + c = 0. In this case, the given equation is 2x² + 5x + 5 = 0. First, identify the coefficients: a = 2 b = 5 c = 5 Next, plug these … Read more