devyy To determine the number of roots for the given equations, we will analyze each one separately. 1. Quadratic Equation: 12x² + 25x + 5 = 0 The equation is a quadratic equation of the form ax² + bx + c = 0, where: a = 12 b = 25 c = 5 To find the … Read more
To find the difference between two numbers given that their LCM (Least Common Multiple) is 495, their HCF (Highest Common Factor) is 5, and the sum of the numbers is 100, we can follow these steps: 1. **Understanding the Relationship**: The relationship between the LCM, HCF, and the two numbers (let’s denote them as x … Read more
To find the first six terms of the sequence defined by a_n = a_(n-1) + 8 with the initial condition a_1 = 4, we will calculate each subsequent term based on the previous term. 1. First term: a_1 = 4 2. Second term: a_2 = a_1 + 8 = 4 + 8 = 12 3. … Read more
To find the value of x in the logarithmic equation log3(x) = 2 and the equality 2 = 4096, we first understand that having logb(a) = c can be rewritten as a = bc. In this case, we convert the logarithmic equation to its exponential form: x = 32 Calculating that gives: x = 9 … Read more
To find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of the integers 112, 15, 21, 217, 23, 29, 38, 9, and 25 using the prime factorization method, we follow these steps: Step 1: Prime Factorization First, we need to perform the prime factorization of each integer: 112: 112 = 24 × 7 … Read more
Evaluating the Integral To evaluate the integral, let’s consider a definite integral of a function f(x) over the interval [a, b]. The integral can be expressed as: ∫ab f(x) dx This integral calculates the net area between the curve of the function f(x) and the x-axis from x = a to x = b. To … Read more
To determine whether the sequence 3, 12, 21, 30 is a geometric sequence, we first need to understand what a geometric sequence is. In a geometric sequence, each term after the first is found by multiplying the previous term by a constant called the common ratio. Let’s examine the sequence: The first term is 3. … Read more
To solve the system of equations 5x + y = 9 and 3x + 2y = 4, we can use either the substitution method or the elimination method. Here, we’ll use the substitution method for clarity. 1. **Rearranging the First Equation**: Start by rearranging the first equation to express one variable in terms of the … Read more
To analyze the equation log6x + 1 = log22(2x + 2), we will begin by exploring its components and how they behave when graphed. The left-hand side, log6x + 1, represents the logarithm of x to the base 6, shifted vertically upwards by 1 unit. As x approaches 0 from the right, this function approaches … Read more
To solve for f(13) in the function f(x) = (4x + 1) / 3, follow these steps: Substitute the value: Start by replacing x with 13 in the function. This gives you: f(13) = (4(13) + 1) / 3 Calculate the expression: First, calculate 4 * 13. This equals 52. f(13) = (52 + 1) … Read more