devyy For the given sequence: 15, 14, 13, 12, 11, 10, 9 we can observe a clear pattern: each number is decreasing by 1. As we analyze the sequence step by step: 15 – 1 = 14 14 – 1 = 13 13 – 1 = 12 12 – 1 = 11 11 – 1 = … Read more
To find the zeros of the cubic function f(x) = 6x³ + 35x² + 26x + 5, we need to determine the values of x for which f(x) = 0. This involves a few steps, as cubic equations can have one real root and two complex roots, or three real roots. 1. **Using the Rational … Read more
To solve the equation log3(x) + 16 = 2, we first isolate the logarithmic term: 1. Subtract 16 from both sides: log3(x) = 2 – 16 This simplifies to: log3(x) = -14 2. Now we need to convert the logarithmic form to exponential form. Recall that if logb(a) = c, then bc = a. Applying … Read more
To identify the maximum or minimum value of the function given by the equation y = 2×2 + 32x + 4, we first need to recognize that this is a quadratic function in standard form, y = ax2 + bx + c, where: a = 2 b = 32 c = 4 Since the coefficient … Read more
In a binomial experiment, each trial has two possible outcomes: success and failure. If we denote the probability of success as p, the probability of failure can be defined as: Probability of failure = 1 – p Here’s a more detailed explanation: In a binomial setup, each trial is independent, meaning the outcome of one … Read more
To find the remainder when multiplying the expression 3x^4, 2x^3, x^2, 2x, and 9x^2, we will first calculate the product of these terms and then determine the remainder of the total product. Let’s break down the steps: Start with the given expressions: 3×4, 2×3, x2, 2x, and 9×2. The total product can be expressed as: … Read more
To find the point-slope form of a line that passes through a specific point and is parallel to another line, we first need to understand the slope of the line we are parallel to. The given line is defined by the equation y = 3x. From this equation, we can directly identify the slope (m) … Read more
To evaluate the statement, we need to consider the properties of limits in calculus. The question implies examining the behavior of two functions, f(x) and g(x), as x approaches 0. Let’s denote: L1 = lim (x -> 0) f(x) L2 = lim (x -> 0) g(x) The claim suggests that if both L1 and L2 … Read more
To simplify the expression 10x² + 8x + 4x² – 8x + 5, you want to combine like terms. Let’s break it down step by step: Identify like terms: In our expression, the like terms are: The quadratic terms: 10x² and 4x² The linear terms: 8x and -8x The constant term: 5 (which does not … Read more
The volume of a rectangular prism (or cuboid) can be calculated using the formula: Volume = Length × Width × Height In this case, we have the following dimensions: Length: 10 cm Width: 5 cm Height: 8 cm Now, plug these values into the formula: Volume = 10 cm × 5 cm × 8 cm … Read more