When you toss a coin, there are two possible outcomes for each toss: heads (H) or tails (T). To determine the size of the sample space when the coin is tossed 5 times in a row, we can use the concept of permutations. For each toss of the coin, there are 2 outcomes. Since the … Read more
To convert 12 milliseconds (ms) into kilometers per minute (km/min), you need to use two main conversion factors: Convert milliseconds to seconds: There are 1,000 milliseconds in one second. Therefore, you first convert milliseconds to seconds with the factor of 1 second / 1,000 milliseconds. Convert seconds to minutes: There are 60 seconds in one … Read more
The equation of a line with an undefined slope represents a vertical line. Vertical lines do not have a slope because they rise infinitely without running horizontally. Instead, they are defined exclusively by their x-coordinate. When we say the line goes through the point (24), we mean that this vertical line will intersect the x-axis … Read more
To solve the quadratic equation 6x² + 24x = 0, we can start by factoring the expression. First, we notice that both terms on the left side of the equation have a common factor of 6x. Thus, we can factor out 6x: 6x(x + 4) = 0 Once we have factored the equation, we can … Read more
To analyze the function f(x) = 2x² + 32x + 1, we’ll identify its vertex, domain, and range. Finding the Vertex The vertex of a quadratic function in the form f(x) = ax² + bx + c can be found using the formula: x = -b / (2a) For our specific function, we have: a … Read more
To solve the division of the polynomial 2×3 + 9×2 + 11x + 6 by x3, we can apply polynomial long division or simply simplify the expression, since dividing by x3 means reducing the polynomial by that degree. First, let’s express the division: Division: rac{2x^3 + 9x^2 + 11x + 6}{x^3} Next, we can break … Read more
To find the unit vector in the same direction as the vector v = 3i + j, we follow a straightforward process that involves calculating the magnitude of the vector and then dividing each component of the vector by its magnitude. Here’s a step-by-step breakdown: Identify the components: The vector v = 3i + j … Read more
To factor the cubic equation x³ + 3x² + 9x + 5, we first look for factors using the Rational Root Theorem. This theorem suggests checking for possible rational roots among the factors of the constant term and the leading coefficient. Here, the constant term is 5 and the leading coefficient is 1. The possible … Read more
Let’s define the ages of Kevin and Daniel: Let D represent Daniel’s current age. Since Kevin is 3 years older than Daniel, Kevin’s current age can be represented as K = D + 3. Now, we need to analyze their ages from two years ago: Two years ago, Daniel’s age was D – 2. Two … Read more
To solve the equation where hx = 6x, we need to first understand the variables involved. Here, ‘h’ and ‘x’ represent some quantities, and we are tasked with finding the expression hh10. Given hx = 6x, we can simplify this equation by dividing both sides by x (assuming x is not zero). This leaves us … Read more