devyy To find the quotient of the expression 5×4 divided by (3×2 * 4x * 1), we will follow these steps: Multiply the terms in the denominator: We have 3×2 * 4x. To multiply these, we multiply the coefficients first: 3 * 4 = 12. Next, we multiply the variable parts: x2 * x = x3. … Read more
When tossing three coins at once, you can expect a variety of outcomes based on how each coin can land. Each coin can either show up as Heads (H) or Tails (T). To determine the total number of outcomes, we can consider the following: Coin 1: 2 possible outcomes (H or T) Coin 2: 2 … Read more
To find the lengths of each side of the triangle when the sides are in the ratio of 2:3:4 and the perimeter is 27 cm, we can follow these steps: Understand the ratio: The sides of the triangle are in the ratio 2:3:4. This means that we can represent the sides as: Sides = 2x, … Read more
To solve the equation x² + 4x + 9 = 29, follow these steps: Step 1: Rearrange the equation. Start by moving all terms to one side to set the equation to zero. We can do this by subtracting 29 from both sides: x² + 4x + 9 – 29 = 0 Which simplifies to: … Read more
Finding Local Maximum and Minimum Values and Saddle Points The function in question is: f(x, y) = x³ + y³ – 3x² – 3y² + 9x To find the local maxima, minima, and saddle points of this function, we must follow these steps: 1. Find the Critical Points First, we need to compute the first … Read more
Understanding the Zeros of the Polynomial A polynomial function is comprised of terms made up of variables raised to whole number powers and constant coefficients. In this case, we are examining the polynomial: f(x) = 3x^12 + 17x^8 + 11x^4 + 6x + 23 Definition of Zeros The zeros of a polynomial function are the … Read more
To find all polar coordinates of a point given in Cartesian coordinates, we use the relationship between Cartesian coordinates (x, y) and polar coordinates (r, θ). Here, the Cartesian coordinates are (9, 75). 1. Calculating the radius (r): The radius in polar coordinates can be calculated using the formula: r = √(x² + y²) Substituting … Read more
To find the completely factored form of the expression d4 + 8d2 + 16, we will start by treating it as a quadratic in terms of d2. We can rewrite the expression as follows: (d2)2 + 8(d2) + 16 Next, we can let x = d2 so that the expression becomes: x2 + 8x + … Read more
To determine the logarithmic function that represents the data in the table, we first need to analyze the provided values: x: 1, fx: 0 x: 3, fx: 1 x: 9, fx: 2 Noting that the fx values might correspond to the logarithm of the x values, we can express the relationship between x and fx … Read more
To find the two numbers based on the conditions given, let’s define the two numbers as x and y. According to the problem, the ratio of these two numbers is: Ratio 1: \( \frac{x}{y} = 23 \ This implies that: x = 23y Next, if we subtract 2 from the first number and 8 from … Read more