Understanding the Probability of Rolling Three Different Numbers on Dice When you toss three dice, there are a total of 6 faces on each die, resulting in 6 imes 6 imes 6 = 216 possible outcomes. Calculating Favorable Outcomes To find the probability that all three numbers show different faces, we first calculate the number … Read more
A rational number is a type of number that can be expressed as a fraction or ratio of two integers, where the numerator is any integer and the denominator is a non-zero integer. In simpler terms, if you can write a number in the form of a/b, where a is an integer (which can be … Read more
To prove that: tan(45) × tan(45) × tan(45) × tan(45) = 1 × sin(2a) First, let’s simplify the left-hand side: We know that: tan(45) = 1 So, if we multiply tan(45) four times: tan(45) × tan(45) × tan(45) × tan(45) = 1 × 1 × 1 × 1 = 1 Now, we have: 1 = … Read more
To simplify the polynomial 8x² + 8x + 2 – 5x, we first need to combine like terms. Let’s break it down step by step: 1. Start with the original polynomial: 8x² + 8x + 2 – 5x 2. Combine the linear terms (the terms containing x): 8x + 2 – 5x = (8 – … Read more
In algebra, when we multiply a number and a variable together in a term, the number is referred to as the numerical coefficient. This coefficient plays a crucial role in defining the value of the term. For example, in the expression 5x, the 5 is the numerical coefficient, and x is the variable. The coefficient … Read more
To determine if the statement is true or false, we first need to solve the equation x² + 6x + 8 = 0. This is a quadratic equation which we can solve using factoring, the quadratic formula, or completing the square. In this case, we can factor the equation. We look for two numbers that … Read more
The expression 4×2 + 19x + 5 is a quadratic equation in the standard form ax2 + bx + c, where: a = 4 b = 19 c = 5 To determine the properties of this quadratic equation, we can analyze its coefficients: 1. Parabola Orientation: Since the coefficient of x2 (which is 4) is … Read more
To solve the equation a² = 4, we will take the following steps: Understand the Equation: The equation states that a squared is equal to 4. We need to find the values of a that satisfy this equation. Isolate the Variable: To find a, we can take the square root of both sides of the … Read more
To find the vertex of the quadratic function f(x) = 3x² + 6x + 3, we can use the formula for the vertex of a parabola given in the standard form f(x) = ax² + bx + c. The coordinates of the vertex (h, k) can be found using the formulas: h = -b / … Read more
To complete the square for the quadratic equation x² + 12x – 11, we need to focus on the quadratic and linear terms, which are x² + 12x. Here’s a step-by-step process to determine the number to add: Take the coefficient of the linear term (which is 12 in this case) and divide it by … Read more