Questions

<p>To find the probability of rolling a sum of 4 or higher with two fair six-sided dice, we first need to determine the total number of possible outcomes when rolling the dice. Each die has 6 sides, so when you roll two dice, the total number of outcomes is:</p>   <p> <strong>Total outcomes:</strong> 6 (from … Read more

Finding the Two Numbers To solve the problem where the sum of two numbers is 24 and one number is twice as large as the other, we can set up a simple equation. Let’s define the two numbers: Let x be the smaller number. Then, the larger number will be 2x (since it is twice … Read more

The domain of a function is the set of all possible input values (x-values) that the function can accept without leading to any mathematical inconsistencies such as division by zero or square roots of negative numbers. In your case, both functions f(x) and g(x) are linear functions defined as f(x) = x + 6 and … Read more

To find the general solution of the second order differential equation given by y” = 25y, we start by rewriting it in a more standard form: y” – 25y = 0 This is a linear homogeneous differential equation with constant coefficients. We can solve it using the characteristic equation method. The characteristic equation corresponding to … Read more

To find the zeros of the function f(x) = x^3 + 15x + 10, we need to determine the values of x for which f(x) = 0. This means we are looking for roots of the equation. The function is a cubic polynomial, and finding its zeros can be done through various methods such as … Read more

To solve the given equations graphically, we will first rewrite each equation in a slope-intercept form (y = mx + b) for easier graphing. Step 1: Rearranging the Equations 1. Starting with the first equation: x + 3y = 6 Rearranging to solve for y: 3y = 6 – x y = -rac{1}{3}x + 2 … Read more

In the realm of quadratic equations, understanding the discriminant is key to unlocking the nature of its roots. The discriminant is calculated using the formula D = b2 – 4ac, where a, b, and c are coefficients of the quadratic equation in the standard form ax2 + bx + c = 0. When the discriminant … Read more

To determine the range of the function f(x) = 3x + 12 for the domain x ∈ [-2, 2], we first need to evaluate the function at the endpoints of the given domain. 1. **Evaluate at the lower endpoint:** – When x = -2: f(-2) = 3(-2) + 12 = -6 + 12 = 6 … Read more

In an isosceles triangle, there are two equal angles known as base angles and one angle known as the vertex angle. In this case, each base angle measures 54 degrees. To find the vertex angle, we can use the property that the sum of all angles in a triangle equals 180 degrees. Hence, we can … Read more