Two sides of a triangle measure 5in and 12in. What could be the length of the third side?
To determine the possible lengths of the third side of a triangle with side lengths of 5 inches and 12 inches, we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let’s […]
Given the function f(x) = 53x, what is the value of f(17)?
To find the value of f(17), we need to substitute 17 into the function f(x) = 53x. We start by replacing x with 17: f(17) = 53 * 17 Now, we perform the multiplication: 53 * 17 = 901 Therefore, the value of f(17) is 901.
What value of x is in the solution set of 2 + 3x + 1 = 4x + 6?
To find the value of x, we start by simplifying the equation: 2 + 3x + 1 = 4x + 6. First, combine the like terms on the left side: 2 + 1 = 3, so we have: 3 + 3x = 4x + 6. Next, let’s isolate the variable x. Subtract 3x from both […]
What is the circumference of a circle with a diameter of 6 yards?
The circumference of a circle can be calculated using the formula: C = π × d where C represents the circumference and d is the diameter of the circle. In this case, the diameter of the circle is 6 yards. Plugging this value into the formula gives: C = π × 6 Using 3.14 as […]
How do you find a polar equation for the curve represented by the Cartesian equation xy = 1?
To convert the Cartesian equation xy = 1 into a polar equation, we start by using the relationships between Cartesian and polar coordinates. In polar coordinates, we have: x = r cos(θ) y = r sin(θ) Substituting these into the Cartesian equation gives: (r cos(θ))(r sin(θ)) = 1 This simplifies to: r2 cos(θ) sin(θ) = […]
What is the equation of the quadratic graph with a focus of (5, 6) and a directrix of y = 2?
To find the equation of a quadratic graph (a parabola) given its focus and directrix, we start by identifying the properties of the parabola. The focus of the parabola is the point where all the light rays reflected off the curve converge. In this case, the focus is located at (5, 6). The directrix is […]
How to Find b(dy/dx) Using the Equation 8y cos(x) + x^2 y^2?
To find the derivative b(dy/dx) from the equation 8y cos(x) + x^2 y^2 = 0, we need to use implicit differentiation. 1. Start by differentiating both sides of the equation with respect to x: 8(dy/dx) cos(x) – 8y sin(x) + 2xy^2 + x^2(2y)(dy/dx) = 0 2. Now, group the terms that contain dy/dx: 8(dy/dx) cos(x) […]
The set containing all the elements that are common to both set A and set B is called the
The set containing all the elements that are common to both set A and set B is called the intersection of the two sets. The intersection of sets is a fundamental concept in set theory, which is a branch of mathematical logic. It can be denoted by the symbol ‘∩’. For example, if we have […]
How to Solve the Inequality 3x < 2x + 1 and Graph the Solution on a Number Line
To solve the inequality 3x < 2x + 1, we first aim to isolate x. Step 1: Subtract 2x from both sides of the inequality: 3x – 2x < 2x + 1 – 2x This simplifies to: x < 1 Step 2: Now that we’ve solved for x, we need to represent this solution graphically […]
How to Classify the Terms 2x^4, x^3, 8x^2, and 12 by Degree?
To classify the terms 2×4, x3, 8×2, and 12 by degree, we first need to understand what ‘degree’ means in the context of polynomials. The degree of a term is determined by the highest exponent of the variable within that term. Now let’s break down each term: 2×4: This term has an exponent of 4. […]