What is a median in a triangle?
A median in a triangle is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. Each triangle has three medians, one from each vertex, and they all meet at a point called the centroid. The centroid is an important point in a triangle because it is the […]
How to Solve the Equation 2x² + 3x – 7 + x² + 5x – 39 for x?
To solve the equation 2x² + 3x – 7 + x² + 5x – 39 = 0, we first need to combine like terms. Start by combining the x² terms: 2x² + x² = 3x² Next, combine the x terms: 3x + 5x = 8x Now, combine the constant terms: -7 – 39 = -46 […]
In Circle O Radius OQ Measures 9 Inches and Arc PQ Measures 6P Inches – What Does This Mean?
In the given circle O, the radius OQ measures 9 inches. This means that any point on the circumference of the circle is 9 inches away from the center point O. The arc PQ, which is a part of the circle between points P and Q, measures 6P inches. To better understand what this signifies, […]
Find the Derivative of the Function Using the Definition of Derivative gt 3 t
To find the derivative of the function f(t) = gt(3t) using the definition of the derivative, we start by recalling what the definition entails. The derivative of a function at a point is defined as: f'(t) = lim (h -> 0) [(f(t+h) – f(t)) / h] We can break this down into steps. Let’s first […]
A function f(x) has x-intercepts of 3 and 5. What is the constant term in the function f(x) = x^2 + 8x?
To find the constant term in the function f(x) = x² + 8x, we begin by considering the fact that the x-intercepts of a function are the values of x where the function equals zero. Given the x-intercepts at 3 and 5, we can express the function in factored form: f(x) = (x – 3)(x […]
AB is tangent to circle O if AO = 30 and BC = 48. What is AB?
To find the length of AB, we can use the tangent-secant theorem. This theorem states that the square of the length of a tangent segment from a point outside the circle (in this case, AB) is equal to the product of the lengths of the entire secant segment and its external part. In our example, […]
Define Double Ordinate
A double ordinate refers to a graphical representation where a point is defined by two vertical measurements from a given baseline or axis. In geometric terms, it can be understood as the two coordinates (x, y) that describe the position of a point in a two-dimensional Cartesian coordinate system. This concept is often used in […]
What is the antiderivative of tan²(x) dx?
To find the antiderivative of tan²(x) dx, we can use a trigonometric identity to simplify our work. The identity we will use is: tan²(x) = sec²(x) – 1 This means that we can rewrite the integral as: ∫ tan²(x) dx = ∫ (sec²(x) – 1) dx This can be split into two separate integrals: ∫ […]
Find the length of an arc of a circle with radius 12cm if the arc subtends a central angle of 30°
To find the length of an arc, we can use the formula: Arc Length = (θ / 360) × 2πr Where: θ is the central angle in degrees r is the radius of the circle In this problem, we have: θ = 30° r = 12 cm Now, we can plug these values into the […]
How do you solve the equation 2x – 20 ÷ 3 = 2x?
To solve the equation 2x – 20 ÷ 3 = 2x, we will follow a few steps to isolate the variable. First, let’s rewrite the equation for clarity: 2x – (20 ÷ 3) = 2x Next, we’ll start by simplifying the left side of the equation. We can calculate 20 ÷ 3, which equals approximately […]