If the measure of arc QR is 100, what is the measure of angle PQR?
To find the measure of angle PQR, we can use the relationship between an inscribed angle and the arc it intercepts. The measure of an inscribed angle is always half the measure of the arc that it intercepts. In this case, angle PQR intercepts arc QR. Therefore, we can calculate the measure of angle PQR […]
What is the additive inverse of the complex number 8 + 3i?
The additive inverse of a complex number is simply the number that, when added to the original complex number, results in zero. For the complex number 8 + 3i, the additive inverse can be found by negating both the real and imaginary parts. This means we change the sign of the real part (8) and […]
What is the velocity of an object that moves 100 m in 10 s?
The velocity of an object can be calculated using the formula: Velocity = Distance / Time. In this case, the object moves a distance of 100 meters in a time span of 10 seconds. So, we can substitute the values into the formula: Velocity = 100 m / 10 s = 10 m/s This means […]
What is a Plane in Geometry?
A plane in geometry can be described as a flat, two-dimensional surface that extends infinitely in all directions. It is defined by any three non-collinear points, meaning the points cannot all lie on the same straight line. To visualize a plane, think of a sheet of paper that goes on forever in all directions; no […]
Find the standard form of the equation of the parabola with the given characteristics: vertex at origin, focus (0, 5)
To find the standard form of the equation of a parabola, we start by identifying its orientation based on the position of the focus and vertex. In this case, the vertex is at the origin (0, 0) and the focus is at (0, 5). Since the focus is located above the vertex, this indicates that […]
1 5 is what percent of 20?
To determine what percent 1.5 is of 20, we can use the formula for finding the percentage: Percentage = (Part / Whole) * 100 In this case, the part is 1.5, and the whole is 20. Plugging in the values: Percentage = (1.5 / 20) * 100 Calculating this gives us: Percentage = 0.075 * […]
Evaluate 1 – cos(θ) – cos(θ)
To evaluate the expression 1 – cos(θ) – cos(θ), we can simplify it first. Let’s combine the terms involving cos(θ): 1 – cos(θ) – cos(θ) = 1 – 2cos(θ) This means the expression simplifies to 1 – 2cos(θ). Now, the value of 1 – 2cos(θ) will depend on the specific angle θ we are evaluating. […]
What is the relative maximum and minimum of the function f(x) = 2x³ + x² – 11x?
To find the relative maximum and minimum of the function f(x) = 2x³ + x² – 11x, we first need to find its critical points. These are the points where the derivative of the function is either zero or undefined. First, we find the derivative of the function: f'(x) = 6x² + 2x – 11 […]
What do we call two sets that contain the same number of elements?
Two sets that contain the same number of elements are called equinumerous sets. The term ‘equinumerous’ comes from the combination of ‘equi’ meaning equal, and ‘numerous’ which refers to the number of elements. In simpler terms, if you can find a one-to-one correspondence between the elements of the two sets, they are equinumerous. This concept […]
What is the solution set of 6x² – 24 = 0?
To solve the equation 6x² – 24 = 0, we first want to isolate the x² term. We can do this by adding 24 to both sides of the equation: 6x² = 24 Next, we divide both sides by 6 to get x² by itself: x² = 4 Now, we take the square root of […]