What is an equation in standard form of an ellipse centered at the origin with vertex 6, 0 and co-vertex 0, 4?
An ellipse centered at the origin with vertices at (±a, 0) and co-vertices at (0, ±b) can be expressed in the standard form of the equation: Standard Form: \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \] In this case, the vertex is given as (6, 0) and the co-vertex as (0, 4). Here, we can see […]
Subtract the quotient of 18 and 2 from the sum of 22 and 9
To solve this problem, we need to break it down into two parts: first, we need to find the sum of 22 and 9, and second, we need to determine the quotient of 18 and 2. Let’s start with the sum: 22 + 9 = 31 Now, let’s find the quotient: 18 ÷ 2 = […]
What is the slope of the line containing the points (2, 3) and (3, 1)?
To find the slope of the line that passes through the points (2, 3) and (3, 1), we can use the slope formula: slope (m) = (y₂ – y₁) / (x₂ – x₁) Here, (x₁, y₁) is the first point (2, 3) and (x₂, y₂) is the second point (3, 1). Substituting these values into […]
The Difference Between Integers x and 6 is 5: Find the Value of x
To solve the equation where the difference between an integer x and 6 is 5, we start by understanding what ‘difference’ means in this context. The difference between two numbers means we subtract one from the other. This can be expressed mathematically as: |x – 6| = 5 The absolute value equation means that x […]
What is the volume of the pyramid?
The volume of a pyramid is given by the formula: Volume = (1/3) × Base Area × Height To calculate the volume, you first need to determine the area of the base of the pyramid. The base can be any polygon, but for simplicity, let’s consider it to be a square or rectangular base. Once […]
What is the slope of the line 6x + 8y = 12?
To find the slope of the line represented by the equation 6x + 8y = 12, we first need to rearrange this equation into the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. We start with the original equation: 6x + 8y = 12 […]
How to Find the Function hx = fx * gx if fx = x² + x and gx = 3x?
To find the function h(x) defined as h(x) = f(x) * g(x), we first need to define the given functions: f(x) = x² + x g(x) = 3x Now, substituting these functions into the equation for h(x): h(x) = f(x) * g(x) = (x² + x) * (3x) Next, we distribute (3x) across the terms […]
What is the equation of the line with an undefined slope and goes through point (2, 4)?
When we talk about a line with an undefined slope, we’re referring to a vertical line. Vertical lines have an equation in the form of x = a, where a is a constant. This means that no matter what the value of y is, x will always be equal to a. In this case, the […]
What is the length of line segment AC using the equation sin(40°)?
To determine the length of line segment AC using the equation sin(40°), we first need to understand how trigonometric functions work in the context of a right triangle. Assuming that AC is the opposite side and we have the hypotenuse or an adjacent side, we can use the sine function, which is defined as: sin(θ) […]
Which conversion factors are used to multiply to 12 ms to get kilometers per minute?
To convert 12 meters per second (ms) to kilometers per minute (km/min), we need to apply two conversion factors: one to convert meters to kilometers and another to convert seconds to minutes. First, let’s break down the conversions: 1 kilometer = 1000 meters 1 minute = 60 seconds Now, we can set up the conversion: […]