Graphically, What is the Solution to a System of Two Independent Linear Equations?
The solution to a system of two independent linear equations is usually represented graphically as the point where the two lines intersect. When you have two independent linear equations, it means that their graphs will form lines that are not parallel and will therefore have one unique point of intersection. This point represents the set […]
Find the points on the surface y² = 4xz that are closest to the origin
To find the points on the surface defined by the equation y² = 4xz that are closest to the origin (0, 0, 0), we need to minimize the distance from a point (x, y, z) on the surface to the origin. The distance D from the origin to a point (x, y, z) is given […]
How to Write an Equation for a Line Parallel to a Given Line That Contains a Point?
To find the equation of a line parallel to a given line and containing a specific point, follow these steps: Identify the slope of the given line: If you have the equation of the given line, express it in the slope-intercept form, which is y = mx + b, where m is the slope. Use […]
How to Find the Standard Deviation of a Probability Distribution
The standard deviation is a key measure of variability in a probability distribution. To find it, follow these steps: Determine the mean (μ): Begin by calculating the mean of the probability distribution. For a discrete distribution, this is done by summing the products of each outcome and its probability: μ = Σ (xᵢ * P(xᵢ)), […]
How to Simplify 3x 5 2x 9 4x 3?
To simplify the expression 3x 5 2x 9 4x 3, we should first convert it into a more standard mathematical expression, assuming it means multiplication of the terms. When we rewrite it, we get: 3x * 5 * 2x * 9 * 4x * 3 Now, let’s combine all of the numeric coefficients and the […]
The length, breadth and height of a room are in the ratio 3:2:1. What will be the total area of the four walls of the room?
To calculate the total area of the four walls of the room, we start by letting the dimensions be represented as follows: Let the height of the room be x. Then, the length and breadth can be defined as: Length = 3x Breadth = 2x The formula to find the total area of the four […]
Find the degree measure of each angle in the triangle
To find the degree measures of each angle in a triangle, you need to use the basic property that the sum of the interior angles in a triangle is always 180 degrees. If you know the measures of two angles, you can easily find the third angle by subtracting the sum of the known angles […]
What comes next in the sequence 5, 13, 29, 61?
The next number in the sequence is 125. To explain why, let’s take a closer look at how the sequence is formed. The given sequence is: 5, 13, 29, 61. If we analyze the differences between each pair of successive numbers, we get: 13 – 5 = 8 29 – 13 = 16 61 – […]
How to solve for b2 in the equation A = 1/2 * h * (b1 + b2) with given values
To solve for b2 in the equation A = 1/2 * h * (b1 + b2), we need to substitute the known values and rearrange the equation accordingly. We are given: A = 16 h = 4 b1 = 3 Now, let’s substitute these values into the equation: 16 = 1/2 * 4 * (3 […]
Given the sequence 2, 6, 18, 54, which expression would give the fifteenth term?
To find the fifteenth term of the sequence 2, 6, 18, 54, we first need to identify the pattern. Looking closely, we can see that each term is derived by multiplying the previous term by 3: 2 × 3 = 6 6 × 3 = 18 18 × 3 = 54 This suggests that the […]