What is the slope of line m if it is parallel to line k with a slope of 23?
If line k has a slope of 23, then line m, which is parallel to line k, will also have a slope of 23. Explanation: In geometry, parallel lines are defined as lines in the same plane that never meet. For two lines to remain parallel, they must have the same slope. Therefore, if line […]
Determine Which Function is a Solution to the Differential Equation xy 2y 0
To determine which function is a solution to the differential equation xy 2y 0, we first need to clarify the equation itself. It seems to indicate a relationship where xy multiplied by some function of y leads to a result of zero. This typically points to a scenario where either x or y (or both) […]
Which equation represents a line that has a slope of 4 and passes through the point (3, 8)?
To find the equation of a line given a slope and a point, we can use the point-slope form of a linear equation, which is: y – y1 = m(x – x1) In this formula, m represents the slope of the line, and (x1, y1) represents a point on the line. Here, the slope (m) […]
Match the Following
In many educational settings, matching exercises are a popular way to assess knowledge and understanding of a topic. These tasks require students to pair items from two different columns that relate to each other in a meaningful way. For example, one column may list terms, while the other lists their definitions or relevant examples. Purpose […]
Which equations are true for x² and x²? Check all that apply.
To determine which equations are true for x², we need to consider the basic properties and identities involving squares and the variable x. 1. **Equation 1**: x² = x * xThis equation is always true by the definition of squares. The square of any number (or variable) is equal to that number multiplied by itself. […]
If f(x) = 9 and g(x) = 6, which describes the value of f(g(x))?
To find the value of f(g(x)), we first need to evaluate g(x), which is given as 6. Now, we substitute this value into f(x). Since f(x) = 9, we can conclude that regardless of the input, the output of f will always be 9. Thus, f(g(x)) = f(6), and since f(x) always equals 9, we […]
Which list of ordered pairs represents solutions to xy = 2?
To find the ordered pairs that satisfy the equation xy = 2, we can rearrange the equation to express y in terms of x: y = 2/x Now we can choose various values for x and calculate the corresponding values of y. Here are some examples: If x = 1, then y = 2/1 = […]
What are the solutions of the equation c² – 10c = 0?
To solve the equation c² – 10c = 0, we can start by factoring the left-hand side of the equation. We can factor out a ‘c’ from both terms: c(c – 10) = 0 According to the zero-product property, if the product of two factors is equal to zero, then at least one of the […]
Identify the Vertical Asymptotes of f(x) = 10 / (x² – 7x – 30)
To find the vertical asymptotes of the function f(x) = 10 / (x² – 7x – 30), we first need to determine where the denominator equals zero since vertical asymptotes occur at these points. We begin by solving the equation: x² – 7x – 30 = 0 Next, we can factor the quadratic. We are […]
If 40 is subtracted from 60 of a number, the result is 50. What is the number?
Let’s denote the unknown number as x. According to the problem, we have the equation: 60 of the number is 60 * x. If we subtract 40 from this, we get: 60 * x – 40. We are told that this results in 50. So, we can set up the equation: 60 * x – […]