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How do you find the linear function when given a table of values for the variables?
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What does it mean to find the value of an algebraic expression?
When a given set of values for the variables are substituted in the expression the result is the value of the expression.
What are limits in maths?
Limits (or limiting values) are values that a function may approach (but not actually reach) as the argument of the function approaches some given value. The function is usually not defined for that particular value of the argument.
How can you evaluate a expression?
replace the variables with the given values and simplify using the order of operations.
When both variables cancel in a linear equation leaving you with a true statement. How should this be interpereted?
It means that whatever you have substituted is the solution of the given linear equation. Or you have substituted the equation in itself.
When you compare two variables how does that turn into slope?
Suppose you have a sample of n points for two variables: (x1, y1), (x2, y2), ... (xn, yn). Without going into various statistical considerations (which are nonetheless important) you can estimate the slope of the 'best' line that can be used to estimate the values of y from the values of x using for formula given for beta-hat in the wikipedia article for simple linear regression.
How do you find a point of a linear function?
Given a linear function in n variables, you need to select values for (n-1) of the variables. Solve the resulting function for the nth variable. Then the ordered n-tuple represents the coordinates, in n-dimensional space, of a point that is on the linear function.Selecting different sets of (n-1) variables, and different values will result in different solutions. Together, these will from a line in n-dimensional space.
How would you find the equation for a linear function when you are given a table of values for the variables?
If the figures in the table are exact and without measurement error then take any two of the points (x1, y1) and (x2, y2) and use these to form the linear relation y - y1 = ((y2 - y1)/(x2 - x1))(x - x1) If, however, you suspect that the values in the table do not exactly follow a linear relationship then use linear regression for which formulae are provided in wikipedia.
How are the independent and dependent variables related?
Independent variables can take values within a given boundary. The dependent variable will take values based on the independent variable and a given relationship at which the former can take its values.
How are dependent variables and independent variable the related?
Independent variables can take values within a given boundary. The dependent variable will take values based on the independent variable and a given relationship at which the former can take its values.
Why are function notation important?
Function notation is important because it helps to clearly communicate how a function operates by providing a compact and standardized way to represent mathematical relationships. It allows us to define, manipulate, and analyze functions more efficiently, enabling us to work with complex mathematical concepts in a concise and organized manner. Additionally, function notation aids in describing the input and output of a function, making it easier to understand and apply in various mathematical contexts.
Is the following function linear or nonlinear If linear, state the rate of change?
o function is given. However, if linear , then the rate of change is the same as the steepness of the graph line.
What does it mean to find the value of an algebraic expression?
When a given set of values for the variables are substituted in the expression the result is the value of the expression.
How do you expressions?
Replace the variables with the given values. Then you calculate using the order of operations.
Is a plus b divisible by c?
Sometimes. It depends on the values given to the variables.
What are limits in maths?
Limits (or limiting values) are values that a function may approach (but not actually reach) as the argument of the function approaches some given value. The function is usually not defined for that particular value of the argument.
How can you evaluate a expression?
replace the variables with the given values and simplify using the order of operations.
What is the maximum number of different Boolean functions involving n Boolean variables?
A Boolean function f is a function that maps Bk->B where B ={0,1} and k is a nonnegative integer. The term "arity" of the function is denoted by k. Fo every k there are 22k k-ary functions for each k. given n input variables, there are 2n bits in function's number. Now given m bits, there are 2m different values. So, for n input variables there are m=2n possible bits and 2m or 22n possible functions.
