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What do the variables stand for in algebraic equations?
The variables stand for an unknown number that has not yet been identified which has been kept as a variable for the purpose of finding the value of.
Describe the procedure used to solve an equation for a variable?
It very much depends on the equation. The procedure for solving an equation with just one variable is so very different from the procedure for finding solutions to non-linear equations in several variables.
What can be useful when finding the value of a variable?
A value of some function of the variable at some point and an equation which links the two.
What is the difference in evaluating a polynomial and solving a polynomial?
Evaluating a polynomial is finding the value of the polynomial for a given value of the variable, usually denoted by x. Solving a polynomial equation is finding the value of the variable, x, for which the polynomial equation is true.
What are the Applications of partial diffrential equations?
in case of finding the center of the ellipse or hyperbola for which axis or non parallel to axis we apply partial differential
What is solving equations about?
It is about finding a value of the variable (or variables) that make the equation a true statement.
What is subtistution in mathematical terms?
It is using a set of two equations, adding them together, eliminating one variable and finding the value of the other variable.
Are tables one of the best ways of finding the value of a variable?
They can be, but not always. Other methods (equations, graphs) may be the best way.
What is the difference in finding the m and n when factoring a polynomial with a leading coefficient that does not equal one?
The difference depends on what m and n equal. If they are both variable then it dpends on what the equations are for each variable.
What do the variables stand for in algebraic equations?
The variables stand for an unknown number that has not yet been identified which has been kept as a variable for the purpose of finding the value of.
Which is most likely the last step in solving a system of non-linear equations by substitution?
The last step in solving a system of non-linear equations by substitution is typically to substitute the value obtained for one variable back into one of the original equations to find the corresponding value of the other variable. After finding both values, it's important to check the solutions by substituting them back into the original equations to ensure they satisfy both equations. This verification confirms the accuracy of the solutions.
Which situation may cause someone to use substitution in order to solve a system of equations?
Substitution is often used when one of the equations in a system is already solved for one variable, or can be easily manipulated to do so. For example, if you have the equations (y = 2x + 3) and (3x + 2y = 12), substituting the expression for (y) from the first equation into the second allows for straightforward solving. This method is particularly useful when dealing with linear equations, as it simplifies the process of finding the variable values.
Describe the procedure used to solve an equation for a variable?
It very much depends on the equation. The procedure for solving an equation with just one variable is so very different from the procedure for finding solutions to non-linear equations in several variables.
Can you explain the significance of the keyword "1x-9" in the context of algebraic expressions?
In algebraic expressions, the keyword "1x-9" represents a linear equation with one variable (x) and a constant term (-9). This expression is significant because it helps to simplify and solve equations by isolating the variable and finding its value.
A replacement for a variable that results in a true sentence?
A replacement for a variable that results in a true sentence is often referred to as a "satisfying assignment." For example, in the logical statement "x > 5," replacing the variable x with 6 makes the sentence true, as 6 is indeed greater than 5. This principle is foundational in logic and mathematics, where finding such replacements can validate propositions or equations.
How are linear equations in one variable used in real world?
Linear equations in one variable are commonly used in various real-world applications, such as budgeting, where they help individuals or businesses determine expenses and income. They are also utilized in fields like physics for calculating distances, speed, and time, and in finance for determining loan payments or interest. Additionally, linear equations aid in problem-solving scenarios, such as finding break-even points in sales or predicting future trends based on current data.
What do you call finding the values of the variables that make equations true?
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