Posts tagged algebra
Solving problems with the formula for distance, rate, and time

Before you can use the distance, rate, and time formula, D=RT, you need to make sure that your units for the distance and time are the same units as your rate. If they aren’t, you’ll need to change them so you’re working with the same units.

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Inverse variation of two variables and the constant of variation

The main idea in inverse variation is that as one variable increases the other variable decreases, which means that if x is increasing y is decreasing, and if x is decreasing y is increasing. The number k is a constant so it’s always the same number throughout the inverse variation problem.

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Using laws of logarithms (laws of logs) to solve log problems

Laws of logarithms (or laws of logs) include product, quotient, and power rules for logarithms, as well as the general rule for logs (and the change of base formula we’ll cover in the next lesson), can all be used together, in any combination, in order to solve log problems.

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How to get the domain and range from the graph of a function

The domain is all x-values or inputs of a function and the range is all y-values or outputs of a function. When looking at a graph, the domain is all the values of the graph from left to right. The range is all the values of the graph from down to up.

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Finding the multiples of a number

It’s helpful to think about multiples and divisibility as two parts of the same idea. We know that 10 is “divisible” by 5 because when we do the division 10/5, the result 2 is a whole number. It’s the fact that the result is a whole number that proves that 10 is divisible by 5.

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How to evaluate logs using the general log rule

You can always evaluate logs using the general log rule, but sometimes, depending on the value of the base and the argument, simplifying the exponential expression can be a little tricky.

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Solving systems of equation three ways: substitution, elimination, and graphing

There are three ways to solve systems of linear equations: substitution, elimination, and graphing. Substitution will have you substitute one equation into the other; elimination will have you add or subtract the equations to eliminate a variable; graphing will have you sketch both curves to visually find the points of intersection.

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Factoring to find common denominators for rational expressions

To add rational expressions, you need to find a common denominator, just like when you add fractions in which the numerator and denominator are just numbers. The difference is that finding the common denominator of rational expressions can be more complicated because their denominators can include variables.

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How to multiply multivariable polynomials

Multiplying multivariable polynomials (polynomials with two or more different variables) is very similar to multiplying single-variable polynomials (those that have just one variable). You’ll just need to be careful about combining like terms.

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How to solve uniform motion problems

Uniform motion explains the distance of an object when it travels at a constant speed, the rate, over a period of time. To compare different rates, times, and distances you can use subscripts to keep track of which pieces go with which equation.

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