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Rational numbers can be expressed as fractions, while irrational numbers cannot. For example, the sum of two rational numbers is always rational, but adding an irrational number to a rational number results in an irrational sum.
To simplify the expression | -1 |^3 - 9x - 4, first find the absolute value, then cube it, and combine like terms. The final expression is -3 - 9x.
A radical is a mathematical symbol that represents the root of a number, most commonly the square root (√). For example, √9 equals 3 because 3 multiplied by itself equals 9.
Yes, the square root of 252 can be simplified to 6√7. By factoring 252 into 36 and 7, we find that the square root of 36 is 6, leaving us with 6√7 as the simplified form.
Natural numbers, whole numbers, and integers are fundamental number sets in mathematics. Natural numbers start from 1 and go upwards, whole numbers include 0 and all natural numbers, while integers encompass all positive and negative whole numbers, including zero.
To find the rate of change in waiting times between April and June, subtract the June waiting time from the April waiting time and divide by the number of months. In this case, the rate of change is -3 minutes per month.
To add polynomial expressions, rewrite them in standard form, align like terms, and combine them. For example, adding 3 - 2p - 5p² and p⁴ - 3p + 4 results in p⁴ - 5p² - 5p + 7.
To use the Desmos graphing calculator for parabolas, input the equation y = kx² and adjust the slider for k until the graph fits your points. This visual approach helps you understand the relationship between the equation and its graph.
To simplify $$\sqrt{162x^2y^5}$$, factor the components under the square root. The simplified form is $$3xy^2\sqrt{2y}$$, pulling out perfect squares from each part.
We use opposite operations to isolate variables because they effectively 'undo' the operations applied to the variable. For example, to solve x + 4 = 10, we subtract 4 from both sides to find x.
To add polynomial expressions like (3x² - 2) + (11 - 5x), combine like terms. The result is 3x² - 5x + 9. Always check your signs and group similar terms for accuracy.
To find the perimeter of a shape, add the lengths of all its sides. In the case of the building example, the perimeter is 43 yards, not 36.
A polynomial is a mathematical expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication. Each part of the polynomial is called a term, and the highest exponent in the expression determines its degree.
To determine how vertical stretching affects functions using Desmos, graph the parent function and its stretched version. For example, graph y = |x + 4| and y = 3|x + 4| to visualize the effects.
To expand and simplify the expression (b + 8)(3b - 6), use the distributive property to multiply each term. The result is 3b² + 18b - 48.
The function y = f(x - 3) translates the original graph y = f(x) 3 units to the right. This means that every point on the graph shifts horizontally, maintaining its shape.
An increasing function is one where the output (y-values) rises as the input (x-values) increases. In linear functions, if the slope is positive, the function is increasing.
An expression is a mathematical phrase without an equals sign, like 3x + 5y. An equation, however, is a statement that two expressions are equal, always including an equals sign, such as 3x + 5 = 20.
To add polynomial expressions, combine like terms carefully. For example, adding (4b^2 + b + 6) and (3b + 6) results in 4b^2 + 4b + 12 after simplification.
To combine like terms, identify terms with the same variable parts. In the expression 9 + q²r², you cannot combine the constant 9 with the variable term q²r², so it remains as is.
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