Math

A:

In the third grade, compatible numbers are estimated figures that are used to make mental arithmetic simpler. Compatible numbers are very close to the actual numbers and yield a similar result with less work.

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    • Where did algebra come from?

      Q: Where did algebra come from?

      A: Algebra has been developed over thousands of years in several different countries. The earliest methods for solving mathematical problems with one or more unknown quantities come from ancient Egypt. The word "algebra" itself is derived from the title of Baghdad mathematician Al-Kwarizmi's 9th century book, "Hidab al-jabr wal-muqubala."
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    • How do you simplify imaginary numbers?

      Q: How do you simplify imaginary numbers?

      A: Imaginary numbers are typically simplified in the same way that expressions with the variable x are simplified, with the exception of the expression i^2, which has a value equal to -1. For example, the expression 2i + 8i can be simplified by writing it first as (2 + 8) * i, with the final expression written as 10i.
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    • What is a linear inequality equation?

      Q: What is a linear inequality equation?

      A: A linear inequality is similar to a linear equation; however, where a linear equation has an equals sign, a linear inequality uses an inequality symbol. Inequality symbols include > (greater than), < (less than), ≤ (less than or equal to), ≥ (greater than or equal to) and ≠ (not equal to).
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    • Why is math important in life?

      Q: Why is math important in life?

      A: Math is important in life because it is used to perform many different daily tasks, such as telling time, reading an odometer, counting change and to make strategic decisions in one's work life. Similarly, nearly every profession uses some form of math. For example, nurses, engineers, bank tellers, pharmacists and stock market analysts use math every day to perform their professional duties well.
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    • What is x squared plus x squared?

      Q: What is x squared plus x squared?

      A: The sum of x² plus x² is 2x². The problem requires adding one x squared to one more x squared, which equals two x squared. Substituting 3 for x, 3² + 3² = 2(3²), or 9 + 9 = 18.
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    • What is the procedure for solving equations graphically?

      Q: What is the procedure for solving equations graphically?

      A: To solve an equation in one variable graphically, first manipulate the equation to put it in the form f(x) = 0, where x represents the variable present in the equation. Then use mathematical software, a graphing calculator or graph paper to plot the line y = f(x). The solution to f(x) = 0 is the point or points at which the line crosses the x-axis.
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    • How is math used in the real world?

      Q: How is math used in the real world?

      A: Math is useful for economics, science, sports, social fields and a wide range of other areas for making decisions and analyzing information. Basic math skills are essential for many jobs. Math has been a core component of many human advances.
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    • How big is a stack of one trillion dollar bills?

      Q: How big is a stack of one trillion dollar bills?

      A: A stack of one dollar bills equals $100 and measures .43 inches high, which means that $1 trillion dollar bills would stack to a height of approximately 67,866.16 miles. The moon is about 238,855 miles from the Earth, which would require a stack of $3.5 trillion dollar bills to reach.
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    • How do you multiply fractions with different denominators?

      Q: How do you multiply fractions with different denominators?

      A: To multiply fractions, multiply the first numerator by the second numerator and the first denominator by the second denominator. The product of the two numerators becomes the numerator in your answer, and the product of the two denominators becomes the denominator in your answer. When finished, always be sure to simplify your answer to its lowest term.
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    • How do you calculate the sum of an arithmetic sequence?

      Q: How do you calculate the sum of an arithmetic sequence?

      A: Calculate the sum of an arithmetic sequence with the formula (n/2)(2a + (n-1)d). The sum is represented by the Greek letter sigma, while the variable a is the first value of the sequence, d is the difference between values in the sequence, and n is the number of terms in the series.
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    • Who created numbers?

      Q: Who created numbers?

      A: The Babylonian society used a cuneiform method of writing that included numerical characters; this is the earliest-known form of numbers, meaning that, as far as humans know, the Babylonians created numbers. This system of numerical writing is about 5,000 years old, and it is a base-60 system as opposed to a base-10 system, which is what most humans use for counting and mathematics in the modern world. Time measurements, in which an hour consists of 60 minutes and a minute consists of 60 seconds, are one example of a sexidecimal, or base-60, numerical system that is alive and well in the modern world.
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    • What is an array in math?

      Q: What is an array in math?

      A: In mathematics, an array is a set of numbers or objects placed in rows or columns. Arrays are often used to represent multiplication or division.
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    • What are some common Pythagorean triples?

      Q: What are some common Pythagorean triples?

      A: A Pythagorean triple is a set of three positive integers, (a, b, c), such that a right triangle can be formed with the legs a and b and the hypotenuse c. The most common Pythagorean triples are (3, 4, 5), (5, 12, 13), (8, 15, 17) and (7, 24, 25).
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    • What are the meanings of "sin", "cos", "tan", "csc", "sec" and "cot"?

      Q: What are the meanings of "sin", "cos", "tan", "csc", "sec" and "cot"?

      A: The abbreviations "sin," "cos," "tan," "csc," "sec" and "cot" stand for the six trigonometric functions: sine, cosine, tangent, cosecant, secant and cotangent. Each function represents a particular relationship between the measure of one of the angles and the ratio between two sides of a right triangle.
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    • How is calculus used in medicine?

      Q: How is calculus used in medicine?

      A: According to class notes from Bunker Hill Community College, calculus is often used in medicine in the field of pharmacology to determine the best dosage of a drug that is administered and its rate of dissolving. Usually, the drug is slowly dissolved in the stomach.
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    • How are logarithms used in the world?

      Q: How are logarithms used in the world?

      A: A few examples of how logarithms are used in the real world include measuring the magnitude of earthquakes or the intensity of sound and determining acidity. A logarithm explains how many times a number is multiplied to a power to reach another number. It is expressed as loge(x) and is commonly written as ln(x).
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    • What is the precise definition of a limit in calculus?

      Q: What is the precise definition of a limit in calculus?

      A: The definition of a limit in calculus is the value that a function gets close to but never surpasses as the input changes. Limits are one of the most important aspects of calculus, and they are used to determine continuity and the values of functions in a graphical sense.
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    • How do you calculate the midpoint Riemann sum?

      Q: How do you calculate the midpoint Riemann sum?

      A: A Riemann sum is a method of approximating the area under the curve of a function. It adds together a series of values taken at different points of that function and multiplies them by the intervals between points. The midpoint Riemann sum uses the x-value in the middle of each of the intervals.
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    • What are the names of graphs?

      Q: What are the names of graphs?

      A: Several types of graphs are used for displaying information in mathematics including the bar graph; pie chart or circle graph; histogram; stem and leaf plot; dot plot; scatter plot; and time-series graphs. The type of graph chosen depends on whether the data is quantitative, qualitative or paired.
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    • How is data turned into information?

      Q: How is data turned into information?

      A: According to the BBC, data is transformed into information after being imported into a database or spreadsheet. Information is defined as a collection of facts or data, whereas data is defined as information organized for analysis or used to reason.
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    • What is a pie graph used for?

      Q: What is a pie graph used for?

      A: A pie graph is an effective visual tool used for showing how something breaks into parts. A pie graph is essentially a circle sliced into 100 pieces. Each category or part represented in the pie graph is given a piece of the pie to represent the percentage that it comprises of the whole.
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    • How does a graph help people interpret scientific data?

      Q: How does a graph help people interpret scientific data?

      A: Graphs of various types provide convenient visual representations of scientific data that would otherwise be presented in intimidating blocks of text or a series of numbers. Graphs represent statistics such as changes over time, comparisons, or parts of a whole. Graphs can be used to make date more accessible to both scientists and laypersons.
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    • When do you use a bar graph?

      Q: When do you use a bar graph?

      A: A bar graph is used to compare items between different groups and track changes over a period of time. Bar graphs are best used for changes that happen over a large amount of time instead of just months or weeks.
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    • Why are graphs important?

      Q: Why are graphs important?

      A: Graphs are beneficial because they summarize and display information in a manner that is easy for most people to comprehend. Graphs are used in many academic disciplines, including math, hard sciences and social sciences. They make appearances in corporate settings, serving as useful tools to convey financial information and facilitate data analysis.
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