Variables And Patterns: Investigation 1 And 2 (York)

A table is a representation of data organized in rows and columns. It is a structured way to present information, making it easier to read and analyze. Tables are commonly used in various fields such as statistics, finance, and research, as they provide a clear and concise format for displaying data. With the use of headings and labels, tables can effectively communicate complex information in a visually appealing manner.

A variable is a quantity that can change or vary. It is a symbol or letter that represents an unknown value or a value that can change in a mathematical expression or equation. Variables are used to solve equations, analyze patterns, and represent unknown quantities in various mathematical problems. They are an essential concept in algebra and are commonly used in scientific and mathematical calculations.

A coordinate graph is a type of graph that shows the relationship between two variables. It consists of two perpendicular lines, the x-axis and the y-axis, that intersect at a point called the origin. The x-axis represents one variable, while the y-axis represents the other variable. Points on the graph are plotted based on their corresponding values for each variable. This allows us to visually analyze and understand the relationship between the two variables, such as identifying patterns or trends.

The given sequence of numbers follows a consistent pattern where each number is obtained by adding 5 to the previous number. This pattern allows us to predict the next number in the sequence. Therefore, the correct answer is "pattern".

The term "rule" refers to a set of guidelines or principles that can be used to determine the next value in a sequence or pattern. In this context, the summary suggests that the predictable data provides information on how to find the next value, and this information is likely to be in the form of a rule. The rule could involve a mathematical formula, a logical pattern, or any other consistent relationship between the given values.

The correct answer is "Variables and Patterns" because the other options do not accurately describe the unit being studied. "Variables and Negatives" does not mention patterns, "Accentuate the Variable" does not mention variables, and "Vampires and Patterns" is unrelated to the topic. Therefore, "Variables and Patterns" is the most appropriate choice.

A formula is a rule that represents a mathematical relationship. It is a way to express a mathematical equation or calculation in a concise and symbolic form. Formulas typically involve variables, which are placeholders for specific values, and can be used to solve mathematical problems or make calculations. In the given examples, P = 5h, Raniqua's age = Amy's age + 3, and 3n + 1 are all formulas that represent mathematical relationships.

The word "change" is the correct answer because it is the only option that accurately describes the action of becoming different. The other options, such as "variable," "rule," and "dependent variable," do not directly convey the concept of becoming different. Therefore, "change" is the most appropriate choice.

The correct answer is "all of the above" because every graph should have a title to provide a clear description of the data being presented. Additionally, a label or title for the x-axis is necessary to indicate the variable being measured on the horizontal axis, and a label or title for the y-axis is required to represent the variable being measured on the vertical axis. All of these elements are essential for proper understanding and interpretation of the graph.

The dependent variable is the variable that is influenced or affected by another variable. In this example, the number of customers on a bike tour is dependent on the cost of the tour. The cost of the tour is the independent variable, as it is the factor that determines the number of customers. The dependent variable changes in response to changes in the independent variable.

The correct answer is the y-axis. The vertical axis on a coordinate graph is called the y-axis. It represents the values of the dependent variable in a graph and is perpendicular to the x-axis. The y-axis helps to visualize and understand the relationship between the dependent and independent variables in a graph.

The x-axis is the horizontal line on a coordinate graph. It is used to represent the values of the independent variable, usually denoted by "x". The x-axis intersects with the y-axis at the origin (0,0) and divides the coordinate plane into four quadrants. It is an essential component of a coordinate graph as it helps in locating and plotting points based on their x-coordinate values.