What number completes the pattern, given that a single algebraic …

Mathematics Questions

Question ng.01 * What number completes the pattern? Note that there is a single algebraic equation (limited to the basic arithmetic operations of addition, subtraction, multiplication, and division) that repeats across all rows.

Short Answer

The solution involves identifying a pattern where the equation (a ‚àöo c) ‚àö‚àë b = d governs the numbers across various rows. By applying this formula step by step, values can be calculated, and any unknown variables can be determined reliably, as demonstrated through the rows presented.

Step-by-Step Solution

Step 1: Identify the Pattern

To understand the rule governing the numbers in the rows, observe how they interact with each other using basic operations. The relationship can be defined as follows: for any row with numbers a, b, c, and d, the equation can be written as (a ‚àöo c) ‚àö‚àë b = d. This means that the product of the first and third numbers divided by the second number equals the fourth number.

Step 2: Apply the Formula to Each Row

Now, apply the identified formula to each equation step by step. For the first row: (-4 ‚àöo -9) ‚àö‚àë -6 = -6 gives us a consistent output. Similarly, for the second row, set (a ‚àöo 4) ‚àö‚àë 7 = -44. Rearranging provides the equation a ‚àöo 4 = -44 ‚àöo 7, leading to a = -28 ‚àö‚àë 4.

Step 3: Solve for the Unknown Variable

Once we have the rearranged equation, simplify it to find the value of a. In the second row, this gives us a = -7 after performing the division. By continuing to apply the original formula to the remaining rows, we additionally confirm or find other relationships, ensuring everything aligns perfectly with the established formula.

Related Concepts

Pattern

A consistent relationship or rule that dictates how elements in a set interact or relate to one another, often observed through examples and calculations.

Formula

A mathematical expression that represents a relationship between variables, allowing for the calculation of one variable based on others, typically expressed using specific operations.

Variable

A symbol or letter that represents an unknown or changeable value in mathematical equations, used to solve for specific quantities or relationships.

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