Question
Given 6 collinear points, make a conjecture about the number of ways to connect different pairs of points.
Hint:
Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.
The correct answer is: Hence, the conjecture that can be concluded is “the number of ways to connect the 6 collinear points in different pairs of points is 15”.
Let’s first make a table and then look for the pattern
![](data:image/png;base64,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)
The sequence of the number of connections is 0, 1, 3, 6, 10, ….
We can see that
1 = 0 + 1
3 = 1 + 2
6 = 3 + 3
10 = 6 + 4
So by seeing the pattern the number of connections in 6 points is given as
10 + 5 = 15
So by seeing the pattern the conjecture that can be made is that the number of ways to connect the 6 collinear points in different pairs of points is 15
Final Answer:
Hence, the conjecture that can be concluded is “the number of ways to connect the 6 collinear points in different pairs of points is 15”.
Related Questions to study
Prove that the triangles ABC and XYZ are congruent.
![](data:image/png;base64,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)
Prove that the triangles ABC and XYZ are congruent.
![](data:image/png;base64,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)
Describe the pattern in the numbers 9.001, 9.010, 9.019, 9.028, ... and write the next three numbers in the pattern.
Describe the pattern in the numbers 9.001, 9.010, 9.019, 9.028, ... and write the next three numbers in the pattern.
Solve 49x + 9= 49x + 83
a)Does the equation have one solution , no solution or infinitely many solutions ?
b) Write two equations in one variable that have the same number of solutions as this equation
Solve 49x + 9= 49x + 83
a)Does the equation have one solution , no solution or infinitely many solutions ?
b) Write two equations in one variable that have the same number of solutions as this equation
Describe the pattern in the numbers 5, -15, 45, -215, ... and write the next three numbers in the pattern.
Describe the pattern in the numbers 5, -15, 45, -215, ... and write the next three numbers in the pattern.
– State and prove the AAS congruence postulate using the ASA congruence postulate.
– State and prove the AAS congruence postulate using the ASA congruence postulate.
Solve 0.9x+5.1x - 7 =2(2.5x - 3). How many solutions does the equation have ?
Solve 0.9x+5.1x - 7 =2(2.5x - 3). How many solutions does the equation have ?
Two rival dry cleaners both advertise their prices. Let x equal the number of items dry cleaned. Store A’s prices are represented by the equation 15x - 2. Store B’s prices are represented by the expression 3 (5x + 7). When do the two stores charge the same rate ? Explain.
Mathematical expressions are made up of at least two numbers or variables, one math operation, and a sentence. This mathematical operation allows you to multiply, divide, add, or subtract numbers.
¶Types of Expression
1. Arithmetic operators and numbers make up a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.
2. Unknown variables, numerical values, and arithmetic operators make up an algebraic expression. There are no symbols for equality or inequality in it.
¶In contrast to equations, the equal (=) operator is used between two mathematical expressions. Expressions denote a combination of numbers, variables, and operation symbols. The "equal to" sign also has the same value on both sides.
Two rival dry cleaners both advertise their prices. Let x equal the number of items dry cleaned. Store A’s prices are represented by the equation 15x - 2. Store B’s prices are represented by the expression 3 (5x + 7). When do the two stores charge the same rate ? Explain.
Mathematical expressions are made up of at least two numbers or variables, one math operation, and a sentence. This mathematical operation allows you to multiply, divide, add, or subtract numbers.
¶Types of Expression
1. Arithmetic operators and numbers make up a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.
2. Unknown variables, numerical values, and arithmetic operators make up an algebraic expression. There are no symbols for equality or inequality in it.
¶In contrast to equations, the equal (=) operator is used between two mathematical expressions. Expressions denote a combination of numbers, variables, and operation symbols. The "equal to" sign also has the same value on both sides.