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Question

# Make a table of values for the rule x$^2+x+11$ when x is an integer from 1 to 8. Make a conjecture about the type of number generated by the rule. Continue your table. What value of x generates a counterexample?

Solution

Verified
Step 1
1 of 2

Given expression:

$\begin{equation*} x^2 + x + 11 \end{equation*}$

Substitute $x=1$ and evaluate the value of the expression:

$\begin{equation*} (1)^2 + 1 + 11=13 \end{equation*}$

Substitute $x=2$ and evaluate the value of the expression:

$\begin{equation*} (2)^2 + 2 + 11=17 \end{equation*}$

Substitute $x=3$ and evaluate the value of the expression:

$\begin{equation*} (3)^2 + 3 + 11=23 \end{equation*}$

Substitute $x=4$ and evaluate the value of the expression:

$\begin{equation*} (4)^2 + 4 + 11=31 \end{equation*}$

Substitute $x=5$ and evaluate the value of the expression:

$\begin{equation*} (5)^2 + 5 + 11=41 \end{equation*}$

Substitute $x=6$ and evaluate the value of the expression:

$\begin{equation*} (6)^2 + 6 + 11=53 \end{equation*}$

Substitute $x=7$ and evaluate the value of the expression:

$\begin{equation*} (7)^2 + 7 + 11=67 \end{equation*}$

Substitute $x=8$ and evaluate the value of the expression:

$\begin{equation*} (8)^2 + 8 + 11=83 \end{equation*}$

This expression generates prime numbers in ascending order.

## Recommended textbook solutions

#### Connected Mathematics 3: Shapes and Designs, Two-Dimensional Geometry

1st EditionISBN: 9780133274479Prentice Hall

#### Georgia Analytic Geometry

1st EditionISBN: 9780547867656David J. Chard, Edward B. Burger, Paul A. Kennedy, Steven J. Leinwand
2,313 solutions

#### Eureka Math - A Story of Functions

ISBN: 9781632553270Great Minds

#### 6th Grade Math - Volume 2 (2019-2020 Course Workbook)

ISBN: 9781733055079Algebra Nation
The text passage contains a mathematical question that asks to create a table of values for a given expression and to make a conjecture about the type of number generated. The solution is also provided, showing the evaluation of the expression for integers from 1 to 8 and concluding that the expression generates prime numbers in ascending order.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Try the fastest way to create flashcards
Question

# Make a table of values for the rule x$^2+x+11$ when x is an integer from 1 to 8. Make a conjecture about the type of number generated by the rule. Continue your table. What value of x generates a counterexample?

Solution

Verified
Step 1
1 of 2

Given expression:

$\begin{equation*} x^2 + x + 11 \end{equation*}$

Substitute $x=1$ and evaluate the value of the expression:

$\begin{equation*} (1)^2 + 1 + 11=13 \end{equation*}$

Substitute $x=2$ and evaluate the value of the expression:

$\begin{equation*} (2)^2 + 2 + 11=17 \end{equation*}$

Substitute $x=3$ and evaluate the value of the expression:

$\begin{equation*} (3)^2 + 3 + 11=23 \end{equation*}$

Substitute $x=4$ and evaluate the value of the expression:

$\begin{equation*} (4)^2 + 4 + 11=31 \end{equation*}$

Substitute $x=5$ and evaluate the value of the expression:

$\begin{equation*} (5)^2 + 5 + 11=41 \end{equation*}$

Substitute $x=6$ and evaluate the value of the expression:

$\begin{equation*} (6)^2 + 6 + 11=53 \end{equation*}$

Substitute $x=7$ and evaluate the value of the expression:

$\begin{equation*} (7)^2 + 7 + 11=67 \end{equation*}$

Substitute $x=8$ and evaluate the value of the expression:

$\begin{equation*} (8)^2 + 8 + 11=83 \end{equation*}$

This expression generates prime numbers in ascending order.

## Recommended textbook solutions

#### Connected Mathematics 3: Shapes and Designs, Two-Dimensional Geometry

1st EditionISBN: 9780133274479Prentice Hall

#### Georgia Analytic Geometry

1st EditionISBN: 9780547867656David J. Chard, Edward B. Burger, Paul A. Kennedy, Steven J. Leinwand
2,313 solutions

#### Eureka Math - A Story of Functions

ISBN: 9781632553270Great Minds

#### 6th Grade Math - Volume 2 (2019-2020 Course Workbook)

ISBN: 9781733055079Algebra Nation
user
The text passage contains a mathematical question that asks to create a table of values for a given expression and to make a conjecture about the type of number generated. The solution is also provided, showing the evaluation of the expression for integers from 1 to 8 and concluding that the expression generates prime numbers in ascending order.

TYPE: SINGLE_QUESTION_WITH_ANSWER