Question
Ben is trying to determine if x=23
is a solution to the quadratic equation 9x2+3x−5=6
. Which explanation below demonstrates the correct reasoning?(1 point)
Responses
Yes, x=23
is a solution because substituting it back into the equation results in 6 = 6, which is a true statement.
Yes, x is equal to 2 thirds is a solution because substituting it back into the equation results in 6 = 6, which is a true statement.
No, x=23
is not a solution because substituting it back into the equation results in 6 = 6, which is a false statement.
No, x is equal to 2 thirds is not a solution because substituting it back into the equation results in 6 = 6, which is a false statement.
No, x=23
is not a solution because substituting it back into the equation results in 1 = 6, which is a false statement.
No, x is equal to 2 thirds is not a solution because substituting it back into the equation results in 1 = 6, which is a false statement.
Yes, x=23
is a solution because substituting it back into the equation results in 1 = 6, which is a true statement.
Yes, x is equal to 2 thirds is a solution because substituting it back into the equation results in 1 = 6, which is a true statement.
is a solution to the quadratic equation 9x2+3x−5=6
. Which explanation below demonstrates the correct reasoning?(1 point)
Responses
Yes, x=23
is a solution because substituting it back into the equation results in 6 = 6, which is a true statement.
Yes, x is equal to 2 thirds is a solution because substituting it back into the equation results in 6 = 6, which is a true statement.
No, x=23
is not a solution because substituting it back into the equation results in 6 = 6, which is a false statement.
No, x is equal to 2 thirds is not a solution because substituting it back into the equation results in 6 = 6, which is a false statement.
No, x=23
is not a solution because substituting it back into the equation results in 1 = 6, which is a false statement.
No, x is equal to 2 thirds is not a solution because substituting it back into the equation results in 1 = 6, which is a false statement.
Yes, x=23
is a solution because substituting it back into the equation results in 1 = 6, which is a true statement.
Yes, x is equal to 2 thirds is a solution because substituting it back into the equation results in 1 = 6, which is a true statement.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine if \( x = 23 \) is a solution to the equation \( 9x^2 + 3x - 5 = 6 \), we can substitute \( x = 23 \) into the left-hand side of the equation and check if it equals 6.
First, substitute \( x = 23 \):
\[
9(23^2) + 3(23) - 5
\]
Calculating \( 23^2 \):
\[
23^2 = 529
\]
Now, substitute this value back into the equation:
\[
9(529) + 3(23) - 5 = 4761 + 69 - 5 = 4825
\]
Now, we compare:
\[
4825 \neq 6
\]
Since substituting \( x = 23 \) into the left hand side of the equation does not yield 6, we can conclude that \( x = 23 \) is not a solution.
Among the options, the correct reasoning would be:
**No, x=23 is not a solution because substituting it back into the equation results in \( 4825 \neq 6 \), which is a false statement.**
However, since this specific option is not listed in your responses, based on the available responses, the closest correct reasoning would be:
**No, x=23 is not a solution because substituting it back into the equation results in \( 1 = 6 \), which is a false statement.**
(This option is incorrect as '1' does not equal '6', but it's the only choice indicating that \( x=23 \) is not a solution.)
First, substitute \( x = 23 \):
\[
9(23^2) + 3(23) - 5
\]
Calculating \( 23^2 \):
\[
23^2 = 529
\]
Now, substitute this value back into the equation:
\[
9(529) + 3(23) - 5 = 4761 + 69 - 5 = 4825
\]
Now, we compare:
\[
4825 \neq 6
\]
Since substituting \( x = 23 \) into the left hand side of the equation does not yield 6, we can conclude that \( x = 23 \) is not a solution.
Among the options, the correct reasoning would be:
**No, x=23 is not a solution because substituting it back into the equation results in \( 4825 \neq 6 \), which is a false statement.**
However, since this specific option is not listed in your responses, based on the available responses, the closest correct reasoning would be:
**No, x=23 is not a solution because substituting it back into the equation results in \( 1 = 6 \), which is a false statement.**
(This option is incorrect as '1' does not equal '6', but it's the only choice indicating that \( x=23 \) is not a solution.)
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.