Question
Does (5, 0) make the equation y = 6x^2 − x + –7 true?
Answers
GPT-4o mini
To determine if the point (5, 0) satisfies the equation \( y = 6x^2 - x - 7 \), we can substitute \( x = 5 \) into the equation and check if the result equals \( y = 0 \).
Starting with the equation:
\[
y = 6x^2 - x - 7
\]
Substituting \( x = 5 \):
\[
y = 6(5)^2 - (5) - 7
\]
Calculating \( 6(5)^2 \):
\[
6(25) = 150
\]
Now substituting back:
\[
y = 150 - 5 - 7
\]
Calculating the remaining terms:
\[
y = 150 - 5 = 145
\]
\[
y = 145 - 7 = 138
\]
So when \( x = 5 \), \( y = 138 \).
Now we compare this with the given point (5, 0):
Since \( y = 138 \) does not equal \( 0 \), the point (5, 0) does not satisfy the equation \( y = 6x^2 - x - 7 \). Therefore, (5, 0) does not make the equation true.
Starting with the equation:
\[
y = 6x^2 - x - 7
\]
Substituting \( x = 5 \):
\[
y = 6(5)^2 - (5) - 7
\]
Calculating \( 6(5)^2 \):
\[
6(25) = 150
\]
Now substituting back:
\[
y = 150 - 5 - 7
\]
Calculating the remaining terms:
\[
y = 150 - 5 = 145
\]
\[
y = 145 - 7 = 138
\]
So when \( x = 5 \), \( y = 138 \).
Now we compare this with the given point (5, 0):
Since \( y = 138 \) does not equal \( 0 \), the point (5, 0) does not satisfy the equation \( y = 6x^2 - x - 7 \). Therefore, (5, 0) does not make the equation true.