Question
Does (5, 0) make the equation y = –51x2 + 5x + 5 true?
Answers
GPT-4o mini
To determine if the point \((5, 0)\) makes the equation \(y = -51x^2 + 5x + 5\) true, we need to substitute \(x = 5\) into the equation and see if the resulting \(y\) value equals 0.
Let's do the calculation:
1. Substitute \(x = 5\) into the equation:
\[
y = -51(5^2) + 5(5) + 5
\]
2. Calculate \(5^2\):
\[
5^2 = 25
\]
3. Substitute this value into the equation:
\[
y = -51(25) + 5(5) + 5
\]
4. Calculate each term:
\[
y = -1275 + 25 + 5
\]
5. Combine the terms:
\[
y = -1275 + 30 = -1245
\]
Now we have found that for \(x = 5\), \(y = -1245\), which is not equal to 0.
Thus, the point \((5, 0)\) does not satisfy the equation \(y = -51x^2 + 5x + 5\).
Let's do the calculation:
1. Substitute \(x = 5\) into the equation:
\[
y = -51(5^2) + 5(5) + 5
\]
2. Calculate \(5^2\):
\[
5^2 = 25
\]
3. Substitute this value into the equation:
\[
y = -51(25) + 5(5) + 5
\]
4. Calculate each term:
\[
y = -1275 + 25 + 5
\]
5. Combine the terms:
\[
y = -1275 + 30 = -1245
\]
Now we have found that for \(x = 5\), \(y = -1245\), which is not equal to 0.
Thus, the point \((5, 0)\) does not satisfy the equation \(y = -51x^2 + 5x + 5\).