Question
What is the value of the expression below when z=5? 4z^{2}-7z-2
Ask by Morgan Sandoval.
Feb 07,2025 08:27
UpStudy AI Solution
Tutor-Verified Answer
Answer
When \( z = 5 \), the expression \( 4z^{2} - 7z - 2 \) equals 63.
Solution
To evaluate the expression 4z² - 7z - 2 when z = 5, follow these steps:
1. Substitute 5 for z:
4(5)² - 7(5) - 2
2. Calculate (5)²:
4(25) - 35 - 2
3. Multiply:
100 - 35 - 2
4. Perform the subtractions:
100 - 35 = 65
65 - 2 = 63
Thus, the value of the expression when z = 5 is 63.
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Simplify this solution Extra Insights
To find the value of the expression \( 4 z^{2}-7 z-2 \) when \( z=5 \), we substitute \( z \) with \( 5 \):
\[
4(5)^{2} - 7(5) - 2
\]
Calculating \( 5^2 \):
\[
5^2 = 25
\]
Now substituting this back into the expression:
\[
4(25) - 7(5) - 2
\]
Calculating \( 4(25) \):
\[
4 \times 25 = 100
\]
Calculating \( 7(5) \):
\[
7 \times 5 = 35
\]
Now substituting these values back:
\[
100 - 35 - 2
\]
Now performing the subtraction:
\[
100 - 35 = 65
\]
Now subtract \( 2 \):
\[
65 - 2 = 63
\]
Thus, the value of the expression when \( z=5 \) is \(\boxed{63}\).
