Answer :
To solve the problem of finding [tex]\( f(8, -4) \)[/tex] for the function [tex]\( f(x, y) = 7x^2 - 9xy \)[/tex], follow these steps:
1. Identify the given function:
The function is [tex]\( f(x, y) = 7x^2 - 9xy \)[/tex].
2. Substitute the given values:
You need to find the value of the function at the point [tex]\((8, -4)\)[/tex]. Substitute [tex]\( x = 8 \)[/tex] and [tex]\( y = -4 \)[/tex] into the function.
3. Calculate each term:
- Compute [tex]\( 7x^2 \)[/tex]:
[tex]\[
7(8^2) = 7 \times 64 = 448
\][/tex]
- Compute [tex]\( -9xy \)[/tex]:
[tex]\[
-9 \times 8 \times (-4) = -9 \times -32 = 288
\][/tex]
4. Add the results together:
Now add the results from steps 3 together:
[tex]\[
448 + 288 = 736
\][/tex]
Therefore, the value of [tex]\( f(8, -4) \)[/tex] is [tex]\( 736 \)[/tex].
Thus, none of the given multiple-choice options (A. -76, B. 148, C. 76, D. 160) match the computed result, which is [tex]\( 736 \)[/tex].
1. Identify the given function:
The function is [tex]\( f(x, y) = 7x^2 - 9xy \)[/tex].
2. Substitute the given values:
You need to find the value of the function at the point [tex]\((8, -4)\)[/tex]. Substitute [tex]\( x = 8 \)[/tex] and [tex]\( y = -4 \)[/tex] into the function.
3. Calculate each term:
- Compute [tex]\( 7x^2 \)[/tex]:
[tex]\[
7(8^2) = 7 \times 64 = 448
\][/tex]
- Compute [tex]\( -9xy \)[/tex]:
[tex]\[
-9 \times 8 \times (-4) = -9 \times -32 = 288
\][/tex]
4. Add the results together:
Now add the results from steps 3 together:
[tex]\[
448 + 288 = 736
\][/tex]
Therefore, the value of [tex]\( f(8, -4) \)[/tex] is [tex]\( 736 \)[/tex].
Thus, none of the given multiple-choice options (A. -76, B. 148, C. 76, D. 160) match the computed result, which is [tex]\( 736 \)[/tex].
