Murphy Wagner
02/27/2024 · Junior High School
\( 16 \left. \begin{array} { l } { J = ( - 5 - 7 + 4 ) \times ( - 4 - 5 + 9 ) + ( + 5 ) \times ( + 5 ) + ( - 4 ) \times ( - 7 ) - ( - 4 ) } \\ { K = ( - 4 ) \times ( + 2 ) + ( + 5 ) - ( + 3 ) \times ( - 4 ) - ( + 2 ) \times ( - 7 ) \times ( - 7 ) - ( - 5 ) + ( - 4 ) } \\ { L = ( + 3 ) \times ( - 9 ) \times ( + 5 ) + ( + 3 ) - ( - 4 ) \times ( + 2 ) = ( - 7 ) \times ( - 8 ) - ( - 5 ) - ( - 4 ) } \end{array} \right. \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Let's calculate the values of \( J \), \( K \), and \( L \) step by step.
### Calculation of \( J \)
\[
J = ( - 5 - 7 + 4 ) \times ( - 4 - 5 + 9 ) + ( + 5 ) \times ( + 5 ) + ( - 4 ) \times ( - 7 ) - ( - 4 )
\]
1. Calculate \( -5 - 7 + 4 \):
\[
-5 - 7 = -12 \quad \text{and} \quad -12 + 4 = -8
\]
2. Calculate \( -4 - 5 + 9 \):
\[
-4 - 5 = -9 \quad \text{and} \quad -9 + 9 = 0
\]
3. Now substitute back into \( J \):
\[
J = (-8) \times 0 + 5 \times 5 + (-4) \times (-7) - (-4)
\]
\[
J = 0 + 25 + 28 + 4
\]
\[
J = 0 + 25 + 28 + 4 = 57
\]
### Calculation of \( K \)
\[
K = ( - 4 ) \times ( + 2 ) + ( + 5 ) - ( + 3 ) \times ( - 4 ) - ( + 2 ) \times ( - 7 ) \times ( - 7 ) - ( - 5 ) + ( - 4 )
\]
1. Calculate \( -4 \times 2 \):
\[
-4 \times 2 = -8
\]
2. Calculate \( 3 \times -4 \):
\[
3 \times -4 = -12
\]
3. Calculate \( 2 \times -7 \times -7 \):
\[
-7 \times -7 = 49 \quad \text{and} \quad 2 \times 49 = 98
\]
4. Now substitute back into \( K \):
\[
K = -8 + 5 - (-12) - 98 - (-5) - 4
\]
\[
K = -8 + 5 + 12 - 98 + 5 - 4
\]
\[
K = -8 + 5 + 12 + 5 - 98 - 4
\]
\[
K = 10 - 98 = -88
\]
### Calculation of \( L \)
\[
L = ( + 3 ) \times ( - 9 ) \times ( + 5 ) + ( + 3 ) - ( - 4 ) \times ( + 2 ) = ( - 7 ) \times ( - 8 ) - ( - 5 ) - ( - 4 )
\]
1. Calculate \( 3 \times -9 \times 5 \):
\[
3 \times -9 = -27 \quad \text{and} \quad -27 \times 5 = -135
\]
2. Calculate \( -4 \times 2 \):
\[
-4 \times 2 = -8
\]
3. Now substitute back into \( L \):
\[
L = -135 + 3 - (-8) = -135 + 3 + 8
\]
\[
L = -135 + 11 = -124
\]
4. Calculate the right side:
\[
(-7) \times (-8) = 56
\]
\[
56 - (-5) - (-4) = 56 + 5 + 4 = 65
\]
### Final Results
Thus, we have:
\[
J = 57, \quad K = -88, \quad L = -124
\]
The final values are:
\[
\boxed{57}, \quad \boxed{-88}, \quad \boxed{-124}
\]
Quick Answer
J = 57, K = -88, L = -124
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