To determine which equations hold true when [tex]\( c = 9 \)[/tex], let's substitute [tex]\( c = 9 \)[/tex] into each equation and check for validity.
1. Equation (A): [tex]\( 4 - c = 5 \)[/tex]
[tex]\[
4 - 9 = 5
\][/tex]
[tex]\[
-5 = 5 \quad \text{(False)}
\][/tex]
2. Equation (B): [tex]\( 20 = 14 + c \)[/tex]
[tex]\[
20 = 14 + 9
\][/tex]
[tex]\[
20 = 23 \quad \text{(False)}
\][/tex]
3. Equation (C): [tex]\( 15 = c - 6 \)[/tex]
[tex]\[
15 = 9 - 6
\][/tex]
[tex]\[
15 = 3 \quad \text{(False)}
\][/tex]
4. Equation (D): [tex]\( \frac{c}{3} = 3 \)[/tex]
[tex]\[
\frac{9}{3} = 3
\][/tex]
[tex]\[
3 = 3 \quad \text{(True)}
\][/tex]
5. Equation (E): [tex]\( 36 = 4c \)[/tex]
[tex]\[
36 = 4 \times 9
\][/tex]
[tex]\[
36 = 36 \quad \text{(True)}
\][/tex]
Among the given equations, equations (D) and (E) are satisfied when [tex]\( c = 9 \)[/tex].
So the correct answers are:
- (D) [tex]\( \frac{c}{3} = 3 \)[/tex]
- (E) [tex]\( 36 = 4c \)[/tex]
