Answer :
To determine which of the given equations are equivalent, we will compare the forms of each equation. Let's go through each one step by step to find any that are equivalent.
1. Equation 1: [tex]\( T = 150c - 3 \)[/tex]
This equation is given in the form where [tex]\( T \)[/tex] is defined in terms of [tex]\( c \)[/tex].
2. Equation 2: [tex]\( T = -3c + 150 \)[/tex]
This equation is also presented with [tex]\( T \)[/tex] in terms of [tex]\( c \)[/tex]. We can try to rearrange this equation to see if it matches the form of Equation 1.
- Start with Equation 2:
[tex]\( T = -3c + 150 \)[/tex]
- Rearrange to match the form of Equation 1:
[tex]\( T = 150 - 3c \)[/tex]
If we compare it with [tex]\( T = 150c - 3 \)[/tex], we observe they are not in the same form yet.
The key here is to recognize that these two sets of expressions can actually represent the same line when graphing or solving, depending on the interpretation of the constants and variables involved.
3. Equation 3: [tex]\( T = -150c + 3 \)[/tex]
This equation is fundamentally different from the first two. The coefficients and constant terms vary making it clearly different.
4. Equation 4: [tex]\( T = 3c - 150 \)[/tex]
This equation is also in a different form compared to what's been seen in Equation 1 and 2.
By reviewing Equations 1 and 2, we observe that despite appearing different, they describe the same linear relationship in terms of the variables and constants involved when considering equivalent rearrangement. Therefore, they are equivalent expressions.
The conclusion is:
The equations [tex]\( T = 150c - 3 \)[/tex] and [tex]\( T = -3c + 150 \)[/tex] are equivalent.
1. Equation 1: [tex]\( T = 150c - 3 \)[/tex]
This equation is given in the form where [tex]\( T \)[/tex] is defined in terms of [tex]\( c \)[/tex].
2. Equation 2: [tex]\( T = -3c + 150 \)[/tex]
This equation is also presented with [tex]\( T \)[/tex] in terms of [tex]\( c \)[/tex]. We can try to rearrange this equation to see if it matches the form of Equation 1.
- Start with Equation 2:
[tex]\( T = -3c + 150 \)[/tex]
- Rearrange to match the form of Equation 1:
[tex]\( T = 150 - 3c \)[/tex]
If we compare it with [tex]\( T = 150c - 3 \)[/tex], we observe they are not in the same form yet.
The key here is to recognize that these two sets of expressions can actually represent the same line when graphing or solving, depending on the interpretation of the constants and variables involved.
3. Equation 3: [tex]\( T = -150c + 3 \)[/tex]
This equation is fundamentally different from the first two. The coefficients and constant terms vary making it clearly different.
4. Equation 4: [tex]\( T = 3c - 150 \)[/tex]
This equation is also in a different form compared to what's been seen in Equation 1 and 2.
By reviewing Equations 1 and 2, we observe that despite appearing different, they describe the same linear relationship in terms of the variables and constants involved when considering equivalent rearrangement. Therefore, they are equivalent expressions.
The conclusion is:
The equations [tex]\( T = 150c - 3 \)[/tex] and [tex]\( T = -3c + 150 \)[/tex] are equivalent.
