To determine the value of [tex]\( c \)[/tex] as specified in the given problem, we need to analyze the options provided to identify the correct first step in the solution process:
The options are:
1. [tex]\( 40 + 9 = c \)[/tex]
2. [tex]\( (40 + 9)^2 = c^2 \)[/tex]
3. [tex]\( 40^2 + 9^2 = c^2 \)[/tex]
4. [tex]\( 40^2 + 9^2 = c \)[/tex]
Let's consider what each option represents:
1. [tex]\( 40 + 9 = c \)[/tex]:
- This suggests a simple addition of the two numbers. However, that doesn't apply here as we are dealing with squares of the numbers.
2. [tex]\( (40 + 9)^2 = c^2 \)[/tex]:
- This indicates squaring the sum of 40 and 9 which is not the correct approach for this type of problem.
3. [tex]\( 40^2 + 9^2 = c^2 \)[/tex]:
- This implies the use of the Pythagorean theorem typically used in a right triangle, suggesting [tex]\( c \)[/tex] would be the hypotenuse. However, this doesn't match the form given in the problem.
4. [tex]\( 40^2 + 9^2 = c \)[/tex]:
- Here we square each number individually and then sum these squares to find [tex]\( c \)[/tex]. Typically, if the sum of squares is given directly equal to [tex]\( c \)[/tex] and not [tex]\( c^2 \)[/tex], this format matches the problem's context directly.
Thus, the correct first step to find the value of [tex]\( c \)[/tex] is to use:
[tex]\[ 40^2 + 9^2 = c \][/tex]
Therefore, the correct first step is option 4.
