Certainly! Let's explore the expressions step by step.
Given:
[tex]\[ x = 2 \][/tex]
[tex]\[ y = 32 \][/tex]
We need to find:
(a) [tex]\( x + y + z \)[/tex]
(b) [tex]\( 9x - 3y + 41 \)[/tex]
### (a) [tex]\( x + y + z \)[/tex]
First, let's substitute the known values of [tex]\(x\)[/tex] and [tex]\( y \)[/tex]:
[tex]\[ x = 2 \][/tex]
[tex]\[ y = 32 \][/tex]
So,
[tex]\[ x + y + z = 2 + 32 + z \][/tex]
Let's simplify this expression:
[tex]\[ x + y + z = 34 + z \][/tex]
### (b) [tex]\( 9x - 3y + 41 \)[/tex]
Now, substitute the known values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex]:
[tex]\[ x = 2 \][/tex]
[tex]\[ y = 32 \][/tex]
So:
[tex]\[ 9x - 3y + 41 \][/tex]
Calculating each term separately:
[tex]\[ 9x = 9 \times 2 = 18 \][/tex]
[tex]\[ 3y = 3 \times 32 = 96 \][/tex]
Substituting these into the expression gives us:
[tex]\[ 9x - 3y + 41 = 18 - 96 + 41 \][/tex]
Now, simplify:
[tex]\[ 18 - 96 = -78 \][/tex]
[tex]\[ -78 + 41 = -37 \][/tex]
So:
[tex]\[ 9x - 3y + 41 = -37 \][/tex]
### Summary of Results
(a) The expression [tex]\( x + y + z \)[/tex] in terms of [tex]\(z\)[/tex] is:
[tex]\[ 34 + z \][/tex]
(b) The value of the expression [tex]\( 9x - 3y + 41 \)[/tex] is:
[tex]\[ -37 \][/tex]
Thus, we have [tex]\( 34 + z \)[/tex] for the first expression and [tex]\(-37\)[/tex] for the second one.
