Let's go through each algebraic expression step by step and determine the numerical values given the specific values for the variables:
1. Expression [tex]\( m + 5 \)[/tex] with [tex]\( m = 6 \)[/tex]:
- To find the value of this expression, simply add 5 to the given value of [tex]\( m \)[/tex].
- Calculation: [tex]\( 6 + 5 = 11 \)[/tex]
- Therefore, [tex]\( m + 5 = 11 \)[/tex].
2. Expression [tex]\( 2x - 1 \)[/tex] with [tex]\( x = 8 \)[/tex]:
- For this expression, multiply the given value of [tex]\( x \)[/tex] by 2, and then subtract 1.
- Calculation: [tex]\( 2 \times 8 = 16 \)[/tex] and [tex]\( 16 - 1 = 15 \)[/tex]
- Therefore, [tex]\( 2x - 1 = 15 \)[/tex].
3. Expression [tex]\( x^2 + 4 \)[/tex] with [tex]\( x = 5 \)[/tex]:
- First, square the given value of [tex]\( x \)[/tex], and then add 4.
- Calculation: [tex]\( 5^2 = 25 \)[/tex] and [tex]\( 25 + 4 = 29 \)[/tex]
- Therefore, [tex]\( x^2 + 4 = 29 \)[/tex].
4. Expression [tex]\( 3x^3 - 8 \)[/tex] with [tex]\( x = 2 \)[/tex]:
- Cube the given value of [tex]\( x \)[/tex], multiply by 3, and then subtract 8.
- Calculation: [tex]\( 2^3 = 8 \)[/tex], [tex]\( 3 \times 8 = 24 \)[/tex], and [tex]\( 24 - 8 = 16 \)[/tex]
- Therefore, [tex]\( 3x^3 - 8 = 16 \)[/tex].
So, here are the results for each expression:
- [tex]\( m + 5 = 11 \)[/tex]
- [tex]\( 2x - 1 = 15 \)[/tex]
- [tex]\( x^2 + 4 = 29 \)[/tex]
- [tex]\( 3x^3 - 8 = 16 \)[/tex]
The final numerical values obtained are: [tex]\( 11 \)[/tex], [tex]\( 15 \)[/tex], [tex]\( 29 \)[/tex], and [tex]\( 16 \)[/tex].
