Sure! Let's solve each expression step-by-step given the specified values for [tex]\( x \)[/tex].
First, we need to solve the expression [tex]\( x^2 + 4 \)[/tex] when [tex]\( x = 5 \)[/tex].
1. Start with the expression: [tex]\( x^2 + 4 \)[/tex]
2. Substitute [tex]\( x \)[/tex] with 5: [tex]\( 5^2 + 4 \)[/tex]
3. Calculate [tex]\( 5^2 \)[/tex]: [tex]\( 5^2 = 25 \)[/tex]
4. Add 4 to 25: [tex]\( 25 + 4 = 29 \)[/tex]
So, the value of [tex]\( x^2 + 4 \)[/tex] when [tex]\( x = 5 \)[/tex] is 29.
Next, let's solve the expression [tex]\( 3x^3 - 8 \)[/tex] when [tex]\( x = 2 \)[/tex].
1. Start with the expression: [tex]\( 3x^3 - 8 \)[/tex]
2. Substitute [tex]\( x \)[/tex] with 2: [tex]\( 3 \cdot 2^3 - 8 \)[/tex]
3. Calculate [tex]\( 2^3 \)[/tex]: [tex]\( 2^3 = 8 \)[/tex]
4. Multiply 3 by 8: [tex]\( 3 \cdot 8 = 24 \)[/tex]
5. Subtract 8 from 24: [tex]\( 24 - 8 = 16 \)[/tex]
So, the value of [tex]\( 3x^3 - 8 \)[/tex] when [tex]\( x = 2 \)[/tex] is 16.
Summarizing the results:
- For [tex]\( x = 5 \)[/tex], [tex]\( x^2 + 4 = 29 \)[/tex]
- For [tex]\( x = 2 \)[/tex], [tex]\( 3x^3 - 8 = 16 \)[/tex]
Thus, the values are 29 and 16, respectively.
