Certainly! Let's go through each algebraic expression step-by-step and write the corresponding BASIC expressions/statements for them.
(a) Expression: [tex]\( 3x + 5 \)[/tex]
In BASIC, you can write this expression as follows:
```BASIC
LET result = 3 x + 5
```
Explanation:
- `LET` is used in BASIC to assign a value to a variable.
- `3 x + 5` directly translates to [tex]\( 3x + 5 \)[/tex].
(b) Expression: [tex]\( 5x^2 + 6x - 3 \)[/tex]
In BASIC, you can write this expression as follows:
```BASIC
LET result = 5 x^2 + 6 x - 3
```
Explanation:
- `5 x^2 + 6 x - 3` directly translates to [tex]\( 5x^2 + 6x - 3 \)[/tex]. In BASIC, you can use `^` for exponentiation if the version you're using supports it, or you may need to use a different method if it doesn't.
(c) Expression: [tex]\( y = mx + c \)[/tex]
In BASIC, you can write this expression as follows:
```BASIC
LET y = m x + c
```
Explanation:
- `LET` is used to assign the value to `y`.
- `m x + c` directly translates to [tex]\( mx + c \)[/tex].
(d) Expression: [tex]\( x = (a + b)^2 \)[/tex]
In BASIC, you can write this expression as follows:
```BASIC
LET x = (a + b)^2
```
Explanation:
- `LET` is used to assign the value to `x`.
- `(a + b)^2` directly translates to [tex]\( (a + b)^2 \)[/tex].
(e) Expression: [tex]\( (u + v)^{k - 1} \)[/tex]
In BASIC, you can write this expression as follows:
```BASIC
LET result = (u + v)^(k - 1)
```
Explanation:
- `LET` is used to assign the value to `result`.
- `(u + v)^(k - 1)` directly translates to [tex]\( (u + v)^{k-1} \)[/tex].
If your version of BASIC does not support the use of `^` for exponentiation, you might have to use specific functions or methods provided by the language for calculating powers.
Therefore, the corresponding BASIC expressions/statements for the given algebraic expressions are:
1. [tex]\( 3x + 5 \)[/tex]:
```BASIC
LET result = 3 x + 5
```
2. [tex]\( 5x^2 + 6x - 3 \)[/tex]:
```BASIC
LET result = 5 x^2 + 6 x - 3
```
3. [tex]\( y = mx + c \)[/tex]:
```BASIC
LET y = m x + c
```
4. [tex]\( x = (a + b)^2 \)[/tex]:
```BASIC
LET x = (a + b)^2
```
5. [tex]\( (u + v)^{k-1} \)[/tex]:
```BASIC
LET result = (u + v)^(k - 1)
```
