Let's address each part of the question step-by-step:
### 1.3.1 Length of the Other Part of the Rope
You have an 8-meter piece of rope and it is divided into two parts. One part of the rope is [tex]\( z \)[/tex] meters. To find the length of the other part, you simply subtract the length of the known part from the total length.
[tex]\[
\text{Length of the other part} = 8 - z
\][/tex]
Given [tex]\( z = 5 \)[/tex]:
[tex]\[
\text{Length of the other part} = 8 - 5 = 3 \text{ meters}
\][/tex]
### 1.3.2 Subtract the Product of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] from the Sum of [tex]\( x \)[/tex] and [tex]\( y \)[/tex]
First, write down the sum of [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[
x + y
\][/tex]
Next, write down the product of [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[
x \times y = xy
\][/tex]
To find the result, subtract the product from the sum:
[tex]\[
(x + y) - xy
\][/tex]
Given [tex]\( x = 2 \)[/tex] and [tex]\( y = 3 \)[/tex]:
[tex]\[
(x + y) - xy = (2 + 3) - (2 \times 3) = 5 - 6 = -1
\][/tex]
### 1.3.3 Subtract the Sum of [tex]\( 4x \)[/tex] and [tex]\( 5y \)[/tex] from the Difference Between [tex]\( 4x \)[/tex] and [tex]\( 5y \)[/tex]
First, determine the difference between [tex]\( 4x \)[/tex] and [tex]\( 5y \)[/tex]:
[tex]\[
4x - 5y
\][/tex]
Next, determine the sum of [tex]\( 4x \)[/tex] and [tex]\( 5y \)[/tex]:
[tex]\[
4x + 5y
\][/tex]
To find the result, subtract the sum from the difference:
[tex]\[
(4x - 5y) - (4x + 5y)
\][/tex]
Given [tex]\( x = 2 \)[/tex] and [tex]\( y = 3 \)[/tex]:
[tex]\[
(4x - 5y) - (4x + 5y) = (4 \times 2 - 5 \times 3) - (4 \times 2 + 5 \times 3)
\][/tex]
[tex]\[
= (8 - 15) - (8 + 15) = -7 - 23 = -30
\][/tex]
### Summary of Results
- The length of the other part of the rope is [tex]\( 8 - z \)[/tex]. For [tex]\( z = 5 \)[/tex], it is 3 meters.
- The expression [tex]\((x + y) - xy\)[/tex] for [tex]\( x = 2 \)[/tex] and [tex]\( y = 3 \)[/tex] evaluates to [tex]\(-1\)[/tex].
- The expression [tex]\((4x - 5y) - (4x + 5y)\)[/tex] for [tex]\( x = 2 \)[/tex] and [tex]\( y = 3 \)[/tex] evaluates to [tex]\(-30\)[/tex].
Thus, the results for your algebraic expressions are:
[tex]\[
3, -1, -30
\][/tex]
