1. Write down the numbers that are integers from the following list:

[tex]\[ 117,4; -4561234; \sqrt[3]{\frac{54}{2}}; 67598; \frac{5}{8}; 0,125; -\frac{1}{2}; \sqrt{36} \][/tex]

2. Write the following numbers in ascending order:

[tex]\[ -9942; -16432; -33915; -20020; -8978 \][/tex]

3. The temperature one night in Ulundi was measured at [tex]$-1^{\circ} C$[/tex]. The temperature increased to [tex]$8^{\circ} C$[/tex] the next day. By how many degrees did the temperature rise?

4. Which temperature is lower?

[tex]$-3^{\circ} C$[/tex] or [tex]$-4^{\circ} C$[/tex]

5. Calculate the value of the expression [tex]$-x^2 + 3x - 2$[/tex] when:

a) [tex]$x = -2$[/tex]

b) [tex]$x = 0$[/tex]

6. Calculate:

a) [tex]$-64 - 103 + 75$[/tex]

b) [tex]$58 - (-17) + 12$[/tex]

7. Simplify the following:

a) [tex]$16a^2 - 21b - 32a^2 + 19b$[/tex]

b) [tex]$-5x^2 + 7x - 14x^2 - 32x$[/tex]

Sure! Let's go through each question step by step:

### Question 1: Identify the Integers
We need to determine which numbers from the given list are integers:
- [tex]$117.4$[/tex]: Not an integer.
- [tex]$-4561234$[/tex]: An integer.
- [tex]$\sqrt[3]{\frac{54}{2}}$[/tex]: This evaluates to [tex]$3$[/tex], which is an integer.
- [tex]$67598$[/tex]: An integer.
- [tex]$\frac{5}{8}$[/tex]: Not an integer, as it's a fraction.
- [tex]$0.125$[/tex]: Not an integer, as it's a decimal.
- [tex]$-\frac{1}{2}$[/tex]: Not an integer, as it's a fraction.
- [tex]$\sqrt{36}$[/tex]: This evaluates to [tex]$6$[/tex], which is an integer.

Integers from the list: [tex]$-4561234$[/tex], [tex]$3$[/tex], [tex]$67598$[/tex], [tex]$6$[/tex].

### Question 2: Sorting Numbers in Ascending Order
Given the numbers: [tex]$-9942$[/tex], [tex]$-16432$[/tex], [tex]$-33915$[/tex], [tex]$-20020$[/tex], [tex]$-8978$[/tex]. We sort them from the smallest to the largest:

Ascending order: [tex]$-33915$[/tex], [tex]$-20020$[/tex], [tex]$-16432$[/tex], [tex]$-9942$[/tex], [tex]$-8978$[/tex].

### Question 3: Temperature Rise
- Initial temperature: [tex]$-1^\circ C$[/tex]
- Final temperature: [tex]$8^\circ C$[/tex]
- To find the temperature increase, subtract the initial temperature from the final temperature:
[tex]$8 - (-1) = 9$[/tex]

Temperature rise: [tex]$9^\circ C$[/tex].

### Question 4: Lower Temperature
- Compare [tex]$-3^\circ C$[/tex] and [tex]$-4^\circ C$[/tex].

Since [tex]$-4^\circ C$[/tex] is less than [tex]$-3^\circ C$[/tex], it's the lower temperature.

Lower temperature: [tex]$-4^\circ C$[/tex].

### Question 5: Evaluate the Expression [tex]$-x^2 + 3x - 2$[/tex]
- For [tex]$x = -2$[/tex]:
[tex]\[
-(-2)^2 + 3(-2) - 2 = -4 - 6 - 2 = -12
\][/tex]

- For [tex]$x = 0$[/tex]:
[tex]\[
-(0)^2 + 3(0) - 2 = 0 + 0 - 2 = -2
\][/tex]

Evaluated values:
- [tex]$x = -2$[/tex]: [tex]$-12$[/tex]
- [tex]$x = 0$[/tex]: [tex]$-2$[/tex]

### Question 6: Calculations
- [tex]$ -64 - 103 + 75 $[/tex]:
[tex]\[
= -64 - 103 + 75 = -92
\][/tex]

- [tex]$ 58 - (-17) + 12 $[/tex]:
[tex]\[
= 58 + 17 + 12 = 87
\][/tex]

Results:
- [tex]$ -92 $[/tex]
- [tex]$ 87 $[/tex]

### Question 7: Simplify the Expressions
- [tex]$16a^2 - 21b - 32a^2 + 19b$[/tex]:
- Combine like terms:
[tex]$(16a^2 - 32a^2) + (-21b + 19b) = -16a^2 - 2b$[/tex]

- [tex]$-5x^2 + 7x - 14x^2 - 32x$[/tex]:
- Combine like terms:
[tex]$(-5x^2 - 14x^2) + (7x - 32x) = -19x^2 - 25x$[/tex]

Simplified expressions:
- [tex]$-16a^2 - 2b$[/tex]
- [tex]$-19x^2 - 25x$[/tex]

I hope this detailed explanation helps! Let me know if you have more questions.