Answer :
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.
### 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.
