Answer :
Sure! Let's go through each part step by step:
1. Integer Identification:
We need to identify which numbers in the list are integers. Remember, integers are whole numbers that can be positive, negative, or zero. Here's the list with our determination:
- [tex]\(1174\)[/tex] is an integer.
- [tex]\(-4561234\)[/tex] is an integer.
- [tex]\(\sqrt[3]{\frac{54}{2}}\)[/tex] simplifies to [tex]\(3.0\)[/tex], which is also an integer.
- [tex]\(67598\)[/tex] is an integer.
- [tex]\(\frac{5}{8}\)[/tex] is not an integer because it's a fraction.
- [tex]\(0.125\)[/tex] is not an integer because it's a decimal.
- [tex]\(-\frac{1}{2}\)[/tex] is not an integer because it's a fraction.
- [tex]\(\sqrt{36}\)[/tex] simplifies to [tex]\(6.0\)[/tex], which is an integer.
The integers from the list are: [tex]\(1174, -4561234, 3.0, 67598, 6.0\)[/tex].
2. Ascending Order:
We need to arrange the following numbers in ascending order: [tex]\(-9942, -16432, -33915, -20020, -8978\)[/tex].
Ordered from smallest to largest, the numbers are: [tex]\(-33915, -20020, -16432, -9942, -8978\)[/tex].
3. Temperature Rise:
The initial temperature was [tex]\(-1^{\circ}C\)[/tex] and it increased to [tex]\(8^{\circ}C\)[/tex].
The rise in temperature is calculated as [tex]\(8 - (-1) = 9^{\circ}C\)[/tex].
4. Lower Temperature:
We compare [tex]\(-3^{\circ}C\)[/tex] and [tex]\(-4^{\circ}C\)[/tex].
The lower temperature is [tex]\(-4^{\circ}C\)[/tex].
5. Expression Evaluation:
We need to calculate the expression [tex]\(-x^2 + 3x - 2\)[/tex] for the given values of [tex]\(x\)[/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].
6. Arithmetic Calculations:
- [tex]\(a)\)[/tex] Calculate [tex]\(-64 - 103 + 75\)[/tex]:
Result is [tex]\(-92\)[/tex].
- [tex]\(b)\)[/tex] Calculate [tex]\(58 - (-17) + 12\)[/tex]:
Result is [tex]\(87\)[/tex].
7. Expression Simplification:
- [tex]\(a)\)[/tex] Simplify [tex]\(16a^2 - 21b - 32a^2 + 19b\)[/tex]:
Combine like terms:
[tex]\((16a^2 - 32a^2)\)[/tex] and [tex]\((-21b + 19b)\)[/tex] gives [tex]\(-16a^2 - 2b\)[/tex].
- [tex]\(b)\)[/tex] Simplify [tex]\(-5x^2 + 7x - 14x^2 - 32x\)[/tex]:
Combine like terms:
[tex]\((-5x^2 - 14x^2)\)[/tex] and [tex]\((7x - 32x)\)[/tex] gives [tex]\(-19x^2 - 25x\)[/tex].
I hope this detailed explanation helps you understand how to approach each problem!
1. Integer Identification:
We need to identify which numbers in the list are integers. Remember, integers are whole numbers that can be positive, negative, or zero. Here's the list with our determination:
- [tex]\(1174\)[/tex] is an integer.
- [tex]\(-4561234\)[/tex] is an integer.
- [tex]\(\sqrt[3]{\frac{54}{2}}\)[/tex] simplifies to [tex]\(3.0\)[/tex], which is also an integer.
- [tex]\(67598\)[/tex] is an integer.
- [tex]\(\frac{5}{8}\)[/tex] is not an integer because it's a fraction.
- [tex]\(0.125\)[/tex] is not an integer because it's a decimal.
- [tex]\(-\frac{1}{2}\)[/tex] is not an integer because it's a fraction.
- [tex]\(\sqrt{36}\)[/tex] simplifies to [tex]\(6.0\)[/tex], which is an integer.
The integers from the list are: [tex]\(1174, -4561234, 3.0, 67598, 6.0\)[/tex].
2. Ascending Order:
We need to arrange the following numbers in ascending order: [tex]\(-9942, -16432, -33915, -20020, -8978\)[/tex].
Ordered from smallest to largest, the numbers are: [tex]\(-33915, -20020, -16432, -9942, -8978\)[/tex].
3. Temperature Rise:
The initial temperature was [tex]\(-1^{\circ}C\)[/tex] and it increased to [tex]\(8^{\circ}C\)[/tex].
The rise in temperature is calculated as [tex]\(8 - (-1) = 9^{\circ}C\)[/tex].
4. Lower Temperature:
We compare [tex]\(-3^{\circ}C\)[/tex] and [tex]\(-4^{\circ}C\)[/tex].
The lower temperature is [tex]\(-4^{\circ}C\)[/tex].
5. Expression Evaluation:
We need to calculate the expression [tex]\(-x^2 + 3x - 2\)[/tex] for the given values of [tex]\(x\)[/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].
6. Arithmetic Calculations:
- [tex]\(a)\)[/tex] Calculate [tex]\(-64 - 103 + 75\)[/tex]:
Result is [tex]\(-92\)[/tex].
- [tex]\(b)\)[/tex] Calculate [tex]\(58 - (-17) + 12\)[/tex]:
Result is [tex]\(87\)[/tex].
7. Expression Simplification:
- [tex]\(a)\)[/tex] Simplify [tex]\(16a^2 - 21b - 32a^2 + 19b\)[/tex]:
Combine like terms:
[tex]\((16a^2 - 32a^2)\)[/tex] and [tex]\((-21b + 19b)\)[/tex] gives [tex]\(-16a^2 - 2b\)[/tex].
- [tex]\(b)\)[/tex] Simplify [tex]\(-5x^2 + 7x - 14x^2 - 32x\)[/tex]:
Combine like terms:
[tex]\((-5x^2 - 14x^2)\)[/tex] and [tex]\((7x - 32x)\)[/tex] gives [tex]\(-19x^2 - 25x\)[/tex].
I hope this detailed explanation helps you understand how to approach each problem!
