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Answer :
Distance Between Bird and Fish:
To find the distance between the bird flying 100 feet above sea level and the fish that is 50 feet below sea level, you add their respective distances from sea level:
[tex]\text{Distance} = 100\text{ feet (above sea level)} + 50\text{ feet (below sea level)} = 150\text{ feet}[/tex]
Answer: 150 feet (option d is not correct so it seems to be a typo in the question).
Division of Negative Integer by Positive Integer:
When dividing a negative integer by a positive integer, the result is always negative because the signs are opposite.
Answer: negative (option b).
Additive Inverse of -17:
The additive inverse of a number is what you add to the number to make it zero. For [tex]-17[/tex], the additive inverse is [tex]+17[/tex]. Therefore, [tex]-17)\ or \(17\times(-1)[/tex] both represent [tex]-17[/tex] itself, which are not additive inverses of [tex]-17[/tex].
Answer: (-17) (option c) is not the additive inverse.
Integer Identification:
An integer is a whole number that can be positive, negative, or zero but not a fraction or a decimal. Among the given options, [tex]-51/3 = -17[/tex], which is a whole number.
Answer: -51/3 (option b).
Value of Expression [tex](-5) - 4 + (16/4) - 6 + 2[/tex]:
Simplify step-by-step:
[tex](-5) - 4 + 4 - 6 + 2 \Rightarrow -5 - 4 + 4 - 6 + 2[/tex]
Combine:
[tex]-5 - 4 + 4 - 6 + 2 = -9[/tex]
Answer: -9 (option a).
Value of [tex]-4(-200 + 125)[/tex]:
Simplify inside the parenthesis first: [tex]-200 + 125 = -75[/tex]
Then, multiply:
[tex]-4 \times -75 = 300[/tex]
Negative times negative is positive.
Answer: +300 (option b).
Custom Operation #:
This question seems malformed because "[tex]-2) x (-4)\" does not apply the custom operation described. Typically it states the result of multiplying \(a[/tex] and [tex]b[/tex], not involving any additions.
Pair of Integers for Product and Difference:
To find a pair of numbers which multiply to [tex]-30[/tex] and differ by [tex]+13[/tex]:
Check options or solve possibly to find that the correct numbers aren't part of the given options, or none applied accurately to a provided context.
Identity LHS and RHS of [tex]a \div (-b) = -(a + b)[/tex]:
Given identity [tex]a \div (-b) = -(a + b)[/tex], typically operation would be different in terms of mathematics saying incorrect.
Answer: Statement typically incorrect as showing providing identity.
Comparison Between X and Y:
Calculate [tex]X[/tex]:
[tex](-2 + 5) \times 3 - 8 = 3 \times 3 - 8 = 9 - 8 = 1[/tex]
Compare [tex]X[/tex] and [tex]Y = -1[/tex]:
Since [tex]1 > -1[/tex],
Answer: X > Y (option a).
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