Mathematics: Integers and Absolute Values

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Questions and Answers

What is the absolute value of the temperature recorded at 6:00 a.m. in Peekskill, NY?

-12

12 (correct)

-6

How does the temperature at noon in Peekskill relate to the temperature in Buffalo at the same time?

-12

-6

6 (correct)

Which point on a vertical number line would represent the temperature of Lake Erie?

-614

210

614

-210 (correct)

If point P is an integer between 0 and -5, what could be a valid label for point C, which is greater than P?

-4 Signup and view all the answers

What conclusion about temperatures below zero can be drawn from the meteorologist's statement?

The absolute value decreases as temperatures get less negative. Signup and view all the answers

Which of the following points is less than point P if P is -3?

-4 Signup and view all the answers

What is the elevation of Mount Marcy relative to sea level?

5343 Signup and view all the answers

Which point would be halfway between point P, which is -3, and the integer to its right, -2?

-2.5 Signup and view all the answers

What integer representation corresponds to a gain of $230?

230 Signup and view all the answers

Mr. Kindle's initial loss was misclassified. What was the correct classification?

Gain of $800 Signup and view all the answers

Which statement accurately compares the temperatures −10℉ and −20℉?

−10℉ is warmer than −20℉. Signup and view all the answers

Which inequality correctly represents the relationship between the temperatures 10℉, −10℉, and −20℉?

−20 < −10 < 10 Signup and view all the answers

If Mr. Kindle entered −(−$800) into the program, what is the value he input?

$800 Signup and view all the answers

What does the notation −(−$800) imply in mathematics?

Multiplying by -1 Signup and view all the answers

When comparing −10℉ and 10℉, which statement is true?

−10℉ is colder than 10℉. Signup and view all the answers

Which of these statements correctly describes the relationship of the integers related to Mr. Kindle's transactions when zero represents no change?

Their magnitude is the same but in opposite directions on the number line. Signup and view all the answers

What does a positive integer represent in terms of elevation?

An elevation above sea level Signup and view all the answers

Which of the following coordinates lies in Quadrant III?

(−3, −4.75) Signup and view all the answers

What would be the absolute value of an elevation of -4?

4 Signup and view all the answers

If the elevation is -9 and another is 8, how do their absolute values compare?

8 is greater than -9 Signup and view all the answers

When ordering elevations, what must be considered for elevations below sea level?

Their absolute values Signup and view all the answers

How would you express the distance between point A at (-9, 2) and the origin (0, 0)?

√(9² + 2²) Signup and view all the answers

Which coordinate represents sea level in this context?

(0, 0) Signup and view all the answers

What is the characteristic of elevations that are orders of positive values compared to their absolute values?

They follow the same order as their numerical value Signup and view all the answers

Study Notes

Mr. Kindle's Investment

Mr. Kindle's email shows a loss of 800,againof800, a gain of 800,againof960, and another gain of $230.
The integer representation of each gain and loss is: -800, 960, and 230
Mr. Kindle identified an error, a “loss of 800”shouldhavebeena“gainof800” should have been a “gain of 800”shouldhavebeena“gainof800.”
The opposite of the opposite of 800is800 is 800is800.
The opposite of a number is its reflection across zero on a number line.

Temperature in Buffalo

At 6:00am, the temperature was 10 degrees Fahrenheit.
At noon. the temperature was -10 degrees Fahrenheit.
At midnight, the temperature was -20 degrees Fahrenheit.
-10F is greater than -20F.
The warmest temperature was 10F.
The absolute value of a number is its distance from zero on a number line.
The absolute value of -10 is 10, meaning the temperature was 10 degrees below zero at noon.

Point Placement

The point 𝑃𝑃 is located between 0 and -5 on a number line.
The opposite of point P is point 𝐴𝐴.
Point 𝐵𝐵 is a number less than point 𝑃𝑃.
Point 𝐶𝐶 is a number greater than point 𝑃𝑃
Point 𝐷𝐷 is halfway between point 𝑃𝑃 and the integer to the right of point 𝑃𝑃.

Elevation in New York

Mount Marcy is the highest point in New York State, 5,343 feet above sea level.
Lake Erie is 210 feet below sea level.
Niagara Falls, NY, is 614 feet above sea level.
The lobby of the Empire State Building is 50 feet above sea level.
New York State borders the Atlantic Coast, which is at sea level.
The lowest point of Cayuga Lake is 435 feet below sea level.
Positive integers represent locations above sea level, while negative integers represent locations below sea level.

Sea Serpent Sightings

The last four sightings of the sea serpent were at points 𝐴𝐴 (−9, 2), 𝐵𝐵(−3, −4.75), 𝐶𝐶(9, 2), and 𝐷𝐷(8, −2.5).
Quadrant III is defined as the quadrant where both the x-coordinate and y-coordinate are negative.
The distance between point 𝐴𝐴 and the point 9 2 , 0 is 9.
Point 𝐸𝐸 is located at (8, 2.5).
Point 𝐹𝐹 is located at (8, -2.5).
The distance between points 𝐸𝐸 and 𝐹𝐹 is 5, as their x-coordinates are the same, and their y-coordinates are opposite.

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Description

This quiz covers fundamental concepts of integers, including gains and losses in investments, and temperature analysis. It explores number opposites and absolute values, enhancing your understanding of these key mathematical principles. Test your knowledge and comprehension of these topics in a fun and engaging way!