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Sum of Rational Numbers
Question 1
Which expression is modeled by the number line?
Responses
A 6 − 46 − 4
B −6 + 4−6 + 4
C −6 + (−4)−6 + (−4)
D −6 − (−4)−6 − (−4)
Question 2
What number must be added next to end up at zero?
Responses
A -4-4
B 44
C -10-10
D 10
Question 1: The expression modeled by the number line is C) -6 + (-4) = -6 - 4.
Question 2: The number that must be added next to end up at zero is A) -4.
A submarine is 650 feet below sea level. If it descends 400 feet, which integer represents its new position?
Responses
A −1,050−1,050
B −250−250
C 1,0501,050
D 250250
If a submarine is already 650 feet below sea level and it descends 400 feet further, its new position can be represented by subtracting 400 from 650.
Therefore, the integer that represents its new position is -650 - 400 = -1,050.
So, the correct response is A) -1,050.
A bookstore has 45 copies of a bestseller available on Saturday morning. Twenty-one customers purchase the book that day. On Monday, a shipment of 25 books arrives and 14 copies are sold. Which statements are correct?
Responses
A The integer 14 represents the sale of 14 books.The integer 14 represents the sale of 14 books.
B The integer 25 represents the new shipment.The integer 25 represents the new shipment.
C The integer −21 represents the sale of 21 books.The integer −21 represents the sale of 21 books.
D After Monday's sales, 35 copies are available.After Monday's sales, 35 copies are available.
E After Monday's sales, 26 copies are available.
Statement A is correct. The integer 14 represents the sale of 14 books.
Statement B is correct. The integer 25 represents the new shipment.
Statement C is incorrect. The integer -21 would represent the opposite of the sale of 21 books, which would be a return or loss of books. The correct representation of the sale of 21 books would be the integer 21.
Statement D is incorrect. After Monday's sales, we have 45 (initial stock) + 25 (new shipment) - 14 (sold on Monday) = 56 copies available.
Statement E is incorrect. After Monday's sales, we have 45 (initial stock) + 25 (new shipment) - 14 (sold on Monday) = 56 copies available, not 26 copies.
omg your making me fail
I apologize if my previous responses were not clear or helpful. Let's go through the statements again and make sure we have the correct answers.
Statement A: The integer 14 represents the sale of 14 books. - This statement is correct.
Statement B: The integer 25 represents the new shipment. - This statement is correct.
Statement C: The integer -21 represents the sale of 21 books. - This statement is correct. When books are sold, it is represented with a negative value because the quantity of available books decreases.
Statement D: After Monday's sales, 35 copies are available. - This statement is incorrect. After Monday's sales, we have 45 (initial stock) + 25 (new shipment) - 14 (sold on Monday) = 56 copies available, not 35.
Statement E: After Monday's sales, 26 copies are available. - This statement is incorrect. After Monday's sales, we have 45 (initial stock) + 25 (new shipment) - 14 (sold on Monday) = 56 copies available, not 26.
I hope this clarifies the correct answers for each statement.