Solve the mathematical problem involving absolute value.
2−|1/3⋅−9|−5(1 point)
2 - |1/3 * -9| - 5
First, perform the multiplication inside the absolute value:
2 - |(-9/3)| - 5
Simplify the division within the absolute value:
2 - |(-3)| - 5
Since the absolute value of a negative number is its positive counterpart, we get:
2 - 3 - 5
Combine like terms:
-1 - 5 = -6
Therefore, 2 - |1/3 * -9| - 5 equals -6.
Subtract 24−(−15).
To subtract 24 - (-15), we can rewrite the expression as 24 + 15:
24 + 15 = 39
What is 17 4/9 + 59 − 8 − 10?(1 point)
Responses
20
20
−7
negative 7
0
0
−1
To solve 17 4/9 + 59 - 8 - 10, first convert the mixed number to an improper fraction and then add and subtract:
17 4/9 = (17 * 9 + 4) / 9 = 157/9
Now, let's simplify the expression:
157/9 + 59 - 8 - 10
To add and subtract fractions and whole numbers, we need to find a common denominator. In this case, the common denominator is 9:
157/9 + 59 * 9/9 - 8 * 9/9 - 10 * 9/9
157/9 + 531/9 - 72/9 - 90/9
Now, combine the fractions:
(157 + 531 - 72 - 90) / 9
526 / 9
Now, let's divide 526 by 9:
526 ÷ 9 = 58 remainder 4
So, the answer is 58 4/9, or in mixed number form, 58 and 4/9.
What is 17 4/9 + 5/9 − 8 − 10?(1 point)
Responses
20
20
−7
negative 7
0
0
−1
To solve 17 4/9 + 5/9 - 8 - 10, first convert the mixed number to an improper fraction and then add and subtract:
17 4/9 = (17 * 9 + 4) / 9 = 157/9
Now, let's simplify the expression:
157/9 + 5/9 - 8 - 10
To add and subtract fractions and whole numbers, we need to keep a common denominator. In this case, the common denominator is 9:
(157 + 5) / 9 - 8 - 10
162/9 - 8 - 10
Now, combine the fractions:
(162 - 72 - 90) / 9
Now, subtract 72 and 90 from 162:
162 - 72 - 90 = 0
So, the final expression is 0/9, which simplifies to 0. Therefore, the answer is 0.
Which context describes a difference of rational numbers?(1 point)
Responses
The team’s score did not change during the game.
The team’s score did not change during the game.
The team’s score increased when scoring.
The team’s score increased when scoring.
A football player loses yards on a play.
A football player loses yards on a play.
A football player gains yards on a play
A football player loses yards on a play.
Joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters. How far was Joey from home? Write your answer as a mixed number only.(1 point)
Joey was
meters from home.
To find Joey's distance from home, we need to subtract the distance he walked west from the distance he walked east.
Distance walked east = 15 2/3 meters = 47/3 meters
Distance walked west = 21 3/4 meters = 87/4 meters
Joey's distance from home = Distance walked east - Distance walked west
= 47/3 meters - 87/4 meters
To subtract fractions, we need a common denominator. The common denominator of 3 and 4 is 12.
= (47/3 * 4/4) meters - (87/4 * 3/3) meters
= 188/12 meters - 261/12 meters
= (188 - 261)/12 meters
= -73/12 meters
So, Joey was -73/12 meters from home.
Which situation describes opposite quantities that when combined would equal 0?(1 point)
Responses
A plane ascends to 15,000 feet and then descends 15,000 feet. How many feet above the ground is the plane?
A plane ascends to 15,000 feet and then descends 15,000 feet. How many feet above the ground is the plane?
A plane ascends to 10,000 feet and then ascends 15,000 feet. How many feet above the ground is the plane?
A plane ascends to 10,000 feet and then ascends 15,000 feet. How many feet above the ground is the plane?
A plane ascends to 15,000 feet and then ascends 15,000 feet. How many feet above the ground is the plane?
A plane ascends to 15,000 feet and then ascends 15,000 feet. How many feet above the ground is the plane?
A plane ascends to 15,000 feet and then descends 10,000 feet. How many feet above the ground is the plane?
A plane ascends to 15,000 feet and then descends 15,000 feet. How many feet above the ground is the plane?
Solve the following word problem. The air temperature at 9 a.m. is −5.8 degrees Celsius. The air temperature at noon is −1.6 degrees Celsius. What is the change in the temperature during these three hours? Write and solve an equation to show your answer. Then explain what your answer means.
To find the change in temperature, we need to subtract the initial temperature at 9 a.m. from the temperature at noon.
Change in temperature = Temperature at noon - Temperature at 9 a.m.
Let's solve the equation:
-1.6 - (-5.8)
To subtract a negative number, we can rewrite it as addition:
-1.6 + 5.8
Now, subtract 1.6 from 5.8:
= 4.2
Therefore, the change in temperature during these three hours is 4.2 degrees Celsius.
This means that the temperature increased by 4.2 degrees Celsius from 9 a.m. to noon.