To find the difference between −492.89 and −871.78, we can use the additive inverse of −871.78.
The additive inverse of a number is the number that, when added to the original number, gives a sum of zero. For any number, its additive inverse is found by changing the sign of the number.
So, the additive inverse of −871.78 would be 871.78, since -871.78 + 871.78 = 0.
Therefore, -492.89 - (-871.78) can be rewritten as -492.89 + 871.78, which is equal to 378.89.
Use the additive inverse to find −492.89−(−871.78).(1 point)
20 answers
Determine the distance between −18.26 and −2.45 on a number line.(1 point)
Responses
20.71
20.71
−20.71
negative 20.71
−15.81
negative 15.81
15.81
Responses
20.71
20.71
−20.71
negative 20.71
−15.81
negative 15.81
15.81
To determine the distance between -18.26 and -2.45 on a number line, we can subtract the smaller number from the larger number.
-2.45 - (-18.26) = -2.45 + 18.26 = 15.81
So, the distance between -18.26 and -2.45 on a number line is 15.81.
-2.45 - (-18.26) = -2.45 + 18.26 = 15.81
So, the distance between -18.26 and -2.45 on a number line is 15.81.
Solve the mathematical problem involving absolute value.
2−|13⋅−9|−5(1 point)
2−|13⋅−9|−5(1 point)
To solve the mathematical problem involving absolute value, we need to follow the order of operations.
First, let's evaluate the expression inside the absolute value: 13 * (-9) = -117.
Next, let's take the absolute value of -117: | -117 | = 117.
Now, let's substitute the absolute value back into the original expression: 2 - 117 - 5.
Finally, let's perform the subtraction and multiplication: 2 - 117 - 5 = -120.
So, the solution to the mathematical problem 2 - |13 * -9| - 5 is -120.
First, let's evaluate the expression inside the absolute value: 13 * (-9) = -117.
Next, let's take the absolute value of -117: | -117 | = 117.
Now, let's substitute the absolute value back into the original expression: 2 - 117 - 5.
Finally, let's perform the subtraction and multiplication: 2 - 117 - 5 = -120.
So, the solution to the mathematical problem 2 - |13 * -9| - 5 is -120.
Solve the mathematical problem involving absolute value.
2−|1/3*−9|−5(1 point)
2−|1/3*−9|−5(1 point)
To solve the mathematical problem involving absolute value, we need to follow the order of operations.
First, let's evaluate the expression inside the absolute value: 1/3 * (-9) = -3.
Next, let's take the absolute value of -3: | -3 | = 3.
Now, let's substitute the absolute value back into the original expression: 2 - 3 - 5.
Finally, let's perform the subtraction and multiplication: 2 - 3 - 5 = -6.
So, the solution to the mathematical problem 2 - |1/3 * -9| - 5 is -6.
First, let's evaluate the expression inside the absolute value: 1/3 * (-9) = -3.
Next, let's take the absolute value of -3: | -3 | = 3.
Now, let's substitute the absolute value back into the original expression: 2 - 3 - 5.
Finally, let's perform the subtraction and multiplication: 2 - 3 - 5 = -6.
So, the solution to the mathematical problem 2 - |1/3 * -9| - 5 is -6.
Subtract 24−(−15).(1 point)
To subtract 24 - (-15), we can use the additive inverse of -15.
The additive inverse of a number is the number that, when added to the original number, gives a sum of zero. For any number, its additive inverse is found by changing the sign of the number.
So, the additive inverse of -15 would be 15, since -15 + 15 = 0.
Therefore, 24 - (-15) can be rewritten as 24 + 15, which is equal to 39.
Hence, the solution to 24 - (-15) is 39.
The additive inverse of a number is the number that, when added to the original number, gives a sum of zero. For any number, its additive inverse is found by changing the sign of the number.
So, the additive inverse of -15 would be 15, since -15 + 15 = 0.
Therefore, 24 - (-15) can be rewritten as 24 + 15, which is equal to 39.
Hence, the solution to 24 - (-15) is 39.
What is 17 4/9 + 5/9 − 8 − 10?(1 point)
Responses
−1
negative 1
20
20
0
0
−7
Responses
−1
negative 1
20
20
0
0
−7
To solve the expression 17 4/9 + 5/9 - 8 - 10, we need to convert the mixed number to an improper fraction first.
17 4/9 is equal to (17 * 9 + 4)/9 = 157/9.
Now we can rewrite the expression as (157/9) + 5/9 - 8 - 10.
Now, let's add and subtract the fractions:
(157/9) + 5/9 = (157+5)/9 = 162/9 = 18.
Now, we can rewrite the expression as 18 - 8 - 10.
Finally, subtract to get the final answer: 18 - 8 - 10 = 0.
Therefore, the solution to the expression 17 4/9 + 5/9 - 8 - 10 is 0.
17 4/9 is equal to (17 * 9 + 4)/9 = 157/9.
Now we can rewrite the expression as (157/9) + 5/9 - 8 - 10.
Now, let's add and subtract the fractions:
(157/9) + 5/9 = (157+5)/9 = 162/9 = 18.
Now, we can rewrite the expression as 18 - 8 - 10.
Finally, subtract to get the final answer: 18 - 8 - 10 = 0.
Therefore, the solution to the expression 17 4/9 + 5/9 - 8 - 10 is 0.
Which context describes a difference of rational numbers?(1 point)
Responses
A football player gains yards on a play.
A football player gains yards on a play.
The team’s score did not change during the game.
The team’s score did not change during the game.
A football player loses yards on a play.
A football player loses yards on a play.
The team’s score increased when scoring.
Responses
A football player gains yards on a play.
A football player gains yards on a play.
The team’s score did not change during the game.
The team’s score did not change during the game.
A football player loses yards on a play.
A football player loses yards on a play.
The team’s score increased when scoring.
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?(1 point)
Joey was ? meters from home.
Joey was ? meters from home.
To solve the problem, we need to calculate the total distance Joey walked from home.
Step 1: Convert the mixed numbers to improper fractions.
15 2/3 can be written as (15 * 3 + 2)/3 = 47/3 meters.
21 3/4 can be written as (21 * 4 + 3)/4 = 87/4 meters.
Step 2: Subtract the distance Joey walked west from the distance he walked east.
47/3 - 87/4
To subtract fractions, we need to find a common denominator. The least common multiple (LCM) of 3 and 4 is 12.
So, we can rewrite the fractions with a common denominator of 12:
(47/3) * (4/4) = 188/12
(87/4) * (3/3) = 261/12
Now we can subtract: 188/12 - 261/12 = -73/12
Step 3: Simplify the resulting fraction, if needed.
The fraction -73/12 is already simplified as there are no common factors between the numerator and denominator.
Therefore, Joey was -73/12 meters from home.
Step 1: Convert the mixed numbers to improper fractions.
15 2/3 can be written as (15 * 3 + 2)/3 = 47/3 meters.
21 3/4 can be written as (21 * 4 + 3)/4 = 87/4 meters.
Step 2: Subtract the distance Joey walked west from the distance he walked east.
47/3 - 87/4
To subtract fractions, we need to find a common denominator. The least common multiple (LCM) of 3 and 4 is 12.
So, we can rewrite the fractions with a common denominator of 12:
(47/3) * (4/4) = 188/12
(87/4) * (3/3) = 261/12
Now we can subtract: 188/12 - 261/12 = -73/12
Step 3: Simplify the resulting fraction, if needed.
The fraction -73/12 is already simplified as there are no common factors between the numerator and denominator.
Therefore, 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 descends 10,000 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 ascends 15,000 feet. How many feet above the ground is the plane?
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 descends 10,000 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 ascends 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?
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 during the three hours, we need to subtract the temperature at 9 a.m. from the temperature at noon.
Let T1 be the temperature at 9 a.m. (-5.8 degrees Celsius), and let T2 be the temperature at noon (-1.6 degrees Celsius).
The change in temperature can be calculated by subtracting T1 from T2:
T2 - T1 = (-1.6) - (-5.8)
When we subtract a negative number, it is equivalent to adding a positive number.
(-1.6) + 5.8 = 4.2
So, the change in temperature during the three hours is 4.2 degrees Celsius.
This means that the temperature increased by 4.2 degrees Celsius from 9 a.m. to noon.
Let T1 be the temperature at 9 a.m. (-5.8 degrees Celsius), and let T2 be the temperature at noon (-1.6 degrees Celsius).
The change in temperature can be calculated by subtracting T1 from T2:
T2 - T1 = (-1.6) - (-5.8)
When we subtract a negative number, it is equivalent to adding a positive number.
(-1.6) + 5.8 = 4.2
So, the change in temperature during the three hours is 4.2 degrees Celsius.
This means that the temperature increased by 4.2 degrees Celsius from 9 a.m. to noon.
Man cracked the code