Determine which of these illustrates two quantities that combine to make 0.
To determine which of these illustrates two quantities that combine to make 0, we need to look for pairs of numbers that add up to 0.
1. 5 + (-5) = 0: This pair of numbers combines to make 0.
2. -2 + (-7) = -9: This pair of numbers does not combine to make 0.
3. 4 + 4 = 8: This pair of numbers does not combine to make 0.
4. -12 + 12 = 0: This pair of numbers combines to make 0.
5. 1 + (-8) = -7: This pair of numbers does not combine to make 0.
So, option 1: 5 + (-5) = 0 illustrates two quantities that combine to make 0.
To determine which of the given options illustrates two quantities that combine to make 0, we need to understand the concept of additive inverses.
An additive inverse is a number that, when added to another number, results in a sum of zero. In other words, if a and b are two quantities and a + b = 0, then b is the additive inverse of a, and vice versa.
Now let's examine the given options and see which pairs of quantities combine to make 0:
1. 3 and -3: When we add 3 and -3, the sum is 0. Thus, this option illustrates two quantities that combine to make 0.
2. 5 and -4: When we add 5 and -4, the sum is not 0. Therefore, this option does not illustrate two quantities that combine to make 0.
3. -2 and -6: When we add -2 and -6, the sum is not 0. Hence, this option does not illustrate two quantities that combine to make 0.
4. 7 and -7: When we add 7 and -7, the sum is 0. Therefore, this option also illustrates two quantities that combine to make 0.
Based on our analysis, options 1 and 4 illustrate two quantities that combine to make 0.
To determine which of the given options illustrate two quantities that combine to make 0, we need to understand the concept of "additive inverse" or "opposite." In mathematics, the additive inverse of a number is the value that, when added to the original number, yields a sum of zero.
Let's look at each option and check if they meet this condition:
1. -2 and 2: When you add -2 and 2, you get 0. So this option does illustrate two quantities that combine to make 0.
2. 3 and 5: Combining 3 and 5, you get 8, not 0. So this option does not illustrate two quantities that combine to make 0.
3. -9 and 9: When you add -9 and 9, you get 0. So this option does illustrate two quantities that combine to make 0.
4. -4 and -6: Combining -4 and -6, you get -10, not 0. So this option does not illustrate two quantities that combine to make 0.
Therefore, the options that illustrate two quantities that combine to make 0 are option 1 (-2 and 2) and option 3 (-9 and 9).