Find the missing length.
1 answer:
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Answer: 2
Step-by-step explanation: To find the greatest common factor or GCF of 8 and 18, we begin by finding all of the factors of each number.
To find the factors of 8, we know that 8 ÷ 1 is 8 so 1 and 8 are factors.
8 ÷ 2 is 4 so 2 and 4 are factors.
However, if we continue to divide 8 by 3, 4, 5, and so on, we won't find any new factors. So the factors of 8 are 1, 2, 4, and 8.
Now let's find the factors of 18.
18 ÷ 1 is 18 so 1 and 18 are factors.
18 ÷ 2 is 9 so 2 and 9 are factors.
18 ÷ 3 is 6 so 3 and 6 are factors.
However, if we continue to divide by 4, 5, 6, and so on, we won't find any new factors. So the factors of 18 are 1, 2, 3, 6, 9, and 18.
Now that we have our list of factors, to find the greatest common factor, we simply find the largest number that is shared by the two lists.
Notice that our lists share a 1 but the largest number they share is a <em>2</em><em>.</em>
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So the greatest common factor or <em>gcf</em> of 8 and 18 is 2.
I have also shown my work on the whiteboard.
Given:
The table of values of an exponential function.
To find:
The missing values in the exponential function.
Solution:
The general exponential function is defined as:
...(i)
Where, a is the initial value and b is the growth factor.
First point from the given table is (1,10). It means, the equation (i) must be true for (1,10).
...(ii)
Second point from the given table is (2,20). It means, the equation (i) must be true for (2,20).
...(iii)
Dividing (iii) by (ii), we get
Putting in (ii), we get
Putting in (i), we get
The required exponential function for the given table of values is . So, the missing values are 2 and x, where 2 is in the base and x is in the power.