Answer:
- digits used once: 12
- repeated digits: 128
Step-by-step explanation:
In order for a number to be divisible by 4, its last two digits must be divisible by 4. This will be the case if either of these conditions holds:
- the ones digit is an even multiple of 2, and the tens digit is even
- the ones digit is an odd multiple of 2, and the tens digit is odd.
We must count the ways these conditions can be met with the given digits.
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Since we only have even numbers to work with, the ones digit must be an even multiple of 2: 4 or 8. (The tens digit cannot be odd.) The digits 4 and 8 comprise half of the available digits, so half of all possible numbers made from these digits will be divisible by 4.
<h3>digits used once</h3>
If the numbers must use each digit exactly once, there will be 4! = 24 of them. 24/2 = 12 of these 4-digit numbers will be divisible by 4.
<h3>repeated digits</h3>
Each of the four digits can have any of four values, so there will be 4^4 = 256 possible 4-digit numbers. Of these, 256/2 = 128 will be divisible by 4.
The answer to this question is true.
The function represents a linear relation so I assume the answer is B neither
Remark
You are using the midpoint formula. Instead of finding the midpoint, you are looking for one of the points, so you have to rearrange the formula a little bit.
Givens
Midpoint (4,2)
One endpoint (6,1)
Object
Find the other endpoint.
Formula
m(x,y) = (x1 + x2)/2, (y1 + y2)/2)
Solution
Find the x value
4 = (6 + x2)/2 Multiply both sides by 2
4*2 = 6 + x2 Subtract 6 from both sides.
8 - 6 = x2
x2 = 2
Find the y value
2 = (1 + y2)/2 Multiply by 2
4 = 1 + y2 Subtract 1 from both sides.
4 - 1 = y2
y2 = 3
Conclusion
R(x,y) = (2,3)
