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Social Security numbers are of the form XYZ - MN - ABCD
Part A:
The first three digits XYZ are referred to as the area number
X is a number 1 - 7 (1, 2, 3, 4, 5, 6, 7)
That means we have 7 choices for X
Y and Z can be any number 0 - 9 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
That means we have 10 choices for Y and also 10 choices for Z
So, the number of possible ways are
But we know that the area code 666 has never been used.
So we need to subtract this one from the total.
Therefore, the total number of possible area codes is 699.
The question asks for the length of CD and HJ. To find those, we need to find a connection between them.
In the given statement, it says ABCD ≅ FGHJ. When we look at the equation, the corresponding letters are equal. For example, angle A is congruent to Angle F. Or BC ≅ GH.
So we know that CD and HJ are congruent.
Set them equal:
Subtract 2x from both sides:
Subtract 2 from both sides:
If x is 3, plug it in:
Simplify:
So, HJ is 11. And because HJ ≅ CD, CD is 11 too.
In the given statement, it says ABCD ≅ FGHJ. When we look at the equation, the corresponding letters are equal. For example, angle A is congruent to Angle F. Or BC ≅ GH.
So we know that CD and HJ are congruent.
Set them equal:
Subtract 2x from both sides:
Subtract 2 from both sides:
If x is 3, plug it in:
Simplify:
So, HJ is 11. And because HJ ≅ CD, CD is 11 too.