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sattari [20]
3 years ago
7

The sum of the digits of a two-digit number is 12. The number formed by interchanging the digits is 54 more than the original nu

mber. What is the original number?
Mathematics
1 answer:
-BARSIC- [3]3 years ago
8 0
Let X and Y be the digits.
If a two-digit number is written XY, then its value is 10x+y.
When the digits of the number are interchanged, it's YX, and its value is 10y+x.

The sum of the digits is 12.
The number formed by interchaning the digits is 54 more than the original number.

x+y=12 \\
10x+y+54=10y+x \\ \\
x+y=12 \\
10x-x+y-10y=-54 \\ \\
x+y=12 \\
9x-9y=-54 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div 9 \\ \\
x+y=12 \\
\underline{x-y=-6} \\
x+x=12-6 \\
2x=6 \\
x=\frac{6}{2} \\
x=3 \\ \\
x+y=12 \\
3+y=12 \\
y=12-3 \\
y=9

The digits X and Y are 3 and 9, so the original number is 39.
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It's both!

This is a might tricky. First you have to find the altitude. You have to determine if this is a real triangle.

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What have you learned?

Since 42 is larger than 41.58 you have 2 solutions to the triangle. One of the angles is acute, and the other one is obtuse. They are supplementary angles.

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Sin(C) = 81.9

So that's your first answer. The second answer comes from Finding the supplement to this angle

supplement + 81.9 = 180

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Step-by-step explanation:

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Step-by-step explanation:

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