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bearhunter [10]
2 years ago
12

how many numbers have this property: when you subtract 297 from it, you get the same number but in reverse.

Mathematics
1 answer:
jasenka [17]2 years ago
8 0

9514 1404 393

Answer:

  60

Step-by-step explanation:

Consider the number with digits x, y, z. Its value will be 100z+10y+z. We want the same value when we reverse the digits after subtracting 297.

  100x +10y +z -297 = 100z +10y +x

  99x -99z = 297 . . . . . subtract 100z+10y+x-297

  x -z = 3 . . . . . . . . . . . . divide by 99

The first digit of the number is 3 more than the last digit. There are 60 such numbers. The first digit may be 4..9, and the middle digit may be 0..9.

  401, 502, 603, ..., 906; 411, 512, 613, ..., 916, ..., 491, 592, 693, ... 996

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Step-by-step explanation:

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Answer:

Example system with no solution

We're asked to find the number of solutions to this system of equations:

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y

y

​  

 

=−3x+9

=−3x−7

​  

 

Without graphing these equations, we can observe that they both have a slope of -3−3minus, 3. This means that the lines must be parallel. And since the yyy-intercepts are different, we know the lines are not on top of each other.

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Example system with infinite solutions

We're asked to find the number of solutions to this system of equations:

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−6x+4y

3x−2y

​  

 

=2

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​  

 

Interestingly, if we multiply the second equation by -2−2minus, 2, we get the first equation:

\begin{aligned} 3x-2y &= -1\\\\ \blueD{-2}(3x-2y)&=\blueD{-2}(-1)\\\\ -6x+4y &= 2 \end{aligned}  

3x−2y

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​  

 

=−1

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​  

 

In other words, the equations are equivalent and share the same graph. Any solution that works for one equation will also work for the other equation, so there are infinite solutions to the system.

Step-by-step explanation:

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