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ch4aika [34]
3 years ago
7

In 1997 there were 31 laptop computers at grove high school. starting in 1998 the school bought 20 more laptop computers at the

end of each year. the equation t=20x 31 can be used to determine t, the total number of laptop computers at the school x years after 1997. what was the total number of laptop computers at grove high school at the end of 2005?
Mathematics
1 answer:
Ksenya-84 [330]3 years ago
7 0
We have equation:
t=20x+31
x is number of years after 1997.

To calculate number of laptops in 2005:
x=2005-1997
x=8

t=20*8+31
t=160+31
t=191

In year 2005 school had 191 laptops.
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To see the steps to the diagonal form see the step-by-step explanation. The solution to the system is x =  -\frac{1}{9}, y= -\frac{1}{9}, z= \frac{4}{9} and w = \frac{7}{9}

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  • R_4 - 1 R_1 \rightarrow R_4 (multiply 1 row by 1 and subtract it from 4 row)
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  • R_4 + 3 R_3 \rightarrow R_4 (multiply 3 row by 3 and add it to 4 row)
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After this step, the system has an upper triangular form

The triangular matrix looks like:

\left[\begin{array}{cccc|c}1 & 0 & 0 & -0.5 & -0.5  \\0 & 1 & 0 & -0.5 & -0.5\\0 & 0 & 1 & 2 &  2 \\0 & 0 & 0 & 1 &  \frac{7}{9}\end{array}\right]

If you later perform the following operations you can find the solution to the system.

  • R_1 + 0.5 R_4 \rightarrow R_1 (multiply 4 row by 0.5 and add it to 1 row)
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After this operations, the matrix should look like:

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Thus, the solution is:

x =  -\frac{1}{9}, y= -\frac{1}{9}, z= \frac{4}{9} and w = \frac{7}{9}

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