The net shows four equilateral triangles. What is the total surface area of the triangular pryamid

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  A) -75, the change in balance per day

  B)

  C) g(x) = -75x +1500

  D) $1,125

Step-by-step explanation:

Part A:

The slope can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (1350 -1500)/(2 -0) = -150/2

  m = -75

The slope of -75 is the average change in the bank balance each day. It means the balance is decreasing at the rate of $75 per day.

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Part B:

In point-slope form, the equation of the line is ...

  y -y1 = m(x -x1) . . . . . line with slope m through point (x1, y1)

Here, we have m = -75 and (x1, y1) = (0, 1500), so the equation is ...

  y -1500 = -75(x -0) . . . . . . point-slope form

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We can add 1500 and simplify to get to slope-intercept form:

  y = -75x +1500 . . . . . . slope-intercept form

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We can add 75x to put this in standard form.

  75x +y = 1500 . . . . . . standard form

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Part C:

Function notation replaces y with g(x):

  g(x) = -75x +1500

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Part D:

The balance after 5 days is the value of the function for x=5. (It will be $75 less than the balance after 4 days as given in the table.)

  g(5) = -75·5 +1500 = 1125

The balance after 5 days is $1,125.