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EleoNora [17]
3 years ago
14

Rearrange the equation so q is the independent variable. -7q + 12r = 3q - 4r

Mathematics
1 answer:
babunello [35]3 years ago
5 0

Answer:

q = 8/5r or q = 1.6r

Step-by-step explanation:

-7q + 12r = 3q - 4r

+7q           +7q

12r = 10q - 4r

+4r           +4r

16r = 10q

/10    /10

16/10 = 8/5     8/5 = 1.6

<u>q = 8/5r</u> or <u>q = 1.6r</u>

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If you would like to find the decimal number which is equivalent to 1/10, you can do this using the following step:

1/10 = 0.1

The correct result would be B. 0.1.
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Ierofanga [76]

Answer:

  • vertical scaling by a factor of 1/3 (compression)
  • reflection over the y-axis
  • horizontal scaling by a factor of 3 (expansion)
  • translation left 1 unit
  • translation up 3 units

Step-by-step explanation:

These are the transformations of interest:

  g(x) = k·f(x) . . . . . vertical scaling (expansion) by a factor of k

  g(x) = f(x) +k . . . . vertical translation by k units (upward)

  g(x) = f(x/k) . . . . . horizontal expansion by a factor of k. When k < 0, the function is also reflected over the y-axis

  g(x) = f(x-k) . . . . . horizontal translation to the right by k units

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Here, we have ...

  g(x) = 1/3f(-1/3(x+1)) +3

The vertical and horizontal transformations can be applied in either order, since neither affects the other. If we work left-to-right through the expression for g(x), we can see these transformations have been applied:

  • vertical scaling by a factor of 1/3 (compression) . . . 1/3f(x)
  • reflection over the y-axis . . . 1/3f(-x)
  • horizontal scaling by a factor of 3 (expansion) . . . 1/3f(-1/3x)
  • translation left 1 unit . . . 1/3f(-1/3(x+1))
  • translation up 3 units . . . 1/3f(-1/3(x+1)) +3

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<em>Additional comment</em>

The "working" is a matter of matching the form of g(x) to the forms of the different transformations. It is a pattern-matching problem.

The horizontal transformations could also be described as ...

  • translation right 1/3 unit . . . f(x -1/3)
  • reflection over y and expansion by a factor of 3 . . . f(-1/3x -1/3)

The initial translation in this scenario would be reflected to a translation left 1/3 unit, then the horizontal expansion would turn that into a translation left 1 unit, as described above. Order matters.

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