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max2010maxim [7]
3 years ago
11

Sophie has 5 pieces of string that are 4 yards each. She uses 3 pieces that are each 3 feet long. How much string does Sophie ha

ve left?
2 feet


2 yards


31 feet


51 feet
Mathematics
2 answers:
Gekata [30.6K]3 years ago
6 0
Sophie has 2 yards left.
stich3 [128]3 years ago
5 0

Alright, lets get started.

Sophie has 5 pieces of string that are 4 yards each.

1 yards = 3 feet,

So, 4 yards = 4 * 3 =12 feet

Total number of string she has = 5 piece

So, total length she has = 5*12 = 60 feet

It means she had 60 feet string in starting.

Now, She uses 3 pieces that are each 3 feet long, means

She uses = 3*3 = 9 feet

So, remaining string length will be = 60 - 9 = 51 feet

Means 51 feet string does Sophie have. : Answer

Hope it will help :)


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  • The sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is <u>translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis</u>.

Explanation:

By inspection (watching the figure), you can tell that to transform the triangle XY onto triangle X"Y"Z", you must slide the former 5 units to the left, 1 unit down, and, finally, reflect it across the x-axys.

You can check that analitically

Departing from the triangle: XYZ

  • <u>Translation 5 units to the left</u>: (x,y) → (x - 5, y)

  • Vertex X: (-6,2) → (-6 - 5, 2) = (-11,2)
  • Vertex Y: (-4, 7) → (-4 - 5, 7) = (-9,7)
  • Vertex Z: (-2, 2) → (-2 -5, 2) = (-7, 2)

  • <u>Translation 1 unit down</u>: (x,y) → (x, y-1)

  • (-11,2) → (-11, 2 - 1) = (-11, 1)
  • (-9,7) → (-9, 7 - 1) = (-9, 6)
  • (-7, 2) → (-7, 2 - 1) = (-7, 1)

  • <u>Reflextion accross the x-axis</u>: (x,y) → (x, -y)

  • (-11, 1) → (-11, -1), which are the coordinates of vertex X"
  • (-9, 6) → (-9, -6), which are the coordinates of vertex Y""
  • (-7, 1) → (-7, -1), which are the coordinates of vertex Z"

Thus, in conclusion, it is proved that the sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis.

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