Find the value of each variable

9514 1404 393

  11.  x = 13, y = 13√2

  12.  x = 8, y = 4√3

  13.  x = 14√3, y = 7√3

  14.  x = y = 11√2

  15.  x = 12√2, y = 12, z = 12√3

Step-by-step explanation:

The ratios of side lengths in the "special" triangles are (shortest to longest)

  1 : 1 : √2 . . . . . isosceles right triangle

  1 : √3 : 2 . . . . 30°-60°-90° triangle

These ratios make answering these questions much easier.

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11. 13 : x : y = 1 : 1 : √2

  x = 13, y = 13√2

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12. 4 : y : x = 1 : √3 : 2

  x = 8, y = 4√3

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13. y : 21 : x = 1 : √3 : 2

  y = 21/√3 = 7√3

  x = 14√3

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14. x : y : 22 = 1 : 1 : √2

  x = 22/√2 = 11√2

  x = y = 11√2

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15. Let 'a' represent the altitude. Then we have ...

  a : z : 24 = 1 : √3 : 2

  a = 12, z = 12√3

and ...

  a : y : x = 1 : 1 : √2

  y = 12, x = 12√2

Additional comment

It is worth remembering that 1/√n = (√n)/n. This is useful when you have to divide by √2 or √3 in the above problems.

it is contrapositive

i could not see the question too well so check yourself again too . this is because i want you to get it correct.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1