1.Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and cos ∠X = 2.5/5.59 Part A: Use complete sentences to explain the special relationship between the trigonometric ratios of triangles XYZ and ACB. You must show all work and calculations to receive full credit.

Step-by-step explanation:

Given

and

See attachment for triangles

Required

Determine the relationship between the trigonometry ratios of both triangles

Using the attachment as a point of reference, we can say that:

implies that:

Because:

Next, is to calculate YZ using Pythagoras theorem.

Collect like terms

Take positive square roots

So, the trigonometry ratio of is:

Given that:

is similar to

This means that:

The following sides are similar

XY and AC; YZ and CB; XZ and AB

And both triangles will have the same trigonometry ratios;

So, the trigonometry ratio of is:

Both ratios can be written together as:

answer: the area of the parallelogram below is 42 square meters.

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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