Find sin(x-y) if cos= 4/5 and sin = 5/13

please explain the work if you can I need help

tan 2x=56/33

Step-by-step explanation:

Since x and y lie between 0 and π/4, therefore, their sum (x+y) lies between 0 and π/2. Moreover, since sin(x-y) = 5/13 > 0, therefore, (x-y) also lies between 0 and π/2.

We can now solve the quadratic, (sin(u)) + (cos(u)) = 1 to obtain the value of sin(u) or cos(u), where u = x+y or x-y, since we know that in both cases, u lies in the first quadrant and so, both sin(u) and cos(u) must be positive. Since tan(u) = sin(u)/cos(u), we obtain

tan(x+y) = 3/4 ,  tan(x-y) = 5/12.

tan(2x) = tan((x+y)+(x-y)) = [tan(x+y) + tan(x-y)]/[1 - (tan(x+y))×(tan(x-y))].

Substituting the values for tan(x+y) and tan(x-y), we get

tan(2x) = 56/33.

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the answer is a

step-by-step explanation:

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .