Me asap! !
triangle xyz was dilated by a scale factor of 2 to create triangle abc and sin angle x = 5/5.59.
part a: use complete sentences to explain the special relationship between the trigonometric ratios of triangles xyz and abc. you must show all work and calculations to receive full credit. (5 points)
part b: explain how to find the measures of segments cn and ab. you must show all work and calculations to receive full credit. (5 points)

part a) ratios of corresponding sides are equal

part b) cb=10

            ab=11.18

step-by-step explanation:

given:

δabc= 2δxyz

sinx=5/5.59

from trigonometric ratios we know

sinx=opposite side/hypotenuse

thus zy=opposite side=5

and xz= hypotenuse= 5.59

from pythagoras theorem we get

c^2= a^2 + b^2

xz^2=yz^2 + xy^2

5.59^2= 5^2 +xy^2

xy^2=6.2418

xy=2.5

part a)

when a triangle is multiplied or scaled by k, a constant scalar number to form another triangle then these two triangle are similar. and similar triangles have proportional lengths of corresponding sides. ratios within the triangle sides will be equal to the corresponding sides ratios of the other triangle. that is

xy/yz= ac/bc

xz/yz= ab/cb

yz/xz= bc/ab

          = ab/ac

part b)

from part a we know that

bc/ab=yz/xz

also yz/xz= 5/5.59

so bc/ab= 5/5.59

the scalar factor= 2

corresponding side of cb is yz, so

cb=2(yz)

      = 2(5)

      = 10

corresponding side of ab is xz, so

ab=2(xz)

      = 2(5.59)

      = 11.18!

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.