A. Explain how you know the right triangles are similar. b. Write a ratio that is equivalent to z/x

c. Which ratios of side lengths are equal to tan(a)?

d. Explain why the values of the trigonometric ratios only depend on the angle a and not on the particular lengths x, y, 2, q. r, s.
E. If Y/Z =0.7. what is the measure of a to the nearest degree?

Simonne used the following steps to simplify the given expression. 12 - 3(-2x + 4) step 1: 12 + (–3)·(–2x) + (–3)·(4) step 2: 12 + 6x + (–12) step 3: 12 + (–12) + 6x step 4: 0 + 6x step 5: 6x what property of real numbers was used to transition from step 3 to step 4? a. identity property of addition b. inverse property of addition c. associative property of addition d. commutative property of addition

5.(04.07) two different plants grow each year at different rates, which are represented by the functions f(x) = 4* and g(x) = 5x + 2. what is the first year the f(x) height is greater than the g(x) height? year 3 year 0 year 2 year 1

As part of an annual fundraiser to raise money for diabetes research, diane joined a bikeathon. the track she biked on was 1,920 yards long. diane biked 38.5 laps. her sponsors agreed to donate an amount of money for each mile she biked. how many miles did she bike? first fill in the blanks on the left side using the ratios shown. then write your answer. given ratios: 5280ft / 1 mi , 1 mi /5280 ft , 1,920 yards / 1 lap , 1 lap / 1,920 yards , 3 ft / 1 yard , 1 yard / 3 ft. blanks: 38.5 laps / 1 yard x (blank) x (blank) x (blank) = (blank) miles i'm really confused on how to do this, and the explanations aren't exactly . if you could walk me through how to do this, it would be greatly appreciated.