In this diagram, the area of the large square is equal to the combined areas of the tilted square and the four right triangles. (the picture)
When written as an equation, this relationship can be simplified algebraically, as shown in these 4 steps.

Step 1: (a + b) (a + b) = c2+ 2ab

Step 2: a2 + 2ab + b2 = c2 + 2ab

Step 3: a2 + 2ab ─ 2ab + b2 = c2 + 2ab ─ 2ab

Step 4:

What equation fits in the box in Step 4 to complete the proof

(part B)
Builders use the equation from Part A to determine the number, height, and depth of stairs necessary to extend from the first floor to the second floor of a building.

Given that the ceiling is 12 feet high, stairs are 8 inches high and the stairwell is 16 feet long, describe in detail how a builder could use the equation to determine the number, height, and depth of the stairs.

Which of the following could be the ratio of the length of the longer leg 30-60-90 triangle to the length of its hypotenuse? check all that apply. a. 313 6 b. 3: 215 c. 18: 13 d. 1: 13 e. 13: 2 of. 3: 15

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?

Without multiplying, tell which product is larger and why. 5 × 1/3 or 5 × 2/3 a)5 × 1/3 because 1/3 is less than 2/3 b) 5 × 1/3 because 1/3 is greater than 2/3 c) 5 × 2/3 because 1/3 is less than 23 d) 5 × 23 because 1/3 is greater than 2/3