Owen has enough materials to build up to 10 birdhouses in shop class. Each birdhouse needs 12 square feet of wood. The function W(b) = 12b represents the total amount of wood that Owen would need to build b birdhouses. What domain and range are reasonable for the function? A. D: 0 ≤ b ≤ 10 R: 0 ≤ W(b) ≤ 120 B. D: 0 ≤ b ≤ 120 R: 0 ≤ W(b) ≤ 10 C. D: 0 ≤ b ≤ 10 R: 12 ≤ W(b) ≤ 120 D. D: 10 ≤ b ≤ 12 R: 0 ≤ W(b) ≤ 120

  A. D: 0 ≤ b ≤ 10 R: 0 ≤ W(b) ≤ 120

Step-by-step explanation:

Since b represents the number of birdhouses, it is reasonable for that to have non-negative values. The maximum material availability means that b > 10 is not of practical use. This eliminates choices B and D.

Since W represents the amount of wood required for b birdhouses, it is reasonable for the range of it to match 12 times the domain: 12·0 = 0 to 12·10 = 120. This eliminates choice C.

The appropriate choice is ...

  A. D: 0 ≤ b ≤ 10 R: 0 ≤ W(b) ≤ 120

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation:

the answer will be