2. the table shows a linear function. x) -5, -4, -3, -2, -1, 0, 1, 2, 3 f(x) -11, -5, 1, 7, 13, 19, 25, 31, 37 (a) determine the difference of outputs of any two inputs that are 1 unit apart. show your work. (b) determine the difference of outputs of any two inputs that are 2 units apart. show your work. (c) determine the difference of outputs of any two inputs that are 3 units apart. show your work. (d) what do you notice about the ratios of the differences in the outputs to the input intervals? explain your answer.

(a) 6

(b) 12

(c) 18

(d) The ratios are all equal.

Step-by-step explanation:

I assume that -5 goes with -11, -4 goes with -5, -3 goes with 1, etc.

(a) Look at the points (0, 19) and (1, 25). The inputs are 0 and 1, so the inputs are 1 unit apart since 1 - 0 = 1. Now look at the outputs. They are 19 and 25, and 25 - 19 = 6. The difference of outputs is 6 for a difference of inputs of 1.

(b) Look at points (0, 19) and (2, 31). The inputs are 2 units apart since 2 - 0 = 2. The outputs are 12 units apart since 31 - 19 = 12.

(c) Look at points (0, 19) and (3, 37). The inputs are 3 units apart since 3 - 0 = 0. The outputs are 18 units apart since 37 - 19 = 18.

(d) In part (a), with inputs 1 unit apart, the ratio of output difference to input difference was 6/1. In part (b), with inputs 2 units apart, the ratio of output difference to input difference was 12/2 which is the same as 6/1. In part (c), with inputs 3 units apart, the ratio of output difference to input difference was 18/3 which is the same as 6/1. The ratios are all equal.

answer: d. $20

step-by-step explanation:

just took the test

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,