1.        the table shows a linear function. x -5 -4 -3 -2 -1 0 1 2 3 f (x) -11 -5 3 13 21 29 37 45 53   (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) I used the equation x=-5; f(x)=-11 and x=-4; f(x)=-3. We get the range = -3-(-11)=8

b) I used the equation x=-5; f(x)=-11 and x=-3; f(x)=5. We get the range = 5-(-11)=16

c) I used the equation x=-5; f(x)=-11 and x=-2; f(x)=13. We get the range = 13-(-11)=24

d) Range of input is equal with the ratios of the output. You can find the pattern of output above 8,16,and 24 can divided by 8 and give the result 1,2 and 3

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet