Which table shows a function that is decreasing over the interval (−2, 0)? image for option 1 image for option 2 image for option 3

Answer : Image 3

Which table shows a function that is decreasing over the interval (−2, 0)?

We look at the interval -2 to 0 on x

In option 1 table , f(x) is 0 then -5 and then becomes 0

It means -2 to -1 , f(x) decreases but from -1 to 0 y values increases

In option 2 table , f(x) is increasing from -15 to -5

In option 3 table, f(x) values goes on decreasing over the interval -2 to 0

So , option 3 table shows a function that is decreasing over the interval (−2, 0)

Table 3  shows that f(x) decreases in the interval (-2,0)

Step-by-step explanation:

Decreasing function: A decreasing function is a function that decreases continuously for a given interval of values

If we see the interval (-2.0) in the first image

the value of f(x) decreases from 0 to -5 and then increases to 0

So it is not decreasing continuously over the interval

For the second image in the interval (-2,0) the value of f(x) increases from -15 to -5 but decreases to -20

So it is also not decreasing continuously for the given interval

For the third image

At x=-2, f(x)= 0

At x=-1, f(x)= -10

At x=0,  f(x)=-24

Here the value of f(x) is continuously decreasing over the interval (-2,0)

Hence table 3 shows that the function is decreasing continuously over (-2,0)

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

7

step-by-step explanation:

the answer would be 7