30 will vote brainiest
the table shows a linear function
(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.

Part A:

Consider from x = -5 to x = -4, they are 1 unit apart and the difference of their outputs is given by:

-3 - (-11) = -3 + 11 = 8.

Thus, the value of the output increases by 8 units for each one unit increase in the input.

Part B:

Consider from x = -3 to x = -1, they are 2 units apart and the difference of their outputs is given by:

21 - 5 = 16.

Thus, the value of the output increases by 16 units for each two units increase in the input.

Part C:

Consider from x = 0 to x = 3, they are 3 units apart and the difference of their outputs is given by:

53 - 29 = 24.

Thus, the value of the output increases by 24 units for each three units increase in the input.

Part D:

It can be noticed that the ratio difference in the outputs to the input intervals are equal for all the given input intervals.

i.e 8 / 1 = 16 / 2 = 24 / 3.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12