Determine whether the points on the line rise, fall, are horizontal, or vertical. (2, -4) and (4, -1)

The points rise.

Step-by-step explanation:

Points on a line have the following format: (x,y)

They rise if: As x increases, so does y.

They fall if: As x increases, y decreases.

They are horizontal if: As x increases, y remains constant.

They are vertical if: x is constant as y changes.

In this question:

Points (2,-4) and (4,-1).

x increases from 2 to 4.

y increases from -4 to -1.

That is, both increase, so the points rise.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation: