Dakota made this pattern. 8, 13, 18, 23, 28 Coby uses the same rule as Dakota to make a pattern. He begins his pattern with the number 11. Which is Coby's pattern?

11, 16, 21, 26, 31

Step-by-step explanation:

Dakota pattern = 8, 13, 18, 23, 28

The common difference in Dakota patter is 5

8, 8 + 5, 8 + 5 + 5, 8 + 5 + 5 + 5, 8 + 5 + 5 + 5 + 5

= 8, 13, 18, 23, 28

Coby uses the same rule as Dakota to make a pattern

He begins his pattern with the number 11.

= 11, 11+5, 11+5+5, 11+5+5+5, 11+5+5+5+5

= 11, 16, 21, 26, 31

Coby's pattern starting from 11 using the same rule as Dakota is 11, 16, 21, 26, 31

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