Write an explicit formula for the arithmetic sequence 15.6, 15, 14.4, 13.8,..., and then find the 32nd term.

the 32nd term is - 3

Step-by-step explanation:

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + d(n - 1)

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 15.6

d = 15 - 15.6 = 14.4 - 15 = - 0.6

n = 32

The explicit formula for the arithmetic sequence is

Tn = 15.6 - 0.6(n - 1)

We want to determine the value of the 32nd term, T32. Therefore,

T32= 15.6 - 0.6 (32 - 1)

T32 = 15.6 - 18.6

T32 = - 3

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation:

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