An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is x. Another side is 12 more than four times the length of the bottom of the triangle. The last side is 2 more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle

6x + 14

Step-by-step explanation:

Givens

P = s1 + s2 + s3

s1 = x

s2 = 4x + 12

s3 = x +2

Solution

P = x + 4x + 12 + x + 2

P = 6x + 14

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}