A 132-inch board is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece

The length of the shorter piece is 33 inches.

132 inches of the board is cut into 2 pieces. The board is divided into 2 parts.

One piece is three times the length of the other. Therefore,

let

one piece = x

The other piece = 3x

The length(x) of the shorter part  can be found below

4x = 132

divide both sides by 4

x = 132 / 4

x = 33

The length of the shorter piece is 33 inches.

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Here are the two pieces:

x and 3x

Here is the needed equation:

x + 3x = 132

4x = 132

x = 132/4

x = 33

The two pieces are 33 inches and 99 inches.

function 2 has a greater rate of change than function 1

function 2 has a greater y-intercept than function 1

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for