Jeremy is building a large deck for a community center. the deck is shaped as a rectangle. the width of the deck is 29 feet. the perimeter of the deck is to be at least 134 feet.
  a. write an inequality that represents all possible values for the length of the deck.  b. solve algebraically to find all possible values for the length of the deck. show all work

By definition, the perimeter of a rectangle is given by:

Where,

w: width of the rectangle

l: length of the rectangle

We write then the inequality that represents the problem:

Rewriting we have:

Then, solving the inequality for "l" we have:

Therefore, the length must be at least 38 feet.

An inequality that represents all possible values for the length of the deck is:

The possible values for the length of the deck is:

[38, inf)

1. 34

2. 268

3. x=14.4

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1