The dimensions of a rectangular building used to store tools for electrical lineman has a length of 12x + 24 feet and a width of 20x - 10 feet. Write the expression that represents the area of the building, in terms of x.

Write the expression that represents the perimeter of the building, in terms of x.

If the perimeter is going to be 220 feet, what are the dimensions of the building

a) Area = 2x^2 + 3x - 2

b) Perimeter = 64x + 28

c) Length = 60 feet and Width = 50 feet

Step-by-step explanation:

The computation is shown below:

Given that

length = 12x + 24 feet

And, the width be 20x - 10 feet

Now as we know that

Area of the rectangle = length × width

= (12x + 24) × (20x - 10)

= 12x (20x -10) + 24(20x - 10)

= 240x^2 - 120x + 480x - 240

= 240x^2 + 360x - 240

= 2x^2 + 3x - 2

Now for perimeter

As we know that

Perimeter of the rectangle = 2(Length + width)

= 2(12x + 24 + 20x - 10)

= 2(32x + 14)

= 64x + 28

In the case when the perimeter is 220

So,

220 = 64x + 28

64x = 220 - 28

64x = 192

x = 3

Now length is 12(3) + 24

= 36 + 24

= 60 feet

And, the width is

= 20(3) - 10

= 60 - 10

= 50 feet

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.