A rectangular yard has a length that is 5 feet more than the width. Around the outside of the yard is a path made of bricks that is 3 feet wide.

a) What expression can be used to represent the area of the path?

b) If the area of the yard and the path is 546 sq. ft, find x

c) What is the area of the yard?

d) What is the area of the path?

A) A = X^2 + 11X + 24

B) X = 18 ft

C) 414 ft^2

D) 132 ft^2

Step-by-step explanation:

A) Width W of yard and path = X + 3

Lenght L of path = X + 5 + 3 = X + 8 ft, therefore,

Area of yard and path = L x W = (X +3) x (X +8)

A = X^2 + 11X + 24

B) if area of the yard and path is 546 ft^2,

546 = X^2 + 11X + 24

X^2 +115X - 522 = 0 (quadratic equation)

Solving the quadratic equation gives

X = 18 and X = -29

Our answer can only be positive so we choose X = 18 ft

C) lenght of yard = 5 + 18 = 23 ft

Width = 18 ft

Therefore area = L x W = 23 x 18 = 414 ft^2

D) area of path = area of path and yard minus area of yard

= 546 - 414 = 132 ft^2

step-by-step explanation:

ok one would be money, and the other would be refreshments or something similar. if each bag of popcorn is 5.00 and each drink is half of that that means drinks are 2.50 the proper way to do that would to look and see how much of each you can buy without exceeding a limit of 30.00

answers

\3. yes the presentation (i.e. odd numbers being written as differences of two squares) is possible for all odd natural number however the presentation may not be unique. for example,  57=112−82=292−28257=112−82=292−282.

\4. 2 can't be written as a difference of two squares because 4-1=3 and 1-1=0 and the difference of squares grows to integers larger that 3.

can i get some in proving questions 1 and 2?