A23-ft by 47-ft rectangular swimming pool is surrounded by a walkway of uniform width. if the total area of the walkway is 456ft^2, how wide is the walkway?

The wide of the walkway is 3 feet

Step-by-step explanation:

* Lets explain how to solve the problem

- A 23-ft by 47-ft rectangular swimming pool is surrounded by a

 walkway of uniform width

- Assume that the uniform width is x

- That means each dimensions of the the rectangular pool will exceed

 by 2x (x from each side)

- The dimensions of the pool with the walkway are 23 + 2x and 47 + 2x

- The total area of the walkway is the difference between the area of

 the pool with walkway and the area of the pool

- Area of any rectangle = l × w, where l, w are its dimensions

∴ The area of the pool = 23 × 47 = 1081 ft²

∴ The area of the pool with walkway = (23 + 2x)(47 + 2x)

∴ The area of walkway = (23 + 2x)(47 + 2x) - 1081 ⇒ (1)

∵ The area of the walkway is 456 ft² ⇒ (2)

- Equate (1) and (2)

∴ (23 + 2x)(47 + 2x) - 1081 = 456

- Add 1081 for both sides

∴ (23 + 2x)(47 + 2x) = 1537

- Multiply 2 brackets

∴ (23 × 47) + (23 × 2x) + (2x × 47) + (2x × 2x) = 1537

∴ 1081 + 46x + 94x + 4x² = 1537

∴ 1081 + 140x + 4x² = 1537

- Subtract 1081 from both sides

∴ 4x² + 140x - 456 = 0

- Divide all terms by 4 because 4 is a common factor in all terms

∴ x² + 35x - 114 = 0

- Factorize it

∴ (x - 3)(x + 38) = 0

- Equate each bracket by 0

∴ x - 3 = 0

- Add 3 for both sides

∴ x = 3

OR

∴ x + 38 = 0

- Subtract 38 from both sides

∴ x = -38 ⇒ rejected because no negative answer for dimensions

∴ The value of x is 3

* The wide of the walkway is 3 feet

5/6

step-by-step explanation:

if i remember correctly with perpendicular stuff you just take away the negative

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.