A walkway of uniform width is to be built around a square swimming pool with 18-foot edges. How wide should the walkway be to make the area of the walkway’s surface 400 feet?

Given

an 18 ft square with a uniform border of width x

the area of the border is 400 ft²

Find

x

Solution

The outside dimension of the square with the border added is 18+2x, so the total area of square and border is (18+2x)². Subtracting the area of the original square gives the area of the border.

... (18+2x)² -18² = 400

... 4x² +72x = 400 . . . . . simplify

... x² + 18x = 100 . . . . . . .divid by 4

... x² +18x +9² = 100 +9² . . . . complete the square

... (x +9)² = 181 . . . . . . . . .simplify

... x = √181 -9 . . . . . . . . . take the square root, subtract 9

... x ≈ 4.4536 . . . . . . . . . evaluate

The appropriate choice is ...

... c. 4.45 ft

answer:

(-8,7)

explanation:

we know that  

f

(

−

3

)

=

7

therefore, if we wish to get the output as 7, in the function, we need to have our input to be -3.

looking at the function  

f

(

x

+

5

)

, what should the value of x be, such that the input in the function becomes 7?

we simply equate the terms,

x

+

5

=

−

3

x

=

−

8

thus, the point on the new function would be  

(

−

8

,

7

)

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.