11. A landscaper is designing a rectangular garden, which will be 5.00 m wide by 6.25 m long. She has enough crushed rock to cover an area
of 6.0 m² and wants to make a uniform border around the garden.
How wide should the border be, if she wants to use all the crushed
rock?

9514 1404 393

  25.5 cm

Step-by-step explanation:

If the walk is x meters wide, it adds 2x to the overall length and width. Then the area of the walkway is ...

  (2x +5)(2x +6.25) -(5)(6.25) = 6

  4x^2 +22.5x = 6 . . . . simplify left side

  4x^2 +22.5x -6 = 0 . . . subtract 6 to put into standard form

Using the quadratic formula, the walkway width can be found to be ...

  x = (-22.5 +√(22.5² -4(4)(-6)))/(2(4)) = (-22.5 +√602.25)/8

  x ≈ 0.25510

The border width should be about 25.5 cm.

the answer is c. 23/3

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for