Arectangle has an area of 1050 square feet. its width is eight feet less than twice the length. find the measures of the length and width of the rectangle.

Step-by-step explanation:

If L represents the length, then the width is (2L-8) and the area is ...

  A = LW

  1050 = L(2L-8)

  525 = L(L-4) . . . . . divide by 2

Completing the square, we have ...

  525 +4 = L² -4L +4 . . . . . add the square of half the L coefficient

  529 = (L -2)² . . . .simplify

  ±23 = L -2 . . . . . . take the square root

  L = 25 . . . . . . . the negative root doesn't work in this scenario

  (2L-8) = 42 . . . width

The length is 25 feet; the width is 42 feet.

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40

x = 2

step-by-step explanation:

if sr parallel to ba then the sides bc and ac are in proportion, that is

= ← substitute values

= ( cross- multiply )

27x = 6(4x + 1)

27x = 24x + 6 ( subtract 24x from both sides )

3x = 6 ( divide both sides by 3 )

x = 2