A rectangle with an area of 81 cm² has a length that is 3 times the width. How long is the width of the rectangle? Round to the nearest tenth.

W ≈ 5.2 cm

Step-by-step explanation:

Represent the length and width by L and W respectively.

Then L * W = 81 cm^2, and L = 3W.

Substituting 3W for L in the first equation, we get:

3W * W - 81 = 0, or 3W^2 - 81 = 0.

To make it easier to find the final answer, rewrite 3W^2 - 81 = 0 as

            81

W^2 = = 27

              3

Then W (the width) is the positive square root of 27, or W ≈ 5.2 cm

60.75 ≈ 60.8

Step-by-step explanation:

4u-> 81

1u -> 20.25 (width)

3u-> 60.75 (length)

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

the answer is 1030 it's very simple math.