Nidhi is creating a rectangular garden in her backyard. the length of the garden is 10 feet. the perimeter of the garden must be at least 40 feet and no more than 76 feet. use a compound inequality to find the range of values for the width w of the garden.

fill in the blanks
__ ≤ w ≤ __

The range of width is 10 ≤ W ≤ 28

Step-by-step explanation:

* lets study the meaning of compound inequality

- If x is greater than a and x is smaller than b, then x is between a and b

∵ x > a and x < b

∴ The compound inequality is ⇒ a < x < b

# Ex: ∵ x > -2 and x < 10

∴ The compound inequality is ⇒ -2 < x < 10

- If x is greater than or equal a and x is smaller than or equal b, then

 x is from a and b

∵ x ≥ a and x ≤ b

∴ The compound inequality is ⇒ a ≤ x ≤ b

# Ex: ∵ x ≥ -2 and x ≤ 10

∴ The compound inequality is ⇒ -2 ≤ x ≤ 10

* Now lets solve the problem

- The garden in the shape of a rectangle with dimensions length (L)

 and width (W)

- The length of the garden is 10 feet

- The perimeter (P) of the garden is at least 40 feet and not more than

  76 feet

∵ L = 10 feet

∵ P = 2L + 2W

- At least means greater than or equal (≥) and not more than means

 smaller than or equal (≤)

∴ P ≥ 40 feet

∴ P ≤ 76 feet

- lets use the rule of the perimeter

∴ 2(10) + 2(W) ≥ 40 ⇒ simplify

∴ 20 + 2W ≥ 40 ⇒ subtract 20 from both sides

∴ 2W ≥ 20 ⇒ divide both sides by 2

∴ W ≥ 10 ⇒ (1)

- Do similar with P ≤ 76

∴ 2(10) + 2(W) ≤ 76 ⇒ simplify

∴ 20 + 2W ≤ 76 ⇒ subtract 20 from both sides

∴ 2W ≤ 56 ⇒ divide both sides by 2

∴ W ≤ 28 ⇒ (2)

- From (1) and (2)

∴ 10 ≤ W ≤ 28 ⇒ compound inequality

* The range of the width is from 10 feet to 28 feet

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.