Morgan is making a square quilt with an area of 49 square feet for her nephew. The quilt is made out of square pieces that have a perimeter of 24 square inches. How many patches of material will Morgan need to complete the quilt for her nephew?

196 patches

Step-by-step explanation:

We are told that the quilt is made out of square pieces that have a perimeter of 24 square inches.

This means that, length of one side = 24/4 = 6 inches.

Now since Morgan is making a square quilt with an area of 49 square feet for her nephew, let's convert 6 inches to ft.

6 inches = 6 × 1/12 = 0.5 ft

Thus, the area of a small quilt = 0.5 × 0.5 = 0.25 ft²

Number of patches = 49/0.25 = 196 patches

Part 1: x ≥ 17/9

Part 2: x is greater than or equal to seventeen ninths.

Part 3: using x= 3 and 4 respectively, the solution was verified

The complete statement related to this found on (ID: 2020133) is stated below:

Use the inequality to answer Parts 1-3.

-3(x - 2) ≤ one third

Part 1: Solve the inequality. Leave answer in terms of a whole number or reduced improper fraction.

Part 2: Write a verbal statement describing the solution to the inequality.

Part 3: Verify your solution to the inequality using two elements of the solution set.

Use a word processing program or handwrite your responses to Parts 1-3. Turn in all three responses.

Step-by-step explanation:

Part 1) The inequality: -3(x - 2) ≤ one third

-3(x - 2) ≤ ⅓

Multiply through by 3

-3(3)(x-2) ≤ 3(⅓)

-9(x-2) ≤ 1

Expand the bracket

-9x + 18 ≤ 1

Collect like terms

-9x ≤ 1-18

-9x ≤ -17

Divide through by coefficient of x (-9)

-9x/-9 ≤ -17/-9

When you divide an expression in inequality by a negative sign, the inequality sign changes

x ≥ 17/9

Part 2) the verbal statement of the solution:

x is greater than or equal to seventeen ninths.

Part 3) We would verify the solution to the inequality using two elements of the solution set greater than 17/9.

17/9 = 1.89

Let's use x= 3 and x = 4. As they are greater than 17/9

-3(x - 2) ≤ ⅓

When x= 3

-3(3 - 2) ≤ ⅓

-3(1) ≤ ⅓

-3 ≤ ⅓

This satisfies the solution of the inequality

When x= 4

-3(4 - 2) ≤ ⅓

-3(2) ≤ ⅓

-6 ≤ ⅓

This satisfies the solution of the inequality