Question

practice & problem solving leveled practice in 6 and 7, fill in the boxes to solve each inequality. then graph the solutions. 7. $x - 4 geq 12$ $x - 4 square square geq 12 square square$ problem 6 — donut frosting a donut has a radius of 4 inches, and frosting covers the entire top surface. how many square inches of frosting are on top? problem 7 — small fountain a small circular fountain has a diameter of 16 feet. find the circumference of the fountains edge.

Explanation:

Problem 6: Donut Frosting

Step1: Recall the formula for the area of a circle

The area \( A \) of a circle is given by the formula \( A = \pi r^2 \), where \( r \) is the radius of the circle.

Step2: Substitute the given radius into the formula

We are given that the radius \( r = 4 \) inches. Substituting this into the formula, we get \( A = \pi(4)^2 \).

Step3: Calculate the area

First, calculate \( 4^2 = 16 \). Then, \( A = 16\pi \). If we use \( \pi \approx 3.14 \), then \( A \approx 16\times3.14 = 50.24 \) square inches.

Step1: Recall the formula for the circumference of a circle

The circumference \( C \) of a circle is given by the formula \( C = \pi d \) (or \( C = 2\pi r \)), where \( d \) is the diameter of the circle.

Step2: Substitute the given diameter into the formula

We are given that the diameter \( d = 16 \) feet. Substituting this into the formula, we get \( C = \pi\times16 \).

Step3: Calculate the circumference

If we use \( \pi \approx 3.14 \), then \( C \approx 3.14\times16 = 50.24 \) feet.

Step1: Isolate the variable \( x \)

To solve the inequality \( x - 4 \geq 12 \), we need to isolate \( x \). We can do this by adding 4 to both sides of the inequality (by the addition property of inequalities, which states that if we add the same number to both sides of an inequality, the direction of the inequality remains the same).
So, we have \( x - 4 + 4 \geq 12 + 4 \).

Step2: Simplify both sides

Simplifying the left side: \( x - 4 + 4 = x \).
Simplifying the right side: \( 12 + 4 = 16 \).
So, the solution to the inequality is \( x \geq 16 \).
For the boxes in the inequality \( x - 4 \square \square \geq 12 \square \square \), we fill in the operation and the number. We add 4 to both sides, so the first box (operation) is \( + \), the second box (number) is \( 4 \), the third box (operation) is \( + \), and the fourth box (number) is \( 4 \).

Answer:

The area of the frosting on top is \( 16\pi \) (or approximately \( 50.24 \)) square inches.

Problem 7: Small Fountain