A private party wants to fill the Gold Ballroom with rows of round tables. The tables are 4 feet in diameter, and each table has to be 5 feet away from the wall and from other tables. How many tables can you fit?
The area of the Ballroom is 1288 ft.

Explanation:

Take first the direction along one wall. If there are n tables they occupy a length of n × 4 feet.

There are (n - 1)  5-feet spaces between them. That is additional 5 × (n - 1) feet.

Also, each table on the ends are separated 5 feet from the wall. That is an additional 5 feet + 5 feet = 10 feet length.

The total length  occupied by n tables is 4n + 5(n-1) + 10 = 4n + 5n - 5 + 10 =9n + 5 feet

The situation is the same in the direction of the perpendicular walls: 9n - 5 feet.

Thus, the area is (9n + 5)² = 1288 ft²

Solve the equation:

           9n + 5 = 35.89

            9n = 30.89

             n = 3.4

You must round to whole number of tables. That is 3 tables in one direction and 3 tables in the other direction.

Then, the number of tables is 3 × 3 = 9 ← answer

9.55 degrees.

step-by-step explanation:

the given angle is

1 cycle is equal to 2π radians. so 4π will be equal to two cycles.

5.166667π-4π = 1.166667π

hence, this angle goes a little more than negative x axis.

1.166667π-π= 0.166667π

hence, the reference angle is 0.166667π radians.

1 radian = 57.2958 degrees

now, in degrees, this should be equals to 9.55 degrees.

x² + 3x + 7 = 0       [ax² + bx + c]

a = 1

b = 3

c = 7

quadratic formula:

    (+/- is this ±)

plug in the numbers into the variables

your answer is a