2. find the area of the regular polygon. give the answer to the nearest tenth. hexagon with a radius of 5 in. a. 65.0 in.^2 b. 129.9 in.^2 c. 259.8^2 d. 53.0^2 3. divers looking for a sunken ship have defined the search area as a triangle with adjacent sides of length 2.75 miles and 1.32 miles. the angle between the sides of the triangle is 35°. to the nearest hundredth, find the search area. a. 2.08 mi.^2 b. 2.97 mi.^2 c. 1.49 mi.^2 d. 1.04 mi.^2

 The correct options are (2). A,  (3). A.

Step-by-step explanation:  The calculations are as follows:

(1) We are to given the area of a regular hexagon with radius 5 in.

The AREA of a regular hexagon with side  'a' units is given by

We know that the radius of a regular hexagon is equal to the length of each side, so we have

a = 5 in.

Therefore, the area of the hexagon will be

Thus, (A) is the correct option.

(2) Given that two adjacent sides of the triangle measure 1.32 miles and 2.75 miles.

The angle lying between the two sides measure 35°.

we are to find the area of the triangle.

We know that the area of a triangle with two adjacent sides of measure 'a' and 'b' units and 'β' be the measure of the angle lying between them is given by

Here, a = 2.75 miles,  b = 1.32 miles  and  β = 35°.

Therefore, the total search area, in the form of triangle is given by

Thus, the correct option is (A) 2.08 mi².

Hence, the correct options are (2). A,  (3). A.

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240