16051 rounded to the nearest thousand

The area of a regular hexagon with an apothem of 16.5 inches and a side of 19 inches is Area of hexagon = 1/2(length of apothem)(perimeter of the hexagon) = 940.5 inches. (Option-B)

Apothem:

Apothem is a perpendicular line from the center of the regular polygon to one of its sides.

Area of Regular polygon with apothem:

Area = 1/2 x (length of apothem) x (perimeter of hexagon)

   • Given,  

     apothem = 16.5 inches and length of a side =19 inches

   • Perimeter = 6 x (side of a hexagon)

                       = 6 x (19)

                       = 114 inches

   • Hence,

      Area = 1/2 x (16.5) x (114) = 940.5 inches(rounded to the nearest tenth)

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Answer: B. 940.5 square inches

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Explanation:

Any regular hexagon is really the combination of six identical (aka congruent) equilateral triangles glued together. If we can find the area of one triangle, then we multiply by 6 to get our final answer.

The apothem is the height of the equilateral triangle with the triangular base being the side length of the hexagon.

area of triangle = (1/2)*base*height

area of triangle = 0.5*(hexagon side length)*(apothem)

area of triangle = 0.5*19*16.5

area of triangle = 156.75

This is the area of one equilateral triangle. Having 6 triangles leads to a total area of 6*156.75 = 940.5 square inches

The given expression can be simplified to obtain -3x³ + 74x - 5. The correct option is (a).

What is an Algebraic expression?

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given algebraic expression is (x + 5)(-3x² + 15x - 1).

It can be evaluated as follows,

(x + 5)(-3x² + 15x - 1)

⇒ x(-3x² + 15x - 1) + 5(-3x² + 15x - 1)

⇒ -3x³ + 15x² - x - 15x² + 75x - 5

⇒ -3x³ + 74x - 5

Hence, the product of the given expression is -3x³ + 74x - 5.

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Answer:

-3x^3+74x-5

Step-by-step explanation:

(x+5)(-3x^2+15x-1)

-3x^3+15x^2-x-15x^2+75x-5

-3x^3+15x^2-15x^2+75x-x-5

-3x^3+74x-5

alternate angle,