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3 years ago

Express answer in exact form. Show all work for full credit.

Mathematics

1 answer:

Ipatiy [6.2K]3 years ago

6 0

Answer:

Area = 23.38 square"

Step-by-step explanation:

It is given that a regular hexagon is having a side = 3"

Since hexagon is inscribed in a circle therefore all the triangles formed by the radii and the sides of hexagon will be equilateral triangles.

In a hexagon number of triangles formed = 6

Area of an equilateral triangle = 1/4s²√3

By putting the value of s = 3"

Area of one triangle = 1/4×3²√3 = (9√3)/4

and we know number of triangles formed inside the hexagon = 6

Therefore area of hexagon = 6×(9√3)/4 = 23.38 square"

Answer is 23.38 square"

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Aleksandr [31]

Let x, y and z denote the weighs of car X, car Y and car Z, respectively.

We know that car X weighs 136 more than car Z, this can be express by the equation:

$x=z+136$

We also know that Y weighs 117 pounds more than car Z, this can be express as:

$y=z+117$

Finally, we know that the total weight of all the cars is 9439, then we have:

$x+y+z=9439$

Hence, we have the system of the equations:

$\begin{gathered} x=z+136 \\ y=z+117 \\ z+y+z=9439 \end{gathered}$

To solve the system we can plug the values of x and y, given in the first two equations, in the last equation; then we have:

$\begin{gathered} z+136+z+117+z=9439 \\ 3z=9439-136-117 \\ 3z=9186 \\ z=\frac{9186}{3} \\ z=3062 \end{gathered}$

Now that we have the value of z we plug it in the first two equations to find x and y:

$\begin{gathered} x=3062+136=3198 \\ y=3062+117=3179 \end{gathered}$

Therefore, car X weighs 3198 pound, car Y weighs 3179 pounds and car Z weighs 3062 pounds.

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Makovka662 [10]

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Step-by-step explanation: The prime factorization of 4320 is

2•2•2•2•2•3•3•3•5

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 4320 = √ 2•2•2•2•2•3•3•3•5 =2•2•3•√ 30 =

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√ 30 , rounded to 4 decimal digits, is 5.4772

So now we are looking at:

w = ( -40 ± 12 • 5.477 ) / -34

Two real solutions:

w =(-40+√4320)/-34=(20-6√ 30 )/17= -0.757

or:

w =(-40-√4320)/-34=(20+6√ 30 )/17= 3.110

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