Solve for x. −6≥10−8x

What is the area of a regular 16-gon with a radius of 15 feet? Round your answer to the nearest tenth.

Sedbober [7]

Split up the 16-gon into 16 congruent isosceles triangles. Cut each of these isosceles triangles in half to get a right triangle.

The radius of the 16-gon corresponds to the hypotenuse of any of these 32 right triangles. As you probably know, the area of a triangle is half the product of its base and height. For a right triangle, the base and height can be taken to be the two legs. So you need to find their lengths.

Recall that the exterior angles of any convex polygon sum to 360º in measure. For a regular polygon, these angles are all congruent. There are 16 of them in this case, so they each have measure (360/16)º = 22.5º.

Interior angles are supplementary to exterior angles, which means each interior angle of the 16-gon has measure (180 - 22.5)º = 157.5º.

When we split up the 16-gon into isosceles triangles, the "base angles" are equal in measure to half the measure of the interior angles, since each hypotenuse bisects the interior angle. So each base angle has measure 78.75º.

In each right triangle, we then have base b and height h such that

sin(78.75º) = h/15

cos(78.75º) = b/15

Solve for h and b to get

b = 15 cos(78.75º)

h = 15 sin(78.75º)

Then the area of each right triangle is

1/2 b h = 225/2 sin(78.75º) cos(78.75º) = 225/4 sin(157.5º)

and so the area of the 16-gon is

32(1/2 b h) = 1800 sin(157.5º) ≈ 688.8 sq. ft.

4 0

3 years ago

How do you graph this f(x)= -3/2|x|+5 if x≤4

LenaWriter [7]

Answer:

see below

Step-by-step explanation:

I enter the equation into a graphing calculator and let it do the graphing.

___

If you're graphing this by hand, you start by looking for the parent function. Here, it is |x|. That has a vertex of (0, 0) and a slope of +1 to the right of the vertex and a slope of -1 to the left of the vertex.

Here, the function is multiplied by -3/2, so will open downward and have slopes of magnitude 3/2 (not 1). The graph has been translated 5 units upward, so the vertex is (0, 5).

I'd start by plotting the vertex point at (0, 5), then identifying points with slope ±3/2 either side of it. To the left, it is left 2 and down 3 to (-2, 2). The points on the right of the vertex are symmetrically located about the y-axis, so one of them will be (2, 2).

Of course, you don't plot any function values for x > 4.

8 0

3 years ago

The entrance fee to the national park is $15. The campsite fee is $25 per night.

lisabon 2012 [21]

Answer:

Step-by-step explanation:

a.) y = 25x + 15

b.) y is the total cost x is the amount of nights stayed 15 is the entrance fee and 25 is the cost per night

i.) x is the amount of nights stayed y is the total cost

ii.) slope (or m) is 25 y-intercept is 15

c.) plug in 3 for x

y = 25(3) + 15

y = 75 + 15

y = 90

its $90 for 3 nights

hope this helps <3

8 0

2 years ago

Hello im in 8th grade and I need to get my grades up so anyone know the answer to

jolli1 [7]

Answer:

x = 3

Step-by-step explanation:

12x = 36

simply 12 will go to the other side and switches to the opposite sign for example + will be -

× will br ÷

so 36 ÷ 12 =3

x = 3

4 0

2 years ago

2 please answer this question

Fittoniya [83]

B. End of the reconstruction.

4 0

3 years ago

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