Find the value of x. 75° 3x° X = degrees

8-35. Use your knowledge of polygons to answer the questions below, if possible.

Nataliya [291]

Answer:

(a)I. 13 Sides II. 7 Sides

(b) 4 Sides, Square

(c)x=52 degrees

(d)x=107 degrees

(e)1620 degrees

Step-by-step explanation:

(a)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

I. If the Interior angle is $1980^0$

Then:

$(n-2)180^0=1980^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=11\\$Add 2 to both sides of the equation\\n-2+2=11+2\\n=13$

The polygon has 13 sides.

II. If the Interior angle is $900^0$

Then:

$(n-2)180^0=900^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=5\\$Add 2 to both sides of the equation\\n-2+2=5+2\\n=7$

The polygon has 7 sides.

(b)The sum of the exterior angle of a polygon is 360 degrees,

Each exterior angle of a n-sided regular polygon is: $\frac{360^0}{n}$

If the exterior angle of a regular polygon is 90°

Then:

$90\°=\frac{360^0}{n}\\ 90n=360\\n=4$

The regular polygon has 4 sides and it is called a Square.

(c)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

Each Interior angle of a regular n-sided polygon is: $\frac{(n-2)180^0}{n}$

For a pentagon, n=5

Then:

$\frac{(5-2)180^0}{5}=2x+4\\108=2x+4\\108-4=2x\\104=2x\\x=52^0$

(d)The sum of the exterior angle of a polygon is 360 degrees.

If four of the exterior angles of a pentagon are 57, 74, 56, and 66.

Let the fifth angle=x

Then:

$57+74+56+66+x=360^0\\253+x=360\\x=107^0$

(e)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

In an 11-gon., n=11

Therefore, the sum of the interior angle=(11-2)180= $1620^0$

The sum of the interior angle does not change either in a regular or irregular polygon.

3 0

2 years ago

Help I need the answer phone plz

barxatty [35]

Answer:

t>-4

I’m not sure if this is right

6 0

3 years ago

PLS ANSWER WHAT IS 3 and 14 hundredths minus 1 and 9 hundredths?

k0ka [10]

Answer:

2 and 5 hundredths

Step-by-step explanation:

3 - 1 = 2

14 hundredths - 9 hundredths = 5 hundredths

hence you get 2 and 5 hundredths

6 0

2 years ago

The graph of a sinusoidal function intersects its midline at (0,5) and then has a maximum point at (\pi,6)

lesya692 [45]

First, let's use the given information to determine the function's amplitude, midline, and period.

Then, we should determine whether to use a sine or a cosine function, based on the point where x=0.

Finally, we should determine the parameters of the function's formula by considering all the above.

Determining the amplitude, midline, and period

The midline intersection is at y=5 so this is the midline.

The maximum point is 1 unit above the midline, so the amplitude is 1.

The maximum point is π units to the right of the midline intersection, so the period is 4 * π.

Determining the type of function to use

Since the graph intersects its midline at x=0, we should use thesine function and not the cosine function.

This means there's no horizontal shift, so the function is of the form -

a sin(bx)+d

Since the midline intersection at x=0 is followed by a maximumpoint, we know that a > 0.

The amplitude is 1, so |a| = 1. Since a >0 we can conclude that a=1.

The midline is y=5, so d=5.

The period is 4π so b = 2π / 4π = 1/2 simplified.

$f(x) = 1 sin ( \dfrac{1}{2}x)+5$ = Solution

4 0

3 years ago

The volume of a shampoo filled into a container is uniformly distributed between 370 and 385 milliliters. (a) What are the mean

Olenka [21]

Answer:

(a) mean = 377.5ml. standard deviation = 4.33

(b) 0.333

(c) 384.25 ml

Step-by-step explanation:

(a)The mean:

$\mu = \frac{385 + 370}{2} = 377.5 ml$