HELP ME PLEASE I DONT UNDERSTAND

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

Joe earns $14 an hour and Blaine earns $18 per hour. Joe receives a raise of $1.75 every six months, and Blaine receives a raise

Katarina [22]

After 4 interval of six months, Joe to earn same hourly rate as Blaine

Solution:

Given that,

Amount earned by Joe = $ 14 per hour

Amount earned by Blaine = $ 18 per hour

Lets assume the number of six month intervals be "x"

Joe receives a raise of $1.75 every six months

Therefore,

Joe earning: 14 + 1.75(number of six month intervals)

Equation for Joe earning: 14 + 1.75x ------- eqn 1

Blaine receives a raise of $0.75 every six months

Therefore,

Blaine earning: 18 + 0.75(number of six month intervals)

Equation for Blaine earning: 18 + 0.75x ------------ eqn 2

The number of six-month intervals it will take Joe to earn the same hourly rate as Blaine,

Eqn 1 must be equal to eqn 2

$14+1.75x = 18+0.75x\\\\1.75x-0.75x = 18-14\\\\1x = 4\\\\x = 4$

Thus after 4 interval of six months, Joe to earn same hourly rate as Blaine.

8 0

3 years ago

Max is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 5 km/h. After two ho

Valentin [98]

You have velocity 1 of 5 km per hour after 1 hour and velocity 2 of 3 km per hour after 2 hours.

Part A)

Let Velocity = a +bt, with t being the time in hours.

For velocity 1 you have a +b = 5

For velocity 2, you have a + 2b =3

Now subtract velocity 1 from velocity 2:

a +2b - (a+b) = 3-5

Simplify to get b = -2

Now solve for a in the first equation:

a + b =5

Replace b with -2:

a - 2 = 5

a = 7

Now replace a and b in the original formula:

Velocity = 7 -2t

Part B)

Create a table with x and Y values to graph.

X axis would be the time and the velocity would be the Y axis

Your time would be 0 , 1, 2 3 and 4 hours.

Using the final equation from part A, replace t with the hours ans solve for the velocities, which become the y axis:

7 - 2(0) = 7-0 = 7

7 - 2(1) = 7-2 = 5

7 - 2(2) = 7-4 = 3

7 - 2(3) = 7-6 = 1

7-2(4) = 7-8 = -1

Now you have your x and y coordinates to plot on a graph:

(0,7) (1,5) (2,3) (3,1) and (4,-1)

7 0

3 years ago

Read 2 more answers

–4.5t49.5t = 40 Please help

dlinn [17]

Answer:

t= -0.18

Step-by-step explanation:

Isolate t to get the unknown number:

(-4.5t)(49.5t) = 40

Multiply (-4.5t)(49.5t):

(-4.5t)(49.5t) = -222.75t

Now, write full equation:

-222.75t = 40

Isolate t by dividing -222.75 on both sides:

$\frac{-222.75}{-222.75}t=\frac{40}{-222.75}$

Cancel out left hand side:

$t=\frac{40}{-222.75}$

Simplify your answer:

$t=-0.17957351$

Approximate to 2 decimals:

$t=-0.18$

5 0

3 years ago

A triangle has an area of 357 square inches. The height of the triangle is 23.8 inches. What is the length of the base of the tr

Nitella [24]

You lay out the triangle formula for area which would be A=(1/2)(b)(h)
plug in for variables
375=(1/2)(23.8)(b)
solve for b

3 0

2 years ago