How many degrees are there in the each interior angle of a polygon, if the sum of its interior angles is 2520°?

Answers

Answer 1

Answer:

$\underset{in~degrees}{\textit{Sum of All Interior Angles}}\n\n S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\n[-0.5em] \hrulefill\n S=2520 \end{cases}\implies 2520=180(n-2) \n\n\n \cfrac{2520}{180}=n-2\implies 14=n-2\implies 16=n \n\n[-0.35em] ~\dotfill$

$\underset{in~degrees}{\textit{Sum of All Interior Angles}}\n\n n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\n \theta = \stackrel{degrees}{angle}\n[-0.5em] \hrulefill\n n=16 \end{cases}\implies 16\theta =180(16-2) \n\n\n 16\theta =2520\implies \theta =\cfrac{2520}{16}\implies \boxed{\theta =157.5^o}$

Answer 2

Answer: To find the measure of each interior angle of a polygon, you can use the formula: (n-2) * 180, where n is the number of sides. So, in this case, we have (n-2) * 180 = 2520. The measure of each interior angle of the polygon is 180 degrees.

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Cot^2x csc^2x + 2 csc^2x –cot^2 = 2
The sum of two rational numbers is -7. if one of the numbers is –15/19, the other number is

During the first hour of operation the farm stand owner sold 15% of the apples he had. On the second hour he sold 20% of the remaining apples. On the third hour he sold 25% of the remaining apples, and so on, selling 5% more each following hour. If during the third hour he sold 34 kg of apples, how many kilograms of apples did he have initially?

Answers

Answer:

75 kg

Step-by-step explanation:

%25 of ___ will give you 34.

____ x 0.20 = 34

____ = 34/0.20

34/0.20=170

___=170

The product of 3 consecutive prime numbers is 2431. What is their sum?

Answers

The required sum of three consecutive number is 41.

Given that,

The product of 3 consecutive prime numbers is 2431.

We have to find,

What is their sum of 3 consecutive prime numbers.

According to the question,

A series of consecutive prime numbers to be a series of numbers, each prime, in which there are no other prime numbers between them.

For finding the 3consecutive numbers is 2431.

Taking LCM of 2431.

The LCM of 2431 is 11×13×17

The product these three numbers is 11×13×17 = 2431

And Sum of these three numbers is = 11 + 13 + 17 = 41.

Hence, The required sum of three consecutive number is 41.

For more information about Consecutive Numbers click the link given below.

brainly.com/question/13393735

2431 is the product of consecutive numbers 11, 13 and also 17. If you add them all together you get 41.

i need help with a math problem it says solve for t: -3(t - 2) + 7t=9t-9 can you show all the work please

Answers

Answer:

t = 3

Step-by-step explanation:

Given

- 3 (t - 2) + 7t = 9t - 9 ← distribute left side and simplify

- 3t + 6 + 7t = 9t - 9

4t + 6 = 9t - 9 ( subtract 9t from both sides )

- 5t + 6 = - 9 ( subtract 6 from both sides )

- 5t = - 15 ( divide both sides by - 5 )

t = 3

Answer:

t = 3.

Step-by-step explanation:

-3(t - 2) + 7t = 9t - 9 Distribute the -3 over the parentheses:

-3t + 6 + 7t = 9t - 9 Subtract 9t from both sides:

-3t - 9t + 7t + 6 = -9 Subtract 6 from both sides:

-3t - 9t + 7t = -9 - 6

-5t = -15

t = -15/-5

t = 3 (answer).

What is the slope of the graph of 8x – 4y = 11?A. 2

B. 1/2

C. -2

D. -1/2

Answers

y = mx + b
where m is the gradient (slope)
-4y = 11 - 8x
4y = 8x - 11
y = 2x - 11/4
m = 2

The correct answer is A.

A ball is released at a height of 27 inches to roll inside a half-cylinder. It rollsto a height of 9 inches on the other side of the cylinder on roll 1. Each time it
rolls up a side of the cylinder, the ball reaches a point th
high as it
had reached on the other side.
This explicit formula models the height of the ball, in inches, the nth time it
rolls up a side of the cylinder.
How high does the ball roll on its 4th time up the cylinder's side?

Answers

Answer:

$(1)/(3)\ in$

Step-by-step explanation:

we have

$a(n)=9((1)/(3))^(n-1)$

For n=4

substitute

$a(4)=9((1)/(3))^(4-1)$

$a(4)=9((1)/(3))^(3)$

$a(4)=9((1)/(27))$

$a(4)=(1)/(3)\ in$

Answer:

1/3

Step-by-step explanation:

Given quadrilateral TUVX ~ quadrilateral MNOP and VX = 5, XT = 10, and OP = 7, what is PM?

Answers

Please see the pic, I'd solved in it.

$(PM)/(OP)$ = $(XT)/(VX)$
$(PM)/(7)$ = $(10)/(5)$
We can either simplify 10/5 to 2 or just continue.
$(PM)/(7)$ =2
PM=7 units
OR
PM×5=10×7
5PM=70
PM=14 units
We get the same answer either ways.

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