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2 years ago

Find the measure of each interior angle and each exterior angle of a regular nonagon (a nine-sided polygon).

Mathematics

1 answer:

antoniya [11.8K]2 years ago

8 0

Answer:

Interior-140° Exterior-40°

Step-by-step explanation:

The sum of the interior angles of a polygon are given by 180(n-2) where n is the number of sides.

Therefore, the sum of all interior angles in a nonagon is 180(9-2) or 180×7. This equals to 1260°.

To get the individual interior angle, you use $\frac{s}{n}$ , with n defined above and s being the sum of interior angles.

Therefore, each angle is $\frac{1260}{9}$ °, which can be solved to 140°.

The value of an individual exterior angle is given by 180-i, with i being the individual interior angle (this is because the 2 angles form a straight line).

In this case, 180-140=40°.

Each interior angle of a nonagon is 140°, and each exterior angle is 40°.

**This content involves angles of polygons, which you may want to revise. I'm always happy to help!

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X² + 3x – 7=0 Solve X= or x=

svetoff [14.1K]

Answer:

x = 2

Step-by-step explanation:

X² = 3x - 7 = 0

X² = 3x = 7

(x + 1) (x + 2) = 7

(x + 1) + x = 7 - 2

x + x = 7 - 3

2x = 4

x = 4/2

x = 2

8 0

2 years ago

Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=4x2 2y2; 3x

nevsk [136]

For given f(x, y) the extremum: (12, 24) which is the minimum.

For given question,

We have been given a function f(x) = 4x² + 2y² under the constraint 3x+3y= 108

We use the constraint to build the constraint function,

g(x, y) = 3x + 3y

We then take all the partial derivatives which will be needed for the Lagrange multiplier equations:

$f_x=8x$

$f_y=4y$

$g_x=3$

$g_y=3$

Setting up the Lagrange multiplier equations:

$f_x=\lambda g_x$

⇒ 8x = 3λ .....................(1)

$f_y=\lambda g_y$

⇒ 4y = 3λ ......................(2)

constraint: 3x + 3y = 108 .......................(3)

Taking (1) / (2), (assuming λ ≠ 0)

⇒ 8x/4y = 1

⇒ 2x = y

Substitute this value of y in equation (3),

⇒ 3x + 3y = 108

⇒ 3x + 3(2x) = 108

⇒ 3x + 6x = 108

⇒ 9x = 108

⇒ x = 12

⇒ y = 2 × 12

⇒ y = 24

So, the saddle point (critical point) is (12, 24)

Now we find the value of f(12, 24)

⇒ f(12, 24) = 4(12)² + 2(24)²

⇒ f(12, 24) = 576 + 1152

⇒ f(12, 24) = 1728 ................(1)

Consider point (18,18)

At this point the value of function f(x, y) is,

⇒ f(18, 18) = 4(18)² + 2(18)²

⇒ f(18, 18) = 1296 + 648

⇒ f(18, 18) = 1944 ..............(2)

From (1) and (2),

1728 < 1944

This means, given extremum (12, 24) is minimum.

Therefore, for given f(x, y) the extremum: (12, 24) which is the minimum.

Learn more about the extremum here:

brainly.com/question/17227640

#SPJ4

6 0

1 year ago

-4 1/2 × -2 1/3 Please include steps☺

Scilla [17]

-4 1/2 × -2 1/3
Convert the mixed numbers into improper fractions.
- 9/2 x -7/3
Multiply the numerator by the other numerator and the denominator by the other denominator.
Final Answer: 63/6 or 10 1/2 or 10 3/6 or 10.5 * All answers are equivalent to each other.

5 0

2 years ago

Read 2 more answers

angelo recently opened a bank account and deposits the same amount each week. After 8 weeks, he deposited $280. He wants to depo

navik [9.2K]

Answer:

$12\ weeks$

Step-by-step explanation:

The complete question is

Angelo recently opened a bank account and deposits the same amount each week. After 8 weeks, he deposited $280. He wants to deposit a total of 420 in his account. How many weeks will it Angelo to deposit a total of $420

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$