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Pavel [41]
2 years ago
5

Find the interior angle sum for each polygon. Round your answer to the nearest tenth if needed

Mathematics
1 answer:
Lerok [7]2 years ago
6 0

Answer:

1) 720

2) 540

3) x = -1

4) x = 10

Step-by-step explanation:

The formula for finding the sum of interior angles in a polygon is the following,

S=180(n-2)

Where (S) represents the sum of interior angles, and (n) represents the number of sides.

1)

The given polygon is a hexagon, meaning it has (6) sides. Substitute the number of sides into the formula and solve for the sum of interior angles.

S=180(n-2)

S=180(6-2)\\\\S=180(4)\\\\S = 720

2)

This polygon is a pentagon, meaning it has (5) sides. Substitute the number of sides into the formula and solve for the sum of interior angles.

S=180(n-2)

S=180(5-2)\\\\S=180(3)\\\\S=540

3)

The sum of interior angles in a triangle is (180) degrees. One can see that one of the measures of an angle is (90) degrees (indicated by the box around the angle). One can form an equation by adding up the expressions for the angle measures and setting it equal to (180) degrees.

(55) + (x + 36) + (90) = 180

Simplify,

181 + x = 180

Inverse operations,

181 + x = 180

x = -1

4)

The remote angles theorem states that when one extends one of the sides of a triangle, the angle formed between the side and the extension is equal to the sum of the two non-adjacent interior angles in the triangle. Based on this theorem, one can form an equation and solve for the unknown.

<F + <G = <FEZ

Substitute,

(4x) + (-5 + 7x) = 105

Simplify,

4x - 5 + 7x = 105

11x - 5 = 105

Inverse operations,

11x - 5 = 105

11x = 110

x = 10

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jonny [76]

Answer:

the answer is A. -16

Step-by-step explanation:

3(-16)+3= -45

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5(-16)-1=-81

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4 0
3 years ago
The average value of a function f over the interval [−2,3] is −6 , and the average value of f over the interval [3,5] is 20. Wha
Xelga [282]

Answer:

The average value of f over the interval [-2,5] is \frac{10}{7}.

Step-by-step explanation:

Let suppose that function f is continuous and integrable in the given intervals, by integral definition of average we have that:

\frac{1}{3-(-2)} \int\limits^{3}_{-2} {f(x)} \, dx = -6 (1)

\frac{1}{5-3} \int\limits^{5}_{3} {f(x)} \, dx = 20 (2)

By Fundamental Theorems of Calculus we expand both expressions:

\frac{F(3)-F(-2)}{3-(-2)} = -6

F(3) - F(-2) = -30 (1b)

\frac{F(5)-F(3)}{5-3} = 20

F(5) - F(3) = 40 (2b)

We obtain the average value of f over the interval [-2, 5] by algebraic handling:

F(5) - F(3) +[F(3)-F(-2)] = 40 + (-30)

F(5) - F(-2) = 10

\frac{F(5)-F(-2)}{5-(-2)} = \frac{10}{5-(-2)}

\bar f = \frac{10}{7}

The average value of f over the interval [-2,5] is \frac{10}{7}.

4 0
2 years ago
What number is 45% of 245
galina1969 [7]
245 x 0.45 = 110.25

110.25 is your answer


hope this helps
8 0
3 years ago
Read 2 more answers
Your friend can clap his hands 28 times in 12 seconds. How many times can your friend clap his hands in 0.5 minute?
Allushta [10]
60 seconds in a minute

12 goes into 60, 5 times,
So 5 * 28 = 140
140 claps per minute

0.5 minute is 30 seconds, half a minute so divide by 2,
140/2 = 70

70 times every 0.5 minutes
7 0
3 years ago
The price of tomatoes went from $1.12 per pound to $1.96 per pound in 3 years. find the rate of change of the price of tomatoes.
ad-work [718]

\bf \begin{array}{|cc|ll} \cline{1-2} \stackrel{x}{year}&\stackrel{y}{price}\\ \cline{1-2} 0&1.12\\ 3&1.96\\ \cline{1-2} \end{array}~\hspace{10em} (\stackrel{x_1}{0}~,~\stackrel{y_1}{1.12})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{1.96}) \\\\\\ \stackrel{\textit{rate of change}}{slope = m\implies} \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1.96-1.12}{3-0}\implies \cfrac{0.84}{3}\implies 0.28

7 0
3 years ago
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