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2 years ago

Each interior angle of a regular polygon has a measure of 40.how many sides does the polygon have?

Mathematics

1 answer:

zysi [14]2 years ago

5 0

Given Information :-

⠀

Each exterior angle of a regular polygon has a measure of 40°

⠀

To Find :-

⠀

The number of sides of the polygon

⠀

Formula Used :-

⠀

$\qquad \star \: \underline{ \boxed{ \green{ \sf No.~of~sides = \dfrac{360^ \circ}{exterior ~angle}}}} \: \star$

⠀

Solution :-

⠀

Using the formula,

⠀

$\sf \dashrightarrow No. ~of~sides= \dfrac{360}{40} \\ \\ \\ \sf \dashrightarrow No. ~of~sides= \frac{ \cancel{360}}{ \cancel{40} } \\ \\ \\ \sf \dashrightarrow No. ~of~sides= \underline{ \boxed{ \blue { \frak{9}}}} \: \star$

⠀

Thus, the polygon is a nonagon, and hence has 9 sides.

⠀

$\underline{\rule{227pt}{2pt}} \\ \\$

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3 years ago

The value of y varies directly with x. If x = 2, then y = 10. What is the value of x when y = 100? *

Fynjy0 [20]

Answer:

Step-by-step explanation:

y=kx

X=2 & y= 10

10=2k

k=5

when y=100

100=5x

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3 years ago

The sea ice area around the North Pole fluctuates between about 6 million square kilometers in September to 14 million square ki

Aleksandr [31]

Answer:

there are approximately 5.035 months when there is less than 9 million square meters of sea ice around the North Pole in a year.

Step-by-step explanation:

Given the data in the question;

Let S(t) represent the amount sea ice around the North Pole in millions of square meters at a given time t,

t is the number of months since January.

Now, we use a cosine curve to model this scenario

Vertical shift will be;

D = ( 6 + 14 ) / 2 = 20 / 2

D = 10

Next is the Amplitude;

|A| = ( 6 - 14 ) / 2

|A| = 4

Now, the horizontal stretch factor will be;

B = 2π / 12

B = π/6

Hence;

S(t) = 4cos( π/6 × t ) + 10 ----------- let this be equation 1

Now we find when there will be less than 9 million square meters of sea ice;

S(t) = 9

so we have

9 = 4cos( π/6 × (t-2) ) + 10

9 - 10 = 4cos( π/6 × (t-2) )

-1 = 4cos( π/6 × (t-2) )

-1/4 = cos( π/6 × (t-2) )

so we have;

cos⁻¹( -1/4 ) = π/6 × (t₁-2) -------- let this be equation 2

2π - cos⁻¹( -1/4 ) = π/6 × (t₂-2) -------- let this be equation 3

so we solve equation 2 and 3

we have'

t₁ - t₂ = 6/π × ( 2π - cos⁻¹( -1/4 ) - cos⁻¹( -1/4 ) )

t₁ - t₂ = 6/π × ( 2π - 2cos⁻¹( -1/4 )

t₁ - t₂ = 6/π × ( π - cos⁻¹( -1/4 )

t₁ - t₂ = 6/π × ( π - 104.4775 )

t₁ - t₂ = 5.035

therefore, there are approximately 5.035 months when there is less than 9 million square meters of sea ice around the North Pole in a year.

6 0

2 years ago

At a certain high school, 15 students play stringed instruments and

Aleks [24]

Answer:

0 is the probability that a randomly selected student plays both a stringed and a brass instrument.

Step-by-step explanation:

Given that:

Number of students who play stringed instruments, N(A) = 15

Number of students who play brass instruments, N(B) = 20

Number of students who play neither, N( $A \cup B$ )' = 5

To find:

The probability that a randomly selected students plays both = ?

Solution:

Total Number of students = N(A)+N(B)+N( $A \cup B$ )' =15 + 20 + 5 = 40

(As there is no student common in both the instruments we can simply add the three values to find the total number of students)

As per the venn diagram, no student plays both the instruments i.e.

$N(A\cap B) =0$

Formula for probability of an event E can be observed as:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

$P(A\cap B) = \dfrac{N(A\cap B)}{N(U)}\\\Rightarrow \dfrac{0}{40}\\\Rightarrow P(A\cap B) = 0$

So, 0 is the probability that a randomly selected student plays both a stringed and a brass instrument.

5 0

2 years ago

The square of a number is 12 less than 7 times the number. What is the number?

hjlf

Answer:

The number is either 3 or 4

Explanation:

Assume that the number we are looking for is x

The square of the number would be x²

7 times the number would be 7x

We are given that:

square of the number (x²) is 12 less than 7 times the number (7x)

Translating this into an equation, we would have:

x² = 7x - 12

Rearranging the quadratic equation:

x² - 7x + 12 = 0

Now, we factor the equation:

(x-4)(x-3) = 0

This means that:

either x-4 = 0 ..................> x = 4

or x-3 = 0 ........................> x = 3

Let's check if any of the solutions is an extrovert:

For x = 3 .............> (3)² = 7(3) - 12 .........> 9 = 21 - 12 .......> 9 = 9 .......> not extrovert

For x = 4 .............> (4)² = 7(4) - 12 .........> 16 = 28 - 12 .....> 16 = 16 ....> not extrovert

Since we have no restrictions on the number, therefore, both solutions would be accepted

Hope this helps :)

7 0

3 years ago

Each interior angle of a regular polygon has a measure of 40.how many sides does the polygon have?​

Each interior angle of a regular polygon has a measure of 40.how many sides does the polygon have?