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3 years ago

The exterior angle of a regular polygon is 30°. What is the measure of an interior angle of the polygon.

Mathematics

1 answer:

astraxan [27]3 years ago

5 0

Answer:

A) Measure of an interior angle of polygon = 150°

B) No of sides = 12

C) Sum of all interior angles = 1800°

Step-by-step explanation:

Measure of interior angle of polygon = 180°- measure of exterior angle of polygon

= 180°-30°

= 150°

$No.\: of \: sides = \frac{360\degree}{30\degree} = 12\\\\C.\\Sum\:of\: all \:interior\: angles \\= (n-2)\times 180\degree\\= (12-2) \times 180\degree\\= 10\times 180\degree\\= 1800\degree$

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A car takes 4 hours to reach a destination traveling at a speed of 63 km/h. How long will it take to cover the same distance if

Gre4nikov [31]

Answer:

It will take 4.5hrs to cover the same distance

The constant of variation,k=252

Step by step explanation

Given that,

$speed = \frac{distance}{time}$

From the question

Time=4hr

Speed=63km

By substitution we obtain,

$63= \frac{distance}{4}$

Cross multiplying we get,

$distance=63 \times 4$

$distance=252km$

Now,

speed=56km

Distance Covered=252km

By substitution:

We obtain,

$56= \frac{252}{time}$

Cross multiply

$56\times time=252$

Divide through by 56

$time= \frac{252}{56}$

$time=4.5hrs$

From the formula,

$speed= \frac{distance}{time}$

Which means that, speed and time varies inversely.

$speed\propto \frac{1}{time}$

Let k be variation constant

This implies that

$speed = k \times \frac{1}{time}$

$k=speed \times{time}$

Taken,

Time=4hrs

speed=56km

$k=56\times4$

$k=252$

4 0

3 years ago

A home alarm system randomly assigns a five-character code for each customer. The code will not repeat a character. The characte

ahrayia [7]

Answer:

The total number of codes which can be assigned is, 55440 .

Step-by-step explanation:

According to the question, the home alarm system randomly assigns a five-character code for each customer.The code will not repeat a character and there are 11 distinct characters.

So, the total number of codes that can be randomly assigned is given by,

$^{11}{P}_{5}$