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2 years ago

11

How many sides does a regular polygon have if each exterior angle measures 72 degrees?

2 answers:

snow_lady [41]2 years ago

7 0

I think you are supposed to divide the sum of the interior angles of the polygon (360 degrees) by the exterior angles of the polygon (72 degrees). When you do this: 360 / 72 = 5 sides.

This would be a pentagon.

damaskus [11]2 years ago

7 0

Answer: 5 sides.

Step-by-step explanation:

We know that the total sum of all exterior angles of a regular polygon = 360°

If each exterior angle measures 72 degrees.

Then the number of sides of the regular polygon

$n=\frac{360^{\circ}}{\text{measure of each exterior angles}}=\frac{360^{\circ}}{72^{\circ}}=5$

Therefore, the regular polygon has 5 sides if each exterior angle measures 72 degrees.

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The line $y = 3$ intersects the graph of $y = 4x^2 + x - 1$ at the points $A$ and $B$. The distance between $A$ and $B$ can be w

raketka [301]

Answer:

61

Step-by-step explanation:

Let's find the points $A$ and $B$ .

We know that the $y$ -coordinates of both are $3$ .

So let's first solve:

$3=4x^2+x-1$

Subtract 3 on both sides:

$0=4x^2+x-1-3$

Simplify:

$0=4x^2+x-4$

I'm going to use the quadratic formula, $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ , to solve.

We must first compare to the quadratic equation, $ax^2+bx+c=0$ .

$a=4$

$b=1$

$c=-4$

$\frac{-1 \pm \sqrt{1^2-4(4)(-4)}}{2(4)}$

$\frac{-1 \pm \sqrt{1+64}}{8}$

$\frac{-1 \pm \sqrt{65}}{8}$

Since the distance between the points $A$ and $B$ is horizontal. We know this because they share the same $y-coordinate$ .This means we just need to find the positive difference between the $x$ -values we found for the points of $A$ and $B$ .

So that is, the distance between $A$ and $B$ is:

$\frac{-1+\sqrt{65}}{8}-\frac{-1-\sqrt{65}}{8}$

$\frac{-1+\sqrt{65}+1+\sqrt{65}}{8}$

$\frac{2\sqrt{65}}{8}$

$\frac{\sqrt{65}}{4}$

If we compare this to $\frac{\sqrt{m}}{n}$ , we should see that:

$m=65 \text{ and } n=4$ .

So $m-n=65-4=61$ .

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3 years ago

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madam [21]

Answer:

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Step-by-step explanation:

Using the identity

sin²x + cos²x = 1, then

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The lcm of 2 numbers is 60 and one of the numbers is 7 less than the other number

brilliants [131]

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DaniilM [7]

Answer:

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Step-by-step explanation:

The square of a number (n) is represented by n². Three times that value is represented by 3n².

The relation "a is subtracted from b" is represented as ...

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When 3n² is subtracted from 54, the appropriate representation is ...

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2 years ago