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agasfer [191]
3 years ago
8

Geometry math question no Guessing and Please show work thank you

Mathematics
1 answer:
Dahasolnce [82]3 years ago
5 0

we can use

each interior angle formula of any regular polygons

\theta=\frac{180(n-2)}{n}

where

n is number of sides

theta is angle

we are given

\theta=157.5

now, we can plug it

157.5=\frac{180(n-2)}{n}

now, we can solve for n

1575n=1800\left(n-2\right)

n=16

so, option-C......Answer

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How do I Simplify i^54
yanalaym [24]

Answer:

i^{54}=-1

Step-by-step explanation:

First, recall the 4 basic imaginary exponents:

i^1=i \text{, }i^2=-1\text{, }i^3=-1\text{ and } i^4=1

So, we want to find:

i^{54}

This is the same as:

=i^{52}\cdot i^2

52 is 4 times 13. Thus:

=(i^4)^{13}\cdot i^2

Since we know that i to the fourth is 1:

=(1)^{13}\cdot i^2

Simplify:

=i^2

And this equals:

=-1

So:

i^{54}=-1

6 0
3 years ago
What is the smallest whole number that can be multiplied by 300 such that the product is a perfect cube?
Neko [114]

300=2×2×5×5×3

We observe that 2 and 5 are grouped in pairs and the 3 is left unpaired.

If we multiply 300 by the factor 3 then  

300×3=2×2×5×5×3×3

900=2×2×5×5×3×3 which is a perfect square.

∴ Required number is 3

root of 900  =30

5 0
3 years ago
Read 2 more answers
PLEASE WILL GIVE 50 POINTS PLEASE ANSWER ​
leva [86]

Answer:

AB = 75

BC = 60

AC = 45

m∠A = 53°

m∠B = 37°

m∠C = 90°

Step-by-step explanation:

<u>Trigonometric ratios</u>

\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}

where:

  • \theta is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle
  • H is the hypotenuse (the side opposite the right angle)

Given:

\sf \tan(A)=\dfrac{60}{45}

Therefore:

  • side opposite angle A = BC = 60
  • side adjacent angle A = AC = 45

To find the length of AB (the hypotenuse), use Pythagoras’ Theorem:

a^2+b^2=c^2

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

⇒ AC² + BC² = AB²

⇒ 45² + 60² = AB²

⇒ AB² = 5625

⇒ AB = √5625

⇒ AB = 75

To find m∠A:

\implies\sf \tan(A)=\dfrac{60}{45}

\implies\sf A=\tan^{-1}\left(\dfrac{60}{45}\right)

\implies\sf A=53^{\circ}\:(nearest\:degree)

m∠C = 90° (as it is a right angle)

The interior angles of a triangle sum to 180°

⇒ m∠A + m∠B + m∠C = 180°

⇒ 53° + m∠B + 90° = 180°

⇒ m∠B = 180° - 53° - 90°

⇒ m∠B = 37°

4 0
2 years ago
Two events, X and Y, are independent of each other. P(Y) = 5/6 and P(X and Y) = 1/3. What is P(X) written as a decimal? Round to
Ksenya-84 [330]
For independent events,
P(X &cap; Y) = P(X)* P(Y)
=>
1/3 = P(X)*(5/6)
solve for P(X) =>
P(X) = (1/3)*(6/5) = 2/5 = 0.4
5 0
3 years ago
Read 2 more answers
When (3,-2) is reflected across the x-axis the resulting image point is:
FromTheMoon [43]

Answer:

(3,2)

Step-by-step explanation:

when reflecting across the x axis the y value becomes - while the x value stays the same

4 0
3 years ago
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