Please help UwU also hope your day is going GREAT if correct i will give BRAINIEST

A stop sign is a regular octagon. The standard stop sign has a 16.2 inch radius. The area of a standard stop sign is ___________

juin [17]

The area of standard stop sign regular octagon is 742.3 squared inches, if the standard stop sign has a 16.2 inch radius.

Step-by-step explanation:

The given is,

Radius of standard stop sign is 16.2 inch radius

Step:1

The regular octagon is equal to the 16 right angled triangle,

Angle of right angle triangle = $\frac{360}{16}$ = 22.5°

Ref attachment,

From the OAB right angle triangle,

Trigonometric ratio,

sin ∅ = $\frac{Opp}{Hyp}$

Where, ∅ = 22.5°

Hyp = Radius = 16.2 inches

Ratio becomes,

sin 22.5°= $\frac{b}{16.2}$

b = (0.374607)(16.2)

b = 6.19947 inches

Trigonometric ratio,

cos ∅ = $\frac{Adj}{Hyp}$

Where, ∅ = 22.5°

Hyp = Radius = 16.2 inches

Adj = h

Ratio becomes,

cos 22.5°= $\frac{h}{16.2}$

h = (0.9238795)(16.2)

h = 14.967 inches

Step:2

From the triangle OAC,

Area, $A = \frac{1}{2} (Height )( Base)$

Where, Height = 14.967 inches

Base = b + x = 6.19947 + 6.19947

= 12.3989 inches

From the values equation becomes,

A = $\frac{1}{2} (14.967)(12.39894)$

A = 92.7875 Squared inches

Step:3

The octagon is equal to sum of 8 triangles

Area of octagon = 8 × Area of triangle

= 8 × 92.7875

= 742.3 squared inches

Result:

The area of standard stop sign regular octagon is 742.3 squared inches, if the standard stop sign has a 16.2 inch radius.

7 0

3 years ago

Keith plans to buy a car in the future.He currently has $3000 saved up to buy a car. How much money does he need to save per mon

Brut [27]

Answer:

about $709 per month

Step-by-step explanation:

Okay, so in order to solve this question, we should follow this formula:

3,000 + 24x $\geq$ 20,000

where 24 is the amount of time we have and x is the variable we are using as to show the unknown amount of money earned per month.

3,000 + 24x $\geq$ 20,000

-3,000 -3,000

24x $\geq$ 17,000

/24 /24

x $\geq$ approximately 709 dollars

so, we substitute x for 709

3,000 + 24(709) $\geq$ 20,000

3,000 + 17,016 $\geq$ 20,000

20,016 $\geq$ 20,000

which is true

Hope this helps :)

3 0

2 years ago

|z−7|−|z−9| , if z<7? Write without absolute value

Deffense [45]

Answer:

z+7-z+9

Step-by-step explanation:

5 0

3 years ago

5. Simplify the expression, (-2 - 5i) - (-4+6i) 2 - 11i -2+i -6 + 11i -5i

monitta

$\qquad\qquad\huge\underline{{\sf Answer}}♨$

Let's simplify ~

$\qquad \sf \dashrightarrow \:( - 2 - 5i) - ( - 4 + 6i)$

$\qquad \sf \dashrightarrow \: - 2 - 5i + 4 - 6i)$

$\qquad \sf \dashrightarrow \: - 2 + 4 - 5i- 6i)$

$\qquad \sf \dashrightarrow \:2 - 11i$

Therefore, A is the Correct choice !

7 0

2 years ago

Will give brainiest :)

avanturin [10]

Answer:

x= 116°

y= 127°

Step-by-step explanation:

x... The angle subtended at the centre is twice the angle subtended at the cicumfernce by the same arch

y.... Angle in a cyclic quadrilateral add up to 180°

hence 180-53=127

6 0

2 years ago

Please help UwUalso hope your day is going GREAT if correct i will give BRAINIEST