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Nonamiya [84]
3 years ago
9

AJ is the bisector of ∠HJI. Determine the value of x.

Mathematics
1 answer:
atroni [7]3 years ago
8 0

Answer:

C

Step-by-step explanation:

If x was equal to 12, 22.5 or 10 the side would be too large compared to 15. This is only correct if the drawing is to scale, however.

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How do you solve his with working
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Check the picture below.

a)

so the perimeter will include "part" of the circumference of the green circle, and it will include "part" of the red encircled section, plus the endpoints where the pathway ends.

the endpoints, are just 2 meters long, as you can see 2+15+2 is 19, or the radius of the "outer radius".

let's find the circumference of the green circle, and then subtract the arc of that sector that's not part of the perimeter.

and then let's get the circumference of the red encircled section, and also subtract the arc of that sector, and then we add the endpoints and that's the perimeter.

\bf \begin{array}{cllll}&#10;\textit{circumference of a circle}\\\\ &#10;2\pi r&#10;\end{array}\qquad \qquad \qquad \qquad &#10;\begin{array}{cllll}&#10;\textit{arc's length}\\\\&#10;s=\cfrac{\theta r\pi }{180}&#10;\end{array}\\\\&#10;-------------------------------

\bf \stackrel{\stackrel{green~circle}{perimeter}}{2\pi(7.5) }~-~\stackrel{\stackrel{green~circle}{arc}}{\cfrac{(135)(7.5)\pi }{180}}~+&#10;\stackrel{\stackrel{red~section}{perimeter}}{2\pi(9.5) }~-~\stackrel{\stackrel{red~section}{arc}}{\cfrac{(135)(9.5)\pi }{180}}+\stackrel{endpoints}{2+2}&#10;\\\\\\&#10;15\pi -\cfrac{45\pi }{8}+19\pi -\cfrac{57\pi }{8}+4\implies \cfrac{85\pi }{4}+4\quad \approx \quad 70.7588438888



b)

we do about the same here as well, we get the full area of the red encircled area, and then subtract the sector with 135°, and then subtract the sector of the green circle that is 360° - 135°, or 225°, the part that wasn't included in the previous subtraction.


\bf \begin{array}{cllll}&#10;\textit{area of a circle}\\\\ &#10;\pi r^2&#10;\end{array}\qquad \qquad \qquad \qquad &#10;\begin{array}{cllll}&#10;\textit{area of a sector of a circle}\\\\&#10;s=\cfrac{\theta r^2\pi }{360}&#10;\end{array}\\\\&#10;-------------------------------

\bf \stackrel{\stackrel{red~section}{area}}{\pi(9.5^2) }~-~\stackrel{\stackrel{red~section}{sector}}{\cfrac{(135)(9.5^2)\pi }{360}}-\stackrel{\stackrel{green~circle}{sector}}{\cfrac{(225)(7.5^2)\pi }{360}}&#10;\\\\\\&#10;90.25\pi -\cfrac{1083\pi }{32}-\cfrac{1125\pi }{32}\implies \cfrac{85\pi }{4}\quad \approx\quad 66.75884

7 0
3 years ago
A tomato plant grew an average of 0.06 m per day. How many days did it take for the plant to grow a total of 0.96 m.            
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If you divide 96 by 6 then you get 16. So it's 16 days!
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3 years ago
The amount Diego charges to detail an SUV is proportional to the time it takes him to detail the vehicle. Diego charges $37.50 t
prisoha [69]

Answer:

d = 15h

Step-by-step explanation:

Given

Charges\ \alpha\ Time

Represent charges with d and time with h

So:

d = \$37.50 when t = 2.50\ hours

Required

Determine the formula

Charges\ \alpha\ Time

In other words,

d\ \alpha\ h

Convert to an equation

d = k * h

Where

k = constant of proportion

Substitute values for Charges and Time

37.50 = k * 2.5

Solve for k

k = 37.50/2.50

k = 15

Substitute 15 for k in d = k * h

d = 15 * h

d = 15h

<em>The above formula models the situation</em>

8 0
3 years ago
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