Answer:
72°
Step-by-step explanation:
Given that the radius(r) of the circle is 10 units and the length of arc ABC is 16π
The length of arc ABC = ![\frac{\theta}{360}*2\pi r](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctheta%7D%7B360%7D%2A2%5Cpi%20r)
Where θ is the central angle in degrees.
Since the length of arc ABC is 16π,
![16\pi=\frac{\theta}{360}*2\pi r\\16\pi=\frac{\theta}{360}*2\pi *10\\\theta=\frac{16\pi *360}{2 \pi *10} \\\theta=288^0](https://tex.z-dn.net/?f=16%5Cpi%3D%5Cfrac%7B%5Ctheta%7D%7B360%7D%2A2%5Cpi%20r%5C%5C16%5Cpi%3D%5Cfrac%7B%5Ctheta%7D%7B360%7D%2A2%5Cpi%20%2A10%5C%5C%5Ctheta%3D%5Cfrac%7B16%5Cpi%20%2A360%7D%7B2%20%5Cpi%20%2A10%7D%20%5C%5C%5Ctheta%3D288%5E0)
The angle in a circle = 360°, therefore:
Central angle for arc AB (θ) = 360 - Central angle for arc ABC = 360 - 288 = 72°
Therefore the arc measure of arc AB is 72°
Step-by-step explanation:
To find the total surface area of a prism, you need to calculate the area of two polygonal bases, i.e., the top face and bottom face. And then calculate the area of lateral faces connecting the bases. Add up the area of the two bases and the area of the lateral faces to get the total surface area of a prism.
Hope this helps!
All the love, Ya boi Fraser :)
![\large{ \tt{❃ \: EXPLANATION}} :](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Ctt%7B%E2%9D%83%20%5C%3A%20EXPLANATION%7D%7D%20%3A%20)
- You'll have to know : Mid-point theorem states that A straight line segment joining the mid-points of any two triangle is parallel to the third side and it is equal to half of the length of the third side.
- We're provided : XY = p , WZ = p - 30 & we're asked to find out the value of WZ. For that , firstly we have to find out the value of p.
![\large{ \tt{❁ \: LET'S \: START }: }](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Ctt%7B%E2%9D%81%20%5C%3A%20LET%27S%20%5C%3A%20START%20%7D%3A%20%7D)
- Set up an equation & solve for p :
![\large{ \bf{☄ \: p - 30 = \frac{1}{2} p }}](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Cbf%7B%E2%98%84%20%5C%3A%20p%20%20-%2030%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%20p%20%7D%7D)
![\large{ \tt{↦ \frac{1}{2} p = p - 30}}](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Ctt%7B%E2%86%A6%20%5Cfrac%7B1%7D%7B2%7D%20p%20%3D%20p%20-%2030%7D%7D)
![\large{ \tt{↦ \frac{1}{2} p - p = - 30}}](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Ctt%7B%E2%86%A6%20%5Cfrac%7B1%7D%7B2%7D%20p%20-%20p%20%3D%20%20-%2030%7D%7D)
![\large{ \tt{↦ \frac{p - 2p}{2} = - 30 }}](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Ctt%7B%E2%86%A6%20%5Cfrac%7Bp%20-%202p%7D%7B2%7D%20%3D%20%20-%2030%20%7D%7D)
![\large{ \tt{↦p - 2p = - 60}}](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Ctt%7B%E2%86%A6p%20-%202p%20%3D%20%20-%2060%7D%7D)
![\large{ \tt{ ↦ \: - p = - 60}}](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Ctt%7B%20%E2%86%A6%20%5C%3A%20-%20p%20%3D%20%20-%2060%7D%7D)
![\large{ \tt{↦p = 60}}](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Ctt%7B%E2%86%A6p%20%3D%2060%7D%7D)
![\large{ \tt{❇ \: REPLACING \: VALUE}} :](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Ctt%7B%E2%9D%87%20%5C%3A%20REPLACING%20%5C%3A%20VALUE%7D%7D%20%3A%20)
![\large{ \tt{↬ \: wz = p - 30 = 60 - 30 = \boxed{\boxed{ \tt{30 }} }✔}}](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Ctt%7B%E2%86%AC%20%5C%3A%20wz%20%3D%20p%20-%2030%20%3D%20%2060%20-%2030%20%3D%20%20%20%5Cboxed%7B%5Cboxed%7B%20%5Ctt%7B30%20%7D%7D%20%7D%E2%9C%94%7D%7D)
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♡ Hope I helped ! ツ
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Emily’s weekly allowance would be $7.
5(2)>3(1)+4
10 > 7. Is True because 10 is greather than 7. All needed to do is evaluate the x and y variables for each possibility. A, B, C D. And see if is a logical answer.
Any other combination gives you a false statement.