Answer:
point - slope form
y - 1 = 3 (x-0)
Step-by-step explanation:
<u><em>step(i):-</em></u>
Given points are (0,1) and (2,7)
The slope of the line
m =3
<u><em>Step(ii):-</em></u>
point -slope form
y - y₁ = m(x-x₁)
Equation of the straight line passing through the point (0,1) and having slope 'm' = 3
y - 1 = 3 (x-0)
y -1 = 3x
3x - y +1=0
Equation of the straight line passing through the point (0,1) and having slope 'm' = 3 is 3x -y +1=0
The answer is D. 9(y + 3) and 27 + 9y because 9(y + 3) when expanded is 9y + 27. I hope this helps!
Answer: 2. Linear pair postulate
4. 60 + mACB=180
5. mACB=120
6. definition of obtuse angle
Answer:
The volume of the balloon is 18.84 inches³
Step-by-step explanation:
* Lets talk about the sphere
- Its a solid
- It has surface area = 4πr²
- It has no lateral area
- It has no faces
- It has no vertices
- It has no edges
- Its volume = (4/3) π r³
* In our problem the balloon shaped a sphere
- Its radius = 4.5 inches
- The value of π = 3.14
* Lets calculate its volume
∵ The radius = 4.5 inches
∵ π = 3.14
∵ The volume = (4/3) π r³
* Substitute the values of r and π in the formula
∴ The volume = (4/3) × 3.14 × 4.5 = 18.84 inches³
* The volume of the balloon is 18.84 inches³
let's first off notice that, on the 2), the sector is really half of the whole circle, and on 3) the sector is one quarter of the whole circle.
now, on 2) AB is the diameter of 4 units, therefore it has a radius of 2, or half that.
![\bf \boxed{2} \\\\\\ \stackrel{\textit{area of a circle}}{A=\pi r^2}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=2 \end{cases}\implies A=\pi 2^2\implies A=4\pi \\\\\\ \stackrel{\textit{half of that}}{A=2\pi}\implies A=\stackrel{\textit{rounded up}}{A=6.3~ft^2} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cboxed%7B2%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Barea%20of%20a%20circle%7D%7D%7BA%3D%5Cpi%20r%5E2%7D~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D2%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Cpi%202%5E2%5Cimplies%20A%3D4%5Cpi%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bhalf%20of%20that%7D%7D%7BA%3D2%5Cpi%7D%5Cimplies%20A%3D%5Cstackrel%7B%5Ctextit%7Brounded%20up%7D%7D%7BA%3D6.3~ft%5E2%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\bf \boxed{3} \\\\\\ \stackrel{\textit{area of a circle}}{A=\pi r^2}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=20 \end{cases}\implies A=\pi 20^2\implies A=400\pi \\\\\\ \stackrel{\textit{one quarter of that}}{A=100\pi }\implies \stackrel{\textit{rounded up}}{A=314.2~in^2}](https://tex.z-dn.net/?f=%5Cbf%20%5Cboxed%7B3%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Barea%20of%20a%20circle%7D%7D%7BA%3D%5Cpi%20r%5E2%7D~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D20%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Cpi%2020%5E2%5Cimplies%20A%3D400%5Cpi%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bone%20quarter%20of%20that%7D%7D%7BA%3D100%5Cpi%20%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Brounded%20up%7D%7D%7BA%3D314.2~in%5E2%7D)
