17mm is the answer.
To solve this:
1.) Find the radius of the entire pencil.
The radius of the graphite is .75 (half the diameter) and the thickness of the wood is 2, so 2 plus .75 gives you a total radius of 2.75.
2.) Using this radius, find the circumference of the entire pencil using the equation C = 2 • pi • r.
C = 2 • pi • r
C = 2 • 3.14 • 2.75
C = 17.27 (17 is the answer after rounding to the nearest millimeter)
Given:
A line passes through two points are (2,11) and (-8,-19).
To find:
The equation of the line.
Solution:
The line passes through two points are (2,11) and (-8,-19). So, the equation of line is
![y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-x_1%29)
![y-11=\dfrac{-19-11}{-8-2}(x-2)](https://tex.z-dn.net/?f=y-11%3D%5Cdfrac%7B-19-11%7D%7B-8-2%7D%28x-2%29)
![y-11=\dfrac{-30}{-10}(x-2)](https://tex.z-dn.net/?f=y-11%3D%5Cdfrac%7B-30%7D%7B-10%7D%28x-2%29)
![y-11=3(x-2)](https://tex.z-dn.net/?f=y-11%3D3%28x-2%29)
Using distributive property, we get
![y-11=3(x)+3(-2)](https://tex.z-dn.net/?f=y-11%3D3%28x%29%2B3%28-2%29)
![y-11=3x-6](https://tex.z-dn.net/?f=y-11%3D3x-6)
Adding 11 on both sides, we get
![y=3x-6+11](https://tex.z-dn.net/?f=y%3D3x-6%2B11)
![y=3x+5](https://tex.z-dn.net/?f=y%3D3x%2B5)
Therefore, the equation of line is
. So, the missing values are 3 and 5 respectively.
When two angles are a linear pair, the sum of their measures is 180°:
∡1 + ∡ 2 = 180°
Substituting the expressions for the angles, you get:
<span>5y − 8 + 12 + 6y = 180
Solve for y:
11y = 176
y = 176/11
Now, substitute this value in the expression for </span>∠2, which is the one we are interested in:
∡2 = 12 + 6y = 12 + 6×(<span>176/11) = 108°
When two angles are vertical angles, it means that they share the same vertex and they have the same measure, therefore:
</span>∡3 = ∡2 = 108°
Hence, the correct answer is <span>C) 108°. </span>
Answer:
See below.
Step-by-step explanation:
The set of all positive integers N is countable so we need to show that there is a 1 to 1 correspondence between the elements in N with the set of all odd positive integers. This is the case as shown below:
1 2 3 4 5 6 ...
| | | | | | ....
1 3 5 7 9 11....