x ≤ 12
Solution:
Let us take the number be x.
A number : x
A number divided by three : ![$\frac{x}{3}](https://tex.z-dn.net/?f=%24%5Cfrac%7Bx%7D%7B3%7D)
A number divided by three less two : ![$\frac{x}{3}-2](https://tex.z-dn.net/?f=%24%5Cfrac%7Bx%7D%7B3%7D-2)
A number divided by three less two is at most two : ![$\frac{x}{3}-2\leq 2](https://tex.z-dn.net/?f=%24%5Cfrac%7Bx%7D%7B3%7D-2%5Cleq%202)
Now, simplify the inequality,
![$\Rightarrow\frac{x}{3}-2\leq 2](https://tex.z-dn.net/?f=%24%5CRightarrow%5Cfrac%7Bx%7D%7B3%7D-2%5Cleq%202)
Add 2 on both sides of the inequality,
![$\Rightarrow\frac{x}{3}-2+2\leq 2+2](https://tex.z-dn.net/?f=%24%5CRightarrow%5Cfrac%7Bx%7D%7B3%7D-2%2B2%5Cleq%202%2B2)
![$\Rightarrow\frac{x}{3}\leq 4](https://tex.z-dn.net/?f=%24%5CRightarrow%5Cfrac%7Bx%7D%7B3%7D%5Cleq%204)
Multiply by 3 on both sides of the equation,
![$\Rightarrow\frac{x}{3}\times3\leq 4\times3](https://tex.z-dn.net/?f=%24%5CRightarrow%5Cfrac%7Bx%7D%7B3%7D%5Ctimes3%5Cleq%204%5Ctimes3)
![$\Rightarrow x\leq 12](https://tex.z-dn.net/?f=%24%5CRightarrow%20x%5Cleq%2012)
Hence x ≤ 12.
We want to get x by itself
First we will multiply both sides by 6 to cancel out the 6 on the left
5x = 120
We then divide by 5 on both sides to get x by itself
x = 24
1 he died In 326 B.C
2 I believe the answer is 120 calories
3 the answer is -14
Answer:
![\boxed{\stackrel{\Large\frown}{PQS}\:= 222°}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%5Cstackrel%7B%5CLarge%5Cfrown%7D%7BPQS%7D%5C%3A%3D%20222%C2%B0%7D%20)
Explanation:
Since
is a diameter, arc ![\stackrel{\Large\frown}{PQR}\:= 180°.](https://tex.z-dn.net/?f=%20%5Cstackrel%7B%5CLarge%5Cfrown%7D%7BPQR%7D%5C%3A%3D%20180%C2%B0.%20)
Given that
is a subtended central angle by two diameters,
.
Using the rule of arcs,
→
![180° + \: 42° = \: \stackrel{\Large\frown}{PQS}](https://tex.z-dn.net/?f=%20180%C2%B0%20%2B%20%5C%3A%2042%C2%B0%20%3D%20%5C%3A%20%5Cstackrel%7B%5CLarge%5Cfrown%7D%7BPQS%7D%20)
![222° = \: \stackrel{\Large\frown}{PQS}](https://tex.z-dn.net/?f=%20222%C2%B0%20%3D%20%5C%3A%20%5Cstackrel%7B%5CLarge%5Cfrown%7D%7BPQS%7D%20)
![\stackrel{\Large\frown}{PQS} \: = \: 222°](https://tex.z-dn.net/?f=%20%5Cstackrel%7B%5CLarge%5Cfrown%7D%7BPQS%7D%20%5C%3A%20%3D%20%5C%3A%20222%C2%B0%20)