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Answer:
y=1 +4.75
Step-by-step explanation:
QUESTION 1
The given inequality is
![|m|-2>0](https://tex.z-dn.net/?f=%7Cm%7C-2%3E0)
We group like terms to get,
![|m|>2](https://tex.z-dn.net/?f=%7Cm%7C%3E2)
This implies that,
or
.
We simplify the inequality to get,
or
.
We can write this interval notation to get,
.
QUESTION 2
.
We group like terms to get,
.
![|x-4|\:>\:8](https://tex.z-dn.net/?f=%7Cx-4%7C%5C%3A%3E%5C%3A8)
We split the absolute value sign to get,
or ![x-4\:>\:8](https://tex.z-dn.net/?f=x-4%5C%3A%3E%5C%3A8)
This implies that,
or ![x-4\:>\:8](https://tex.z-dn.net/?f=x-4%5C%3A%3E%5C%3A8)
or ![x\:>\:8+4](https://tex.z-dn.net/?f=x%5C%3A%3E%5C%3A8%2B4)
or ![x\:>\:12](https://tex.z-dn.net/?f=x%5C%3A%3E%5C%3A12)
We can write this interval notation to get,
.
QUESTION 3
The given inequality is
![|6+9x|\leq 24](https://tex.z-dn.net/?f=%7C6%2B9x%7C%5Cleq%2024)
We split the absolute value sign to obtain,
or ![(6+9x)\leq 24](https://tex.z-dn.net/?f=%286%2B9x%29%5Cleq%2024)
This simplifies to
and ![6+9x\leq 24](https://tex.z-dn.net/?f=6%2B9x%5Cleq%2024)
and ![9x\leq 24-6](https://tex.z-dn.net/?f=9x%5Cleq%2024-6)
and ![9x\leq 18](https://tex.z-dn.net/?f=9x%5Cleq%2018)
and ![x\leq 2](https://tex.z-dn.net/?f=x%5Cleq%202)
![-\frac{10}{3}\leq x\leq2](https://tex.z-dn.net/?f=-%5Cfrac%7B10%7D%7B3%7D%5Cleq%20x%5Cleq2)
We write this in interval form to get,
![[-\frac{10}{3},2]](https://tex.z-dn.net/?f=%5B-%5Cfrac%7B10%7D%7B3%7D%2C2%5D)
QUESTION 4
The given inequality is
![|1-5a|>29](https://tex.z-dn.net/?f=%7C1-5a%7C%3E29)
We split the absolute value sign to get,
or ![1-5a>29](https://tex.z-dn.net/?f=1-5a%3E29)
This simplifies to,
or ![1-5a\:>\:29](https://tex.z-dn.net/?f=1-5a%5C%3A%3E%5C%3A29)
This implies that,
or ![-5a\:>\:29-1](https://tex.z-dn.net/?f=-5a%5C%3A%3E%5C%3A29-1)
or ![-5a\:>\:28](https://tex.z-dn.net/?f=-5a%5C%3A%3E%5C%3A28)
or ![a\:](https://tex.z-dn.net/?f=a%5C%3A%3C%5C%3A-%5Cfrac%7B28%7D%7B5%7D)
We write this in interval notation to get,
![(-\infty,-\frac{28}{5})\cup (6,+\infty)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C-%5Cfrac%7B28%7D%7B5%7D%29%5Ccup%20%286%2C%2B%5Cinfty%29)
Answer:
66
Step-by-step explanation:
Lets say the number is x
So the equation follows : 2x-2=x+64
2x=x+66
x=66
Answer:
60 degrees
Step-by-step explanation:
The bottom and top horizontal lines are parallel. This means x and the bottom right angle in the triangle are the same. Because of the lines going through the triangle's sides we know the triangle's lengths are the same, making it an equilateral triangle. In an equilateral all angles are the same size: 60 degrees.