Hi!
Yes, it is. When we have one inequality composed of two inequalities, we call this a double inequality.
A double inequality would look something like <em>-5 < 4x < 10.
</em>Hopefully, this helps! =)<em>
</em>
They're not equivalent.
(vertical bars) represents the absolute value of x. How it works is that it turns negative numbers positive but leaves 0 and positive numbers alone (hence it gets a number's distance from 0 on the number line).
![[x]](https://tex.z-dn.net/?f=%5Bx%5D)
(square brackets) usually represents the floor function, which returns the largest integer that is less than or equal to x. (The floor of x can also be written as 
--- it depends on what your textbook/source says).
To solve 
, you first transform it into the equivalent equation 
. Then by definition of absolute value, there are only two solutions for the first equation: x = 10 or x = -10.
[x] = 10 has infinitely many solutions. For example, the floor of 10 is 10, so ![[10] = 10](https://tex.z-dn.net/?f=%5B10%5D%20%3D%2010)
, thus a solution for the second equation is x = 10
The floor of 10.1 is 10, so ![[10.1] = 10](https://tex.z-dn.net/?f=%5B10.1%5D%20%3D%2010)
, thus another solution for the second equation is x = 10.1.
The two equations do not have the same solution set (as x = 10.1 does not solve |x| - 3 = 7 but solves [x] = 10), so they're not equivalent.
I believe the answer is 220?
= <-1 +7t, 4 -t, -5>
Multiply the direction vector by the parameter and add that to the given point.
Use cross multiplication. 42 inches is your 100%. your fraction would be 42/100
then, to find by what percent it has increased, since 47 is your new height, and you are trying to find the percentage for that, the fraction will be 47/X.
42 47
----- -----
100 X
(100 * 47) / 42 = X
100 multiplied by 47, then divided by 42, the result is X
your answer should be 111%. Subtract 100 from 111, to get the increased percent.
Answer: 11%
I did this last year, so it may be a little rusty. If im wrong, hopefully someone will correct me, if not, im pretty sure this looks rights. Your methods may also be different. i use cross mulitplication
