Answer:
just type "correct answer" in those 3 boxes..
Step-by-step explanation:
Answer:
In a mathequation when needed
Step-by-step explanation:
X = cups of tea per hour
y = cups of coffee per hour
David makes 30 cups of tea per hour = 30x
David works for D hours this week.
Therefore number of weekly cups of tea = number of hours * cups of tea per hour
This is 30x * D = 30Dx
For Andrew, it is similar
30Ay
Because Andrew made an additional 10 cups, then it is 30Ay + 10
(cups of coffee this week)
What do you mean by ”What is the longest possible length of one strip?”
Hello.
Let's solve the absolute value inequality.
In order to do that, let's imagine that |3x-4| is positive.
Since the absolute value of |3x-4| is 3x-4, we write 3x-4 and solve:
![\mathrm{3x-4\geq 8}](https://tex.z-dn.net/?f=%5Cmathrm%7B3x-4%5Cgeq%208%7D)
Now, move -4 to the right, using the opposite operation:
![\mathrm{3x\geq 8+4}](https://tex.z-dn.net/?f=%5Cmathrm%7B3x%5Cgeq%208%2B4%7D)
Add:
![\mathrm{3x\geq 12}](https://tex.z-dn.net/?f=%5Cmathrm%7B3x%5Cgeq%2012%7D)
Divide both sides by 3:
![\mathrm{x\geq 4}](https://tex.z-dn.net/?f=%5Cmathrm%7Bx%5Cgeq%204%7D)
However, this is only 1 solution.
Let's imagine that |3x-4| is a negative number.
So, the inequality looks like so:
![\mathrm{-3x+4\geq 8}](https://tex.z-dn.net/?f=%5Cmathrm%7B-3x%2B4%5Cgeq%208%7D)
Move 4 to the right:
![\mathrm{-3x\geq 8-4}](https://tex.z-dn.net/?f=%5Cmathrm%7B-3x%5Cgeq%208-4%7D)
![\mathrm{-3x\geq 4}](https://tex.z-dn.net/?f=%5Cmathrm%7B-3x%5Cgeq%204%7D)
Divide both sides by -3:
![\mathrm{x\leq \displaystyle-\frac{4}{3} }](https://tex.z-dn.net/?f=%5Cmathrm%7Bx%5Cleq%20%5Cdisplaystyle-%5Cfrac%7B4%7D%7B3%7D%20%7D)
Therefore, the solutions are
![\mathrm{x\geq 4}\\\mathrm{x\leq \displaystyle-\frac{4}{3} }](https://tex.z-dn.net/?f=%5Cmathrm%7Bx%5Cgeq%204%7D%5C%5C%5Cmathrm%7Bx%5Cleq%20%5Cdisplaystyle-%5Cfrac%7B4%7D%7B3%7D%20%7D)
Note:
If we divide both sides of an inequality by a negative number, we flip the inequality sign.
I hope this helps you.
Have a nice day.
![\boxed{imperturbability}](https://tex.z-dn.net/?f=%5Cboxed%7Bimperturbability%7D)