Answer:
The maximum height of the prism is 
Step-by-step explanation:
Let
x------> the height of the prism
we know that
the area of the rectangular base of the prism is equal to


so
-------> inequality A
------> equation B
-----> equation C
Substitute equation B in equation C

------> equation D
Substitute equation B and equation D in the inequality A
-------> using a graphing tool to solve the inequality
The solution for x is the interval---------->![[0,12]](https://tex.z-dn.net/?f=%5B0%2C12%5D)
see the attached figure
but remember that
The width of the base must be
meters less than the height of the prism
so
the solution for x is the interval ------> ![(9,12]](https://tex.z-dn.net/?f=%289%2C12%5D)
The maximum height of the prism is 
The scale factor is 1/2 or a half
Answer:
-40 < x < 20
Step-by-step explanation:
step 1: -12 < 1/2(x+16) < 18 --> Distribute
step 2: -12 < 1/2x + 8 < 18 --> subtract 8
step 3: -20 < 1/2x < 10 --> Multiply by 2
answer : -40 < x < 20
Answer:
21 + 14x - 56 - 42x + 168
= 133 - 28x
Step-by-step explanation: