Answer:
The inequality which represents the model for this situation is
.
Step-by-step explanation:
Let Mr. Garcia has
number of desks initially.
He has been asked to give
desks to Mrs. Johnson.
Also, he needs to keep at least
desks for his students.
So, after giving
desks to Mrs. Johnson from the total number of desks he has, he must have at least
desks for his students.
Therefore, the inequality is:
.
Hence, the inequality which represents the model for this situation is
.
Answer:
$239.40
Step-by-step explanation:
$2,992.50 × 0.08
$239.40
I arrived at this estimate based on my work shown above.
Answer:


Step-by-step explanation:
Because there are two smaller lines drawn in lines TA and AK, it means that the length of TA is the same as AK.
Hence, 
Subtract 4x from both sides:


Divide both sides by 2:


To find TK,

Answer:
- Base Length of 84cm
- Height of 42 cm.
Step-by-step explanation:
Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.
Step 1:
Let the side length of the base =x
Let the height of the box =h
Since the box has a square base
Volume, 

Surface Area of the box = Base Area + Area of 4 sides

Step 2: Find the derivative of A(x)

Step 3: Set A'(x)=0 and solve for x
![A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84](https://tex.z-dn.net/?f=A%27%28x%29%3D%5Cdfrac%7B2x%5E3-1185408%7D%7Bx%5E2%7D%3D0%5C%5C2x%5E3-1185408%3D0%5C%5C2x%5E3%3D1185408%5C%5C%24Divide%20both%20sides%20by%202%5C%5Cx%5E3%3D592704%5C%5C%24Take%20the%20cube%20root%20of%20both%20sides%5C%5Cx%3D%5Csqrt%5B3%5D%7B592704%7D%5C%5Cx%3D84)
Step 4: Verify that x=84 is a minimum value
We use the second derivative test

Since the second derivative is positive at x=84, then it is a minimum point.
Recall:

Therefore, the dimensions that minimizes the box surface area are:
- Base Length of 84cm
- Height of 42 cm.
Straight line depreciation, the value of the car is given by the following equation, where V is the value of the car, and O is the original value of the car, and x is the number of years since buying the car. V=O-2x This equation follows the form of a straight line, that is: y=mx+b