Answer:
Option b (4,1)
Step-by-step explanation:
The region given by the system of inequalities is shown in the graph. We must look within this region for the point that minimizes the objective function 
The minimum points are found in the lower vertices of the region.
These vertices are found by equating the equations of the lines::

-------------------


---------------------

The lower vertices are:
(4, 1) (2, 4)
Now we substitute both points in the objective function to see which of them we get the lowest value of 

Then the value that minimizes f(x, y) is (4,1).
Option b

Use the product rule first:


Use the chain rule to compute the derivative of
. Let
and take
, so that by the chain rule




So we have

You can rewrite this a bit by factoring
, just to make it look neater:

Answer:
width = 7 and length = 9
Step-by-step explanation:
Let's assume width = w, and length = 2 + w
So area of a rectangle = width * length
63 ft² = w (2 + w)
63 = 2w + w²
w² + 2w - 63 = 0
Use the quadratic formula to solve this
here, a = 1, b = 2 and c = -63
w = 7 or -9
The dimensions of a rectangle cannot be negative. So we take the dimension, w = 7.
Width = 7 and Length = 7+2 = 9
Answer:A
Step-by-step explanation:
You use the equation:
m= (y2-y1) ÷ ( x2-x1)
m= (12-9) ÷ (2-1)
m= 3÷1
m= 3
If the triangle is translated left 9, this shows that all the x values will decrease by nine, becoming, -15, -5, and -8.
If the triangle is translated up 12, this shows that all the y values will increase by twelve, becoming, 13, 12, and 15.
Thus, the new co-ordinates are <u>X(-15,13), Y(-5,12), Z(-8,15).</u>