Answer:
112560
Step-by-step explanation:
We know form our problem that the third day she biked 20 miles, so we have the point (3,20). We also know that <span>on the eighth day she biked 35 miles, so our second point is (8,35).
To relate our two point we are going to use the slope formula: </span>

We can infer form our points that

,

,

, and

. so lets replace those values in our slope formula:



Now that we have the slope, we can use the point-slope formula <span>determine the equation of the line that best fit the set for Maggie’s data.
Point-slope formula: </span>




We can conclude that the equation of the line that best fit the set for Maggie’s data is

.
Let
x------> the length side of the square base of the box
y-------> the height of the box
we know that
volume of the box=b²*h
b=x
h=y
volume=256 cm³
so
256=x²*y------>y=256/x²--------> equation 1
<span>The amount of material used is directly proportional to the surface area, so we will minimize the amount of material by minimizing the surface area.</span>
surface area of the cardboard=area of the base+perimeter of base*height
area of the base=x²
perimeter of the base=4*x
height=y
surface area=x²+4x*y-----> equation 2
substitute equation 1 in equation 2
SA=x²+4x*[256/x²]-----> SA=x²+1024/x
step 1
find the first derivative of SA and equate to zero
2x+1024*(-1)/x²=0------> 2x=1024/x²----> x³=512--------> x=8 cm
y=256/x²------> y=256/8²-----> y=4 cm
the answer is
the length side of the square base of the box is 8 cm
the height of the box is 4 cm
The area is 21cm squared. u would have to find the length of the bottom triangle which is 14. than multiply that by the height which is 3. finally divide that all by 2 and youll get the area
$1.66 because 50-39.59=10.40 so it would also add $8.75 so that = $1.66