let's bear in mind that B is the midpoint and thus it cuts a segment into two equal halves.
![\bf \underset{\leftarrow \qquad \textit{\large 10x-6}\qquad \to }{\boxed{A}\stackrel{4x+2}{\rule[0.35em]{10em}{0.25pt}} B\stackrel{\underline{4x+2}}{\rule[0.35em]{10em}{0.25pt}\boxed{C}}} \\\\\\ AC=AB+BC\implies 10x-6=(4x+2)+(4x+2)\implies 10x-6=8x+4 \\\\\\ 2x-6=4\implies 2x=10\implies x=\cfrac{10}{2}\implies x= 5 \\\\[-0.35em] ~\dotfill\\\\ AC=(4x+2)+(4x+2)\implies AC=[4(5)+2]+[4(5)+2] \\\\\\ AC=22+22\implies AC=44](https://tex.z-dn.net/?f=%5Cbf%20%5Cunderset%7B%5Cleftarrow%20%5Cqquad%20%5Ctextit%7B%5Clarge%2010x-6%7D%5Cqquad%20%5Cto%20%7D%7B%5Cboxed%7BA%7D%5Cstackrel%7B4x%2B2%7D%7B%5Crule%5B0.35em%5D%7B10em%7D%7B0.25pt%7D%7D%20B%5Cstackrel%7B%5Cunderline%7B4x%2B2%7D%7D%7B%5Crule%5B0.35em%5D%7B10em%7D%7B0.25pt%7D%5Cboxed%7BC%7D%7D%7D%20%5C%5C%5C%5C%5C%5C%20AC%3DAB%2BBC%5Cimplies%2010x-6%3D%284x%2B2%29%2B%284x%2B2%29%5Cimplies%2010x-6%3D8x%2B4%20%5C%5C%5C%5C%5C%5C%202x-6%3D4%5Cimplies%202x%3D10%5Cimplies%20x%3D%5Ccfrac%7B10%7D%7B2%7D%5Cimplies%20x%3D%205%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20AC%3D%284x%2B2%29%2B%284x%2B2%29%5Cimplies%20AC%3D%5B4%285%29%2B2%5D%2B%5B4%285%29%2B2%5D%20%5C%5C%5C%5C%5C%5C%20AC%3D22%2B22%5Cimplies%20AC%3D44)
Answer:
d
Step-by-step explanation:
Answer:
Dimensions are 8 Inches by 14 inches by 20 inches
Step-by-step explanation:
The volume of the box is 2240. This means:
lbh = 2240
Where b is the width.
Width is two inches less than twice the height
b = 2h - 2
length is 4 inches less than 3 times the height
l = 3h - 4
Substituting these parameters into the lbh equation will yield the following:
h * (3h - 4) * (2h - 2) = 2240
h[6h^2-14h+8] = 2240
6h^3 -14h^2 + 8h - 2240= 0
Solving this cubic equation will yield one of the values to be 8. The other two values are complex numbers.
b = 2h - 2
l = 3h - 4
b = 2(8) - 2 = 14
l = 3(8) - 4 = 20
