Answer:
The dimensions are height=4 inches, width=8 inches and lenght=12 inches.
Step-by-step explanation:
The volumen of a box is:
![V=(height*lenght*width)\\](https://tex.z-dn.net/?f=V%3D%28height%2Alenght%2Awidth%29%5C%5C)
we don't know the width so let's assume it as x.
![V=4*x*(x+4)\\](https://tex.z-dn.net/?f=V%3D4%2Ax%2A%28x%2B4%29%5C%5C)
that gives us a cuadratic equation:
![4x^{2} +16x=384](https://tex.z-dn.net/?f=4x%5E%7B2%7D%20%2B16x%3D384)
let's rerrangage it:
∞![4x^{2} +16x-384=0](https://tex.z-dn.net/?f=4x%5E%7B2%7D%20%2B16x-384%3D0)
we can obtain the value of x using the quadratic formula:
![\frac{-b^2\±\sqrt{b^2-4a*c} }{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%5E2%5C%C2%B1%5Csqrt%7Bb%5E2-4a%2Ac%7D%20%7D%7B2a%7D)
that formula gave us two results:
![x=8\\x=-12](https://tex.z-dn.net/?f=x%3D8%5C%5Cx%3D-12)
we have to take te possitive number, so the width is 8 inches and the length is 8+4=12 inches
height=4 inches
width=8 inches
lenght=12 inches
Volume=4*8*12=384 cubic inches.
A cup equals 8 ounces.
3 x 8 + 6 + 2 x 8 + 9
24 + 6 +16 + 9
=55 ounces. I hope this helped
Answer:
-3, -2.75, -2, 0.5, 1.55, 1.6
Step-by-step explanation:
Answer:
direct proof, proof by contradiction, proof by induction.