1. a = 1/2x - 3
2. a = 2x + 7
Answer:
x ≤ 3764.72
Step-by-step expl
anation:
The Montanez family cannot use more than 7250.50 gallons, this means that they can use less than or equal to 7250.50 gallons, this tells you which sign to use. The variable x can be used to describe how much water they have left to use and then you add 3,485.78 gallons to x.
x + 3485.78 ≤ 7250.50 This inequality means that the amount of water the family has yet to use added to 3485.78 gallons cannot exceed 7250.50 gallons.
Next, you simplify the inequality using the property of inequalities.
x ≤ 7250.50 - 3485.78
x ≤ 3764.72
![\bf \begin{cases} x=3\implies &x-3=0\\ x=1+3i\implies &x-1-3i=0\\ x=1-3i\implies &x-1+3i=0 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ (x-3)(x-1-3i)(x-1+3i)=0 \\\\\\ (x-3)\underset{\textit{difference of squares}}{([x-1]-3i)([x-1]+3i)}=0\implies (x-3)([x-1]^2-[3i]^2)=0 \\\\\\ (x-3)([x^2-2x+1]-[3^2i^2])=0\implies (x-3)([x^2-2x+1]-[9(-1)])=0](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%20x%3D3%5Cimplies%20%26x-3%3D0%5C%5C%20x%3D1%2B3i%5Cimplies%20%26x-1-3i%3D0%5C%5C%20x%3D1-3i%5Cimplies%20%26x-1%2B3i%3D0%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%28x-3%29%28x-1-3i%29%28x-1%2B3i%29%3D0%20%5C%5C%5C%5C%5C%5C%20%28x-3%29%5Cunderset%7B%5Ctextit%7Bdifference%20of%20squares%7D%7D%7B%28%5Bx-1%5D-3i%29%28%5Bx-1%5D%2B3i%29%7D%3D0%5Cimplies%20%28x-3%29%28%5Bx-1%5D%5E2-%5B3i%5D%5E2%29%3D0%20%5C%5C%5C%5C%5C%5C%20%28x-3%29%28%5Bx%5E2-2x%2B1%5D-%5B3%5E2i%5E2%5D%29%3D0%5Cimplies%20%28x-3%29%28%5Bx%5E2-2x%2B1%5D-%5B9%28-1%29%5D%29%3D0)
[ correction added, Thanks to @stef68 ]
![\bf (x-3)([x^2-2x+1]+9)=0\implies (x-3)(x^2-2x+10)=0 \\\\\\ x^3-2x^2+10x-3x^2+6x-30=0\implies x^3-5x^2+16x-30=f(x) \\\\\\ \stackrel{\textit{applying a translation with a -2f(x)}}{-2(x^3-5x^2+16x-30)=f(x)}\implies -2x^3+10x^2-32x+60=f(x)](https://tex.z-dn.net/?f=%5Cbf%20%28x-3%29%28%5Bx%5E2-2x%2B1%5D%2B9%29%3D0%5Cimplies%20%28x-3%29%28x%5E2-2x%2B10%29%3D0%20%5C%5C%5C%5C%5C%5C%20x%5E3-2x%5E2%2B10x-3x%5E2%2B6x-30%3D0%5Cimplies%20x%5E3-5x%5E2%2B16x-30%3Df%28x%29%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bapplying%20a%20translation%20with%20a%20-2f%28x%29%7D%7D%7B-2%28x%5E3-5x%5E2%2B16x-30%29%3Df%28x%29%7D%5Cimplies%20-2x%5E3%2B10x%5E2-32x%2B60%3Df%28x%29)
Answer:
4 and 5
Step-by-step explanation:
![60x^3 + 145x^2 + 70x=5x(12x^2+29x+14)\\\\=5x(12x^2+21x+8x+14)=5x[3x(4x+7)+2(4x+7)]\\\\=5x(4x+7)(3x+2)\\\\Answer:\\length=5x\\width=4x+7\\height=3x+2](https://tex.z-dn.net/?f=60x%5E3%20%2B%20145x%5E2%20%2B%2070x%3D5x%2812x%5E2%2B29x%2B14%29%5C%5C%5C%5C%3D5x%2812x%5E2%2B21x%2B8x%2B14%29%3D5x%5B3x%284x%2B7%29%2B2%284x%2B7%29%5D%5C%5C%5C%5C%3D5x%284x%2B7%29%283x%2B2%29%5C%5C%5C%5CAnswer%3A%5C%5Clength%3D5x%5C%5Cwidth%3D4x%2B7%5C%5Cheight%3D3x%2B2)
