We'll have a rectangle. In this attached photo, you can easily observe it. Its sides are going to be 6 and 8 and it will be parallel to the sides. The area of this rectangle is A=6*8=48 cm²
well, is noteworthy that an x-intercept is when y = 0 or namely is a solution or root of the quadratic, so we know then that the x-intercepts or solutions are at (-1,0) and (3,0), that simply means that
![\bf (\stackrel{x}{-1},\stackrel{y}{0})\qquad (\stackrel{x}{3},\stackrel{y}{0})\qquad \begin{cases} x = -1\\ x+1=0\\ \cline{1-1} x=3\\ x-3=0 \end{cases}~\hfill \implies ~\hfill \stackrel{\textit{equation of the parabola}}{y = a(x+1)(x-3)} \\\\\\ \textit{we also know that } \begin{cases} x = 1\\ y = -8 \end{cases}\implies \underline{-8}=a(\underline{1}+1)(\underline{1}-3)](https://tex.z-dn.net/?f=%5Cbf%20%28%5Cstackrel%7Bx%7D%7B-1%7D%2C%5Cstackrel%7By%7D%7B0%7D%29%5Cqquad%20%28%5Cstackrel%7Bx%7D%7B3%7D%2C%5Cstackrel%7By%7D%7B0%7D%29%5Cqquad%20%5Cbegin%7Bcases%7D%20x%20%3D%20-1%5C%5C%20x%2B1%3D0%5C%5C%20%5Ccline%7B1-1%7D%20x%3D3%5C%5C%20x-3%3D0%20%5Cend%7Bcases%7D~%5Chfill%20%5Cimplies%20~%5Chfill%20%5Cstackrel%7B%5Ctextit%7Bequation%20of%20the%20parabola%7D%7D%7By%20%3D%20a%28x%2B1%29%28x-3%29%7D%20%5C%5C%5C%5C%5C%5C%20%5Ctextit%7Bwe%20also%20know%20that%20%7D%20%5Cbegin%7Bcases%7D%20x%20%3D%201%5C%5C%20y%20%3D%20-8%20%5Cend%7Bcases%7D%5Cimplies%20%5Cunderline%7B-8%7D%3Da%28%5Cunderline%7B1%7D%2B1%29%28%5Cunderline%7B1%7D-3%29)
![\bf -8=a(2)(-2)\implies -8=-4a\implies \cfrac{-8}{-4}=a\implies \boxed{2=a} \\\\[-0.35em] ~\dotfill\\\\ y=2(x+1)(x-3)\implies y=2(\stackrel{\mathbb{FOIL}}{x^2-2x-3})\implies y=2x^2-4x-6](https://tex.z-dn.net/?f=%5Cbf%20-8%3Da%282%29%28-2%29%5Cimplies%20-8%3D-4a%5Cimplies%20%5Ccfrac%7B-8%7D%7B-4%7D%3Da%5Cimplies%20%5Cboxed%7B2%3Da%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20y%3D2%28x%2B1%29%28x-3%29%5Cimplies%20y%3D2%28%5Cstackrel%7B%5Cmathbb%7BFOIL%7D%7D%7Bx%5E2-2x-3%7D%29%5Cimplies%20y%3D2x%5E2-4x-6)
Answer:
-8a
Step-by-step explanation:
Answer:
6, 7, and 8
Step-by-step explanation:
2x/3 + 7 <u>></u> 11
Subtract 7 from both sides
2x/3 <u>></u> 4
Multiply both sides by 3
2x <u>></u> 12
Divide both sides by 2
x <u>></u> 6
6, 7, and 8 are the ones that work