a cube has side length x. one side of the cube is increased by 4 inches, and another side is doubled. the…

Explanation:

Step1: Set up a system of equations

Let $y = 2x^{3}+8x^{2}$ and $y = 450$.

Step2: Use a graphing - calculator

Graph the functions $y = 2x^{3}+8x^{2}$ and $y = 450$ on a graphing calculator. Find the $x$ - value of the intersection point(s). We can also test the given values by substituting them into the equation $2x^{3}+8x^{2}=450$. For $x = 4$: $2\times4^{3}+8\times4^{2}=2\times64 + 8\times16=128+128 = 256\neq450$. For $x = 5$: $2\times5^{3}+8\times5^{2}=2\times125+8\times25=250 + 200=450$. For $x = 9$: $2\times9^{3}+8\times9^{2}=2\times729+8\times81=1458+648 = 2106\neq450$. For $x = 10$: $2\times10^{3}+8\times10^{2}=2\times1000+8\times100=2000 + 800=2800\neq450$.

Answer:

B. 5 inches