Answer:
Lenght Area
8 338
6.5 247.25
4.5 147.25
7 276
Explanation:
We know that the area is calculated as
A = 3x² + 17x + 10
Where x is the length of the tomato patch.
Then, to complete the first blank in the table, we need to replace the area by 338 and solve for x, so
338 = 3x² + 17x + 10
0 = 3x² + 17x + 10 - 338
0 = 3x² + 17x - 328
So, using the quadratic equation, we get:
[tex]\begin{gathered} x=\frac{-17\pm\sqrt[]{(17)^2-4(3)(-328)}}{2(3)} \\ x=\frac{-17\pm65_{}}{6} \\ \text{Then} \\ x=\frac{-17+65}{6}=8 \\ x=\frac{-17-65}{6}=-\frac{41}{3} \end{gathered}[/tex]
Since x = -41/3 doesn't have sense here, the value in the table should be 8.
To fill the second blank, we need to replace x by 6.5 and calculate the value of A, so
A = 3x² + 17x + 10
A = 3(6.5)² + 17(6.5) + 10
A = 3(42.25) + 110.5 + 10
A = 247.25
Then, the third blank is solved as the first one, so
147.25 = 3x² + 17x + 10
0 = 3x² + 17x + 10 - 147.25
0 = 3x² + 17x - 137.25
Therefore,
[tex]\begin{gathered} x=\frac{-17\pm_{}\sqrt[]{(17)^2-4(3)(-137.25)}}{2(3)} \\ x=\frac{-17\pm44}{6} \\ \text{Then} \\ x=\frac{-17+44}{6}=4.5 \end{gathered}[/tex]
Finally, the value of the last blank is
A = 3x² + 17x + 10
A = 3(7)² + 17(7) + 10
A = 3(49) + 119 + 10
A = 276
Therefore, the answers are:
Lenght Area
8 338
6.5 247.25
4.5 147.25
7 276
