Question

Complete the table by typing the correct answer in each box. Expression for the area isA = 3x^2 + 17x + 10

Answer 1

Lenght Area

8 338

6.5 247.25

4.5 147.25

7 276

Step-by-step 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:

`\begin{gathered} x=\frac{-17\pm\sqrt[]{(17)^2-4(3)(-328)}}{2(3)} \\ x=\frac{-17\pm65_{}}{6} \\ \text{Then} \\ x=(-17+65)/(6)=8 \\ x=(-17-65)/(6)=-(41)/(3) \end{gathered}`

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,

`\begin{gathered} x=\frac{-17\pm_{}\sqrt[]{(17)^2-4(3)(-137.25)}}{2(3)} \\ x=(-17\pm44)/(6) \\ \text{Then} \\ x=(-17+44)/(6)=4.5 \end{gathered}`

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