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olga_2 [115]
3 years ago
11

The area of a rectangular garden is given by the quadratic function: A (x) = -6x^2 + 105x– 294

Mathematics
1 answer:
BaLLatris [955]3 years ago
7 0

Answer:

Bree is correct

Step-by-step explanation:

Given

Area of rectangle;

A (x) = -6x^2 + 105x - 294

Joe's Result:

Length = -6x + 21\\Width = x - 4

Bree' Result

Length = -3x + 42\\Width = 2x - 7

Required

Determine whose result is correct and why.

To determine the correct result, we simply find the roots of the quadratic function

A (x) = -6x^2 + 105x - 294

<em>Such that A(x) = 0</em>

<em />

-6x^2 + 105x - 294 = 0

Start Factorization;

<em>Expand</em>

A (x) = -6x^2 + 105x - 294

<em>Group the above expression in 2s</em>

A(x) = (-6x^2 + 84x) + (21x - 294)

<em>Factorize</em>

A(x) =2x(-3x + 42) -7 (-3x + 42)

A(x) = (2x - 7)(-3x + 42)

Recall that; Area of a rectangle is calculated by;

A(x) = Length * Width

By comparison;

Length = 2x - 7\\Width = -3x + 42

At this point, we can conclude that Bree's computation is correct;

Reason

The product of (-3x + 42) and (2x – 7) will result in the given area of the rectangle

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