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The length of a rectangular garden is represented by 3z-4 and the width is represented by 2x-5. Which of the following represents the total area of the garden?

A: 5x-9
B: 6x+20
C: 6x^2-23x+20
D: 6x^2-14x-9

User Naoko
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1 Answer

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The area of the rectangular garden is equal to the length times the width.

Using the variables given, we have:

Area = (3z-4)(2x-5)

= 6xz - 15z - 8x + 20

We can simplify this expression by factoring out a common factor of 2:

Area = 2(3xz - 4x - 5z + 10)

None of the answer choices match this expression, so we can simplify it further:

Area = 6xz - 8x - 15z + 20

Now we can match this expression with one of the answer choices:

A: 5x-9

6xz ≠ 5x, -15z ≠ -9. So, this is not the correct answer.

B: 6x+20

6xz ≠ 6x, -15z ≠ 20. So, this is not the correct answer.

C: 6x^2-23x+20

This is not a quadratic expression, so it is also not the correct answer.

D: 6x^2-14x-9

This matches the expression we simplified earlier, so the answer is D.

Therefore, the correct answer is D: 6x^2-14x-9.

User Thomas Wilde
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