Respuesta :

gmany

Answer:

[tex]\huge\boxed{A=6x^2-11x+3;\ \text{for}\ x>1.5}[/tex]

Step-by-step explanation:

The formula of an area of a rectangle:

[tex]A=a\cdot b\\\\a,\ b-\text{sides of a rectangle}[/tex]

We have:

[tex]a=2x-3\\b=3x-1[/tex]

The domain:

[tex]2x-3>0\ \wedge\ 3x-1>0\\\\2x-3+3>0+3\ \wedge\ 3x-1+1>0+1\\\\2x>3\ \wedge\ 3x>1\\\\\dfrac{2x}{2}>\dfrac{3}{2}\ \wedge\ \dfrac{3x}{3}>\dfrac{1}{3}\\\\x>1.5\ \wedge\ x>\dfrac{1}{3}\Rightarrow\boxed{x>1.5}[/tex]

Substitute:

[tex]A=(2x-3)(3x-1)[/tex]

use FOIL: (a + b)(c + d) = ac + ad + bc + bd

[tex]A= (2x)(3x)+(2x)(-1)+(-3)(3x)+(-3)(-1)\\\\A=6x^2-2x-9x+3[/tex]

combine like terms

[tex]A= 6x^2+(-2x-9x)+3\\\\A=6x^2-11x+3[/tex]

hbj

Answer:

6x² - 11x + 3

Step-by-step explanation:

To find the area of a rectangle, we multiply the length by the width.

A = l • w

length: 2x-3

width: 3x-1

A = (2x-3) • (3x-1)

To multiply these two binomials, we must FOIL (first | outer | inner | last) them.

F: 2x • 3x = 6x²

O: 2x • -1 = -2x

I: -3 • 3x = -9x

L: -3 • -1 = 3

Combine the terms.

6x² - 2x - 9x + 3

Combine like terms.

6x² - 11x + 3

This is your area.

Hope this helps!

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