The width and the length of a rectangle are consecutive even integers. if the width is decreased by 3 inches, then the area of the resulting rectangle is 24 square inches. what is the area of the original rectangle? a. 12 in²
b. 48 in²
c. 96 in²

Step-by-step explanation:

The width is shorter than the length.  If they are both even integers and they are consecutive as well, then if the width is x, the length is x + 2.  That means that if x is any even integer, say 4, adding 2 to it gives you the next even integer which is 4 + 2 = 6.  Apply that pattern to any even (or odd!) numbers and you will find that it is the general rule.  So we have:

w: x

l: x + 2

It says that "if the width is decreased by 3" then the area is 24.  If the width is x, then decreasing that by 3 is x - 3.  The area formula for a rectangle is length times width, so we have:

FOIL that out to get

Subtract the 24 from both sides and then factor:

so

x = -5, 6

Since length (and time!) are the only 2 things in math that will NEVER EVER BE NEGATIVE we can disregard the -5.  That means that the width is 6 inches.  Plugging that back into the original rectangle, we get that the width is 6 and the length is 6 + 2 or 8.  6 times 8 = 48.  That's the area of the original rectangle.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

i dont know

step-by-step explanation: