Which function models the area of a rectangle with side lengths of 2x - 4 units x - 1 units

The choices are missing but we can find the answer from the given information

The function which models the area of the rectangle is A(x) = 2x² - 6x + 4

Step-by-step explanation:

The formula of the area of a rectangle is A = l w, where l is its length and w is its width

∵ The length of a rectangle is (2x - 4) units

∵ The width of the rectangle is (x - 1) units

- Use the formula of area to find its area

∵ A = l w

∴ A = (2x - 4)(x - 1)

Let us multiply the two brackets

∵ (2x - 4)(x - 1) = (2x)(x) + (2x)(-1) + (-4)(x) + (-4)(-1)

∴ (2x - 4)(x - 1) = 2x² + (-2x) + (-4x) + 4

- Add the like terms

∴ (2x - 4)(x - 1) = 2x² + (-6x) + 4

∴ (2x - 4)(x - 1) = 2x² - 6x + 4

Write A as a function of x

∵ The area of the rectangle is A(x)

∵ The area of the rectangle is 2x² - 6x + 4

∴ A(x) = 2x² - 6x + 4

The function which models the area of the rectangle is A(x) = 2x² - 6x + 4

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

step-by-step explanation:

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