Mathematics, 01.08.2019 07:00 jazminpagan15

If the area of a rectangle is 24a^2b and the length is 8ab^2, what would be the width of the rectangle, given that width is found by dividing area by length? simplify the answer.

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Answer from: leo4687

Set up the formula for area of a rectangle. The formula is {\displaystyle A=(l)(w)}, where {\displaystyle A}equals the area of the rectangle, {\displaystyle l} equals the length of the rectangle, and {\displaystyle w} equals the width of the rectangle.[1]This method will only work if you are given the area and length of the rectangle.You might also see the formula written as {\displaystyle A=(h)(w)}, where {\displaystyle h} equals the height of the rectangle and is used instead of length.[2] These two terms refer to the same measurement.

Plug the values for area and length into the formula. Make sure you substitute for the correct variables.For example, if you are trying to find the width of a rectangle that has an area of 24 square centimeters, and a length of 8 centimeters, your formula will look like this:

Solve for {\displaystyle w}. To do this, you need to divide each side of the equation by the length.For example, in the equation {\displaystyle 24=8w}, you would divide each side by 8.
{\displaystyle 24=8w}
Write your final answer. Don’t forget to include the unit of measurement.For example, for a rectangle with an area of {\displaystyle 24cm^{2}} and a length of {\displaystyle 8cm}, the width would be {\displaystyle 3cm}.

Answer from: Quest

step-by-step explanation:

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

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