Mathematics, 26.11.2019 20:31 cristinavalencia03

Two rectangles have the same width. the length of one is 1 foot longer than the width.
the length of the other is 2 feet longer than the width. the larger rectangle has 4 more
square feet than the smaller. what is the width of the rectangles?

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Answer from: alex7881

The width of the rectangles is 4.

Step-by-step explanation:

Given that two rectangles have same width. So, let be the two rectangles $R_{1}$ and $R_{2}$ and width of rectangle is ‘x’. So, according to question, we have

Length of one rectangle , $R_{1}$ = x + 1

Length of other rectangle, $R_{2}$ = x + 2

But we also know that,

$\text { Area of rectangle } = \text { Length } \times \text { width }$

So, then the area for one rectangle,

$\text { Area of rectangle } R_{1} = x \times(x+1)$

Similarly,

$\text { Area of rectangle } R_{2} = x \times(x+2)$

So, according to question,

$\text {Area of rectangle } R_{2} = 4 \times \text { Area of rectangle } R_{1}$

$x \times(x+2) = 4+x \times(x+1)$

Now, by solving the above equation, we get

$x^{2}+2 x = 4+x^{2}+x$

x = 4

So, from the above equation, we found that width of the rectangle is 4.

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.

Answer from: Quest

answer: c. is your answer

step-by-step explanation: get me a black leather coat

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Two rectangles have the same width. the length of one is 1 foot longer than the width.
the len...