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Amanda [17]
3 years ago
7

The dimensions of a rectangle are:

Mathematics
1 answer:
lara [203]3 years ago
8 0

The dimensions of a rectangle are -3x - 2 and 10x - 9 The simplified expression for the rectangle's perimeter is 14x – 22

<u>Solution:</u>

Given that dimensions of a rectangle are -3x – 2 and 10x – 9

Let’s say width of the rectangle = w = -3x – 2

And length of the rectangle = l = 10x – 9

<em><u>The formula for perimeter of rectangle is given as:</u></em>

Perimeter of rectangle = 2 (l + w)  

By substituting the length and width values we get,

=> Perimeter of rectangle = 2 [(10x – 9  ) + ( -3x – 2 )]

On simplification we get,

= 2 (10x – 9 – 3x – 2 )  = 2 (7x – 11)  

=> Perimeter of rectangle = 14x – 22

Hence simplified expression for the rectangle's perimeter having dimensions as -3x - 2 and 10x – 9 is 14x – 22

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Hi there,
This is the original inequality equation:
\frac{x}{x+1} \ \textless \  \frac{x}{x-1}
So, we first need to find the critical points of equality, and we can do that by switching the less than sign to an equal sign.
\frac{x}{x+1} = \frac{x}{x-1}
Now, we multiply both sides by x + 1:
x= \frac{x^{2} +x}{x-1}
Then, we multiply both sides by x - 1:
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Next, we subtract x² from both sides:
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After that, we solve for x. We do this by adding -x to both sides and dividing by 2. Doing so gives us x = 0, which is our first critical point. We need to find a few more critical points by testing x = -1 and x = 1. Here is how we do that:
<span>x = <span>−1 </span></span>(Makes left denominator equal to 0)<span>x = 1   </span>(Makes right denominator equal to 0)Check intervals in between critical points. (Test values in the intervals to see if they work.)<span>x <<span>−1    </span></span>(Doesn't work in original inequality)<span><span><span>−1 </span>< x </span><0  </span>(Works in original inequality)<span><span>0 < x </span>< 1 </span>(Doesn't work in original inequality)<span>x > 1  </span><span>(Works in original inequality)
Therefore, the answer to your query is -1 < x < 0 or x > 1. Hope this helps and have a phenomenal day!</span>
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