Answer:
-27
Step-by-step explanation:
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Notice the picture below
whateve the length is, is 20 more than whatever the width is
so, the width is "w" units, so the length is w+20 units then
the perimeter is all lengths added, in this case length+length+width+width
or
2l + 2w which is the same as 2(w+20)+2w
now, the smaller side, width, if times 2
and the length, times 3
they give a perimeter of 240
so, one could say that
![\bf \begin{cases} w=width\\ l=length\to w+20\\ p=perimeter\to 2l+2w\to 2(w+20)+2w\\ ---------------\\ p=240\qquad when\qquad 2w\qquad and\qquad 3l \\ \quad \\ 240=2(2w)+2(3l) \\ \quad \\ 240=2(w)+2[3(w+20)]\leftarrow \textit{solve for "w"} \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0Aw%3Dwidth%5C%5C%0Al%3Dlength%5Cto%20w%2B20%5C%5C%0Ap%3Dperimeter%5Cto%202l%2B2w%5Cto%202%28w%2B20%29%2B2w%5C%5C%0A---------------%5C%5C%0Ap%3D240%5Cqquad%20when%5Cqquad%202w%5Cqquad%20and%5Cqquad%203l%0A%5C%5C%20%5Cquad%20%5C%5C%0A240%3D2%282w%29%2B2%283l%29%0A%5C%5C%20%5Cquad%20%5C%5C%0A240%3D2%28w%29%2B2%5B3%28w%2B20%29%5D%5Cleftarrow%20%5Ctextit%7Bsolve%20for%20%22w%22%7D%0A%5Cend%7Bcases%7D)
once you found "w", what is length? well, w+20
The converse of the Pythagorean Theorem is: If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. That is, in ΔABC, if c2=a2+b2 then ∠C is a right triangle, ΔPQR being the right angle.
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Answer
Domain of the function:
In interval notation: [6, ∞)
In set notation: {x: x∈R, x≥6}
Explanation
Remember that the the domain of the square root function are all the values such is is bigger than zero. We can express the later in set notation: {x: x∈R, x≥0}, or in interval notation: [0, ∞)
This is because the square root is not defined, in the real numbers, for negative values.
So, to find the domain of our function, we just need to set the thing inside the radical grater or equal than zero and solve for x:
The domain of the function is all the numbers bigger than 6, including 6.