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aalyn [17]
3 years ago
8

The area of a rectangle is given by the trinomial y^ 2 +4y-45. If the length of the rectangle is y + 9 , what is the width of th

e rectangle?
Mathematics
1 answer:
Tema [17]3 years ago
6 0

Step-by-step explanation:

Area of rectangle =L×W

Width =Area

w idth=  \frac{area \ }{length}  \\  \\width = \frac{ {y}^{2}  + 4y - 45}{y + 9}  \\  \\  =  \frac{(y  - 5)(y + 9)}{(y + 9)}  \\  \\ width = y - 5

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What is the following difference? 11√45 - 4√5 (picture attached)
asambeis [7]
<span>The answer is 29√5. 
</span>
Since 11√45 and 4√5 do not share a common radical, you cannot subtract them. By looking at the equation, you can see that 11√45 is not fully simplified yet by the 45 within the square root.
Breaking it up into squares, you can find that 3 x 3 x 5 = 45, which can be translated into 3<span>² x 5</span>. Since the 3 is a square component in the 45, you can now extract it. Extract the 3 by dividing it from the 45 within the square root and multiplying it into the 11.
Your result is a 33√5, which shares a common radical with 4√5. You can now subtract 33√5 and 4√5, which is 29√5.

Side note: I noticed you got the answer wrong because you chose 7√40. I presume it's because you subtracted the components individually. I suggest that you look up lessons about simplifying radicals, along with adding and subtracting them. Hope this helps!
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