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Pavlova-9 [17]
3 years ago
13

In the figure, side AB is given by the expression 5x+5x+3, and side BC is 3x+92x−4. The simplified expression for the area of re

ctangle ABCD is ________ and the restriction on x is_____
Mathematics
2 answers:
miss Akunina [59]3 years ago
5 0
Area = side AB * side BC  =  (5x + 5x + 3)(3x + 92x - 4)

= (10x + 3)(95x - 4) =  950x^2 - 40x + 285x - 12

=  950x^2 + 245x - 12  Answer

This cannot be negative  so restriction on x  is  950x^2 + 245x > 12
That is x > 0.0421
almond37 [142]3 years ago
5 0

Answer:

A=950x^2+245-12\\\\\{x\in R: (\frac{4}{95}

Step-by-step explanation:

The area of a rectangle is given by:

A=w*h

Where:\\\\w=width\\h=height

Let:

h=\overline{\rm AB}=5x+5x+3=10x+3\\\\and\\\\w=\overline{\rm BC}=3x+92x-4=95x-4

So, the area is given by:

A=(10x+3)*(95x-4)=950x^2-40x+285x-12=950x^2+245x-12

It wouldn't make sense if the result leads us to an area equal to 0 or to a negative area, therefore:

A=950x^2+245x-12>0

Solving for x using the quadratic formula:

x=\frac{-b\pm \sqrt{b^2-4ac} }{2a} =\frac{-245\pm \sqrt{245^2-4(950)(-12)} }{2(950)} =\frac{-245\pm \sqrt{60025+45600} }{1900}\\\\x=\frac{-245\pm \sqrt{105625} }{1900}=\frac{-245\pm 325}{1900}\\\\Hence\\\\x>\frac{4}{95} \\\\and\\\\x

Therefore, the area is given by:

A=950x^2+245-12\\\\\{x\in R: (\frac{4}{95}

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Zelie planned for a square pool to have a side length of 28 ft but found that it needs to be 14 ft long to fit in her backyard.
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Answer:

Step-by-step explanation:

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Zelie planned for a square pool to have a side length of 28 ft but found that it needs to be 14 ft long to fit in her backyard. She found the change of scale below.

Which is Zelie’s error?

Zelie should have divided both numbers by 14.

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If he found that it need to be 14ft longer then the actual measure = 14th

given equation is;

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According to the option, Zelei should have divided both numbers by 14.

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