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eimsori [14]
3 years ago
11

Nick has designed a diamond shaped kite as shown below. The measures of some sides of the kite are marked in the figure. Find th

e value of x.

Mathematics
1 answer:
Zepler [3.9K]3 years ago
7 0

Answer:

<h2>x = 3.499 in</h2>

Step-by-step explanation:

       In a kite, the diagonals are perpendicular. Hence \Delta DOC is a right angled triangle.

       DC=7\text{ }in,\text{ }OC=5\text{ }in

From Pythagoras theorem, since \Delta DOC is a right angled triangle, DO^{2}+OC^{2}=DC^{2}.

      Area of \Delta DOC = \frac{1}{2}\times base\times height

=\frac{1}{2}\times DO\times OC=\frac{1}{2}\times OP\times DC\\(2\sqrt{6})\times(5)=(7)\times(OP)\\OP=3.499\text{ }in

From diagram OP=x

∴ x=3.499\text{ }in

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4. Is the following definition of perpendicular reversible? If yes, write it as a true biconditional.
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City planners anticipate an 8.2% population growth per year, including new residents and births. The population, in millions of
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<h2>Hello!</h2>

The answer is:

The correct option is the third option,

L(p(x))=2.425(1.082)^{x}

<h2>Why?</h2>

From the statement we know the function that models the population growth over the years (p(x)) but we have been told that there is an estimated loss that can be modeled by the function L(p), so in order to find which function represents the final function, we need to composite the function, which is the same that evaluate p(x) into the function L(p).

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L(p(x))=p(0.97)\\\\L(p(x))=2.5(1.082)^{x}*(0.97)=0.97*2.5(1.082)^{x} \\\\L(p(x))=0.97*2.5(1.082)^{x}=2.425(1.082)^{x}\\\\L(p(x))=2.425(1.082)^{x}

Hence, the correct option is:

The third option,  

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Have a nice day!

6 0
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Answer:

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3 years ago
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