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3 years ago

One leg of an isosceles right triangle measures 5 inches. Rounded to the nearest tenth, what is the approximate length of

Mathematics

1 answer:

Firlakuza [10]3 years ago

6 0

The length of the hypotenuse = 7.1 inch

Step-by-step explanation:

In an isosceles right angle triangle if one leg is 5 inch, another side along the right angle is 5 in

hypotenuse = $\sqrt{side^{2} +base^{2} }$ ( by Pythagoras theorem)

= $\sqrt{5^{2}+5^{2} }$

= $\sqrt{50}$

= 7.07106781

= 7.1 inch (approx)

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3 years ago

Which of the following rational functions is graphed below?

vampirchik [111]

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The correct option is D.

i.e.

$f\left(x\right)=\frac{1}{x\left(x+4\right)}$ is the correct option.

The correct graph is shown in attached figure.

Step-by-step explanation:

Considering the function

$f\left(x\right)=\frac{1}{x\left(x+4\right)}$

$\mathrm{Domain\:of\:}\:\frac{1}{x\left(x+4\right)}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x$

$\mathrm{Range\:of\:}\frac{1}{x\left(x+4\right)}:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\le \:-\frac{1}{4}\quad \mathrm{or}\quad \:f\left(x\right)>0\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-\frac{1}{4}]\cup \left(0,\:\infty \:\right)\end{bmatrix}$

$\mathrm{Axis\:interception\:points\:of}\:\frac{1}{x\left(x+4\right)}:\quad \mathrm{None}$

$\mathrm{Extreme\:Points\:of}\:\frac{1}{x\left(x+4\right)}:\quad \mathrm{Maximum}\left(-2,\:-\frac{1}{4}\right)$

So, the correct graph is shown in attached figure.

Therefore, the correct option is D.

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$f\left(x\right)=\frac{1}{x\left(x+4\right)}$ is the correct option.

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