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2 years ago

Simplify the expression shown. You must show your work to receive credit.

Mathematics

1 answer:

ZanzabumX [31]2 years ago

4 0

ANSWER

$12 \sqrt{5}$

EXPLANATION

The given expression is

$\sqrt{2} \times \sqrt{72} \times \sqrt{5}$

The middle radical contains a perfect square.

$\sqrt{2} \times \sqrt{36 \times 2} \times \sqrt{5}$

$\sqrt{2} \times \sqrt{36} \times \sqrt{2} \times \sqrt{5}$

$6\sqrt{2} \times \sqrt{2} \times \sqrt{5}$

Note that:

$\sqrt{a} \times \sqrt{a} = a$

$6\times 2 \sqrt{5} = 12 \sqrt{5}$

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3 years ago

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3 years ago

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2 years ago

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Sindrei [870]

Answer:

$x=16\dfrac{28}{37}\\ \\y=5\dfrac{1}{3}\\ \\z=7.5$

Step-by-step explanation:

The diagram shows three paralel lines which divide the large triangle into three similar triangles.

By Thales theorem,

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Then

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From the similarity of triangles,

$\dfrac{x}{20}=\dfrac{z+8}{z+8+3}\\ \\\dfrac{x}{20}=\dfrac{7.5+8}{7.5+8+3}\\ \\\dfrac{x}{20}=\dfrac{15.5}{18.5}\\ \\x=20\cdot \dfrac{155}{185}=20\cdot \dfrac{31}{37}=\dfrac{620}{37}=16\dfrac{28}{37}$

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3 years ago

You have D dollars to buy fence to enclose a rectangular plot of land (see figure at right). The fence for the top and bottom co

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The perimeter of the rectangular plot of land is given by the expression below

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$A=xy$

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Substituting into the equation for the area,

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To find the maximum possible area, solve A'(y)=0, as shown below

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Therefore, the corresponding value of x is

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