Which expression is equivalent to?

Mathematics

1 answer:

guapka [62]2 years ago

4 0

Answer: $\frac{2x\sqrt[4]{y^{2}}}{3}$

Step-by-step explanation:

$\sqrt[4]{\frac{16}[81}} \sqrt[4]{\frac{x^{11}y^{8}}{x^{7}y^{6}}}\\\\=\frac{2}{3} \sqrt[4]{x^{4}y^{2}}\\\\=\frac{2x\sqrt[4]{y^{2}}}{3}$

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Help me please, Find a, b, and c.

Mama L [17]

Answer:

a = $6*\sqrt{3}$

b = 12

c = $6\sqrt{2}$

Step-by-step explanation:

Since the triangles are right triangles with 60 and 45 degree angles, their side lengths follow special triangles.

A 45-45-90 right triangle has side lengths $1-1-\sqrt{2}$ .

A 30-60-90 right triangle has side lengths $1 - \sqrt{3} -2$ .

Starting with the top triangle which has a 60 degree angle, its side length 6 corresponds to a side length of 1 in the special triangle. It is 6 times bigger so its remaining sides will be 6 times bigger too.

Side a corresponds to side length $\sqrt{3}$ . Therefore, $a = 6*\sqrt{3}$ .

Side b corresponds to side length 2, b = 2*6 = 12.

The bottom triangle has a 45 degree angle, its side length b= 12 corresponds to $\sqrt{2}$ . This means $\sqrt{2}$ was multiplied by $12 = \sqrt{2} * \sqrt{72}$ . This means that side c is $\sqrt{72}=6\sqrt{2}$ .