Simplify and Show your Work

Mathematics

2 answers:

Yuliya22 [10]2 years ago

7 0

Step-by-step explanation:

$\sf \: {2}^{ \frac{1}{2 } } = \sqrt{2}$

$\sf \: {2}^{ \frac{2}{3} } = \sqrt[3]{ {2}^{2} }$

$\sf \: {3}^{ \frac{3}{2} } = \sqrt{ {3}^{3} }$

$\sf \: {3}^{ \frac{1}{3} } = \sqrt[3]{3}$

Digiron [165]2 years ago

5 0

Step-by-step explanation:

$2 ^{ \frac{1}{2} } = 2 ^{1 \times \frac{1}{2} } = \sqrt{2} \\ {2}^{ \frac{2}{3} } = 2 ^{2 \times \frac{1}{3} } = \sqrt[3]{2 ^{2} } \\ 3 ^{ \frac{3}{2} } = {3}^{3 \times \frac{1}{2} } = \sqrt[]{ {3}^{3} } \\ {3}^{ \frac{1}{3} } = 3 ^{1 \times \frac{1}{3} } = \sqrt[3]{3}$

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An angle measures 40.2° more than the measure of its complementary angle. What is the measure of each angle?

vampirchik [111]

<h3>Solving for the measurements of Complementary Angles</h3><h3>Answer:</h3>

$24.9^{\circ}$ and $65.1^{\circ}$

<h3>Step-by-step explanation:</h3>

Recall that Angles that are complementary to each other add up to $90^{\circ}$ .

Let $a$ be the measure of the complementary angle.

If an angle is $40.2^{\circ}$ more than its complementary angle, the measure of that angle is $a +40.2$ . The sum of both angles are expressed $a +(a +40.2)$ but since the have to add to $90$ as they are complementary, $a +(a +40.2) = 90$ .