Aright triangle has a leg with a length of 21 units and a hypotenuse with a length of 42 units. eunice states that because the hypotenuse is twice the length of the given leg, the right triangle is a 30-60-90 triangle. select all statements that are true. 1. the measure of the remaining leg is 21 units 2. the angle opposite the side with length 21 units measures 30° 3. the perimeter of the triangle is 84 units 4. eunice is not correct. it is a 45-45-90 triangle. 5. the measure of the remaining leg is 21 units. you! whoever answers correctly gets 15 points!

1. The measure of the remaining leg is 21\sqrt{3} units

2. The angle opposite the side with length 21 units measures 30°

Step-by-step explanation:

The Pythagorean theorem tells you the remaining side length is ...

  √(42² -21²) = 21√3 . . . . . matches the first statement, discounts statements 3 and 5

The angle opposite the 21-unit leg can be found from ...

  angle = arcsin(21/42) = 30° . . . . . matches the second statement, discounts statement 4.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

step-by-step explanation: