The base is a right triangle with a leg of 12 in. and hypotenuse of 15 in.
The height of the prism is 10 in. what is the volume

V = 540 inches ^3

Step-by-step explanation:

The area of the base is found be finding the other leg

a^2 +b^2 = c^2

12^2+b^2 = 15^2

144 +b^2 = 225

b^2 = 225-144

b^2=81

Take the square root of each side

b = 9

We can find the area of the triangle

B = 1/2 (9*12)

B =54

The Volume is given by

V = Bh

V = 54*10

V = 540 inches ^3

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:

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