Ef= 50 - 14x + x^2 eg= 14 - 2x given that ef and eg are tangent lines, apply the tangent segments theorem to set up an equation and solve for x.

x = 3.28

Step-by-step explanation:

Tangent-Segment Theorem : Tangent segments drawn to the same circle from the same point are equal.

Now, EF = 50 - 14·x - x²

and EG = 14 - 2·x

Since, EF and EG are two tangent segments drawn to the same circle, So they both will be equal in length

⇒ 50 - 14·x - x² = 14 - 2·x

⇒ x² + 12·x - 50 = 0

On solving the above equation :

We get, x = 3.28 and x = -15.28

Since, Length of tangent cannot be negative, So we take x = 3.28

Hence, x = 3.28

6

Step-by-step explanation:

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: