For what value of x does 3 Superscript 2 x Baseline = 9 Superscript 3 x minus 4?
a. 1
b. 2
c. 3
d. 4

b. 2

Step-by-step explanation:

=  ------------------------------------(1)

To solve the equation above, we will follow the steps below;

9 = 3²

Will replace 9 = 3² in equation (1)

=

open the bracket

=  

The 3 on the left-hand side will cancel-out the 3 on the right-hand side of the equation. Thus our equation becomes;

2x = 6x - 8

subtract 6x from both-side of the equation

2x - 6x = -8

-4x = -8

Divide both-side of the equation by -4

 =

(On the left-hand side of the equation, -4 will cancel-out -4 while on the right-hand side of the equation -8 will be divided by -4)

x = 2

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.