The Texas State Legislation is comprised of state senators and state representatives. There is a greater number of representatives than
senators. The sum of the number of representatives and the number of
senators is 181. The difference of the number of representatives and
number of senators 119.
a. Write a system of equations to find the number of state representatives,
r, and senators, s.
b. How many senators and how many representatives make up the Texas
State Legislature?

I. r = 150 state representatives.

II. s = 31 senators.

Step-by-step explanation:

Let the number of state representatives, be r

Let the number of senators be s.

a. The system of equations are given by translating the word problem into an algebraic expression, we have;

r + s = 181 equation 1

r - s = 119 equation 2

b. To find the values;

First of all, let's find the number of senators by using the substitution method.

From equation 1;

r = 181 - s equation 3

Substituting eqn 3 into eqn 2;

181 - s - s = 119

181 - 2s = 119

181 - 119 = 2s

2s = 62

s = 62/2

s = 31 senators.

To find the value of r;

From equation 3;

r = 181 - s

r = 181 - 31

r = 150 state representatives.

where are the choices?

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.