Problem Solving: The function LaTeX: f\left(x\right)=50x+6500\:f ( x ) = 50 x + 6500represents the amount of money in a bank account over time. The function LaTeX: g\left(x\right)=-25x+9300\:g ( x ) = − 25 x + 9300represents the amount of money in another account over time. Write a rule for the total amount of money in the two accounts over time.

25x + 15800

Step-by-step explanation:

Given

The amount of money in both banks over time represented  by the functions;

f ( x ) = 50 x + 6500 and  g( x ) = − 25 x + 9300

The total amount of money in the two accounts over time is expressed as;

h(x)= f(x) + g(x)

Substitute;

h(x) = 50 x + 6500 + (− 25 x + 9300)

h(x) = 50x - 25x +6500+9300

h(x) =25x + 15800

Hence the sum of the money in the account over time is 25x + 15800

m∠CXA=136°

Step-by-step explanation:

In this problem we know that

Triangle ABC is an isosceles triangle

so

m∠BCA=m∠BAC=44°

Segment AD  bisect angle  m∠BAC

so

m∠BAX=m∠XAC=m∠BAC/2=22°

Segment CE  bisect angle  m∠BCA

so

m∠BCX=m∠XCA=m∠BCA/2=22°

Remember that

The sum of the interior angles of triangle must be equal to 180 degrees

so

In the triangle AXC

m∠XCA+m∠XAC+m∠CXA=180°

we have

m∠XCA=22°

m∠XAC=22°

substitute

22°+22°+m∠CXA=180°

m∠CXA=180°-44°=136°