Let
x = first integer
y = second integer
z = third integer
First equation: x + y + z = 194
Second equation: x + y = z + 80
Third equation: z = x - 45
Let's find the values of x, y and z.
Substitute 3rd eq to 1st eq:
x + y + x - 45 = 194
2x + y = 45 + 194
y = -2x + 239
Plug in both we have solved for y and the 3rd eq to the 2nd eq to find x
x + (-2x + 239) = (x - 45) + 80
x - 2x - x = -45 + 80 - 239
-2x = -204
x = -204/-2
x = 102
Solving for y,
y = -2(102) + 239
y = 35
Solving for z,
z = 102 - 45
z = 57
The roots of an equation are simply the x-intercepts of the equation.
See below for the proof that 
has at least two real roots
The equation is given as:
There are several ways to show that an equation has real roots, one of these ways is by using graphs.
See attachment for the graph of
Next, we count the x-intercepts of the graph (i.e. the points where the equation crosses the x-axis)
From the attached graph, we can see that crosses the x-axis at approximately <em>-2000 and 2000 </em>between the domain -2500 and 2500
This means that has at least two real roots
Read more about roots of an equation at:
brainly.com/question/12912962
Answer:
Average employee [Mean] = 43.6
Step-by-step explanation:
Given:
Interval Number of employee
25-35 20
35-45 7
45-55 8
55-65 15
Total 50
Find:
Average employee [Mean]
Computation:
Interval X[u+l]/2 Number of employee fx
25-35 30 20 600
35-45 40 7 280
45-55 50 8 400
55-65 60 15 900
Total 50 2,180
Average employee [Mean] = Sum of fx / Sum of x
Average employee [Mean] = 2,180 / 50
Average employee [Mean] = 43.6
64,000/2=32,000
32,000/12= $2,666.67 per paycheck
