Answer:
x=4, y=4, λ=-16
Step-by-step explanation:
We have this 3x3 system of linear equations:
λ
λ
So, let's rewrite the system in its augmented matrix form
Let´s apply row reduction process to its associated augmented matrix:
Swap R1 and R3
R3-4R1
R3+R2
Now we have a simplified system:
x+y+0=0
0+4y+λ=0
0+0+2λ=-32
Solving for λ, x, and y
λ=-16
x=4
y=4
Complete question :
Suppose the average yearly salary of an individual whose final degree is a master's is $55 thousand less than twice that of an individual whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn ?$116 thousand. Find the average yearly salary of an individual with each of these final degrees.
Answer:
Average salary of a bachelor's degree holder = $57,000
Average salary of a master's degree holder = $59,000
Step-by-step explanation:
Let:
Average salary of a bachelor's degree = b
Salary of a master's holder = 2b - 55000
Combined salary of both degrees :
b + (2b - 55000) = 116000
b + 2b - 55000 = 116000
3b = 116000 + 55000
3b = 171000
Divide both sides by 3
3b/3 = 171000/3
b = 57000
Hence,
Average salary of a bachelor's degree holder = $57,000
Average salary of a master's degree holder = 2(57000) - 55000 = 59,000
Answer:
y = - 3x + 16
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = x + 8 ← is in slope- intercept form
with slope m =
Given a line with slope m then the slope of a line perpendicular to it is
= - = - = - 3, so
y = - 3x + c ← is the partial equation of the perpendicular line
To find c substitute (6, - 2) into the partial equation
- 2 = - 18 + c ⇒ c = - 2 + 18 = 16
y = - 3x + 16 ← equation of perpendicular line
Not sure question is complete, assumptions however
Answer and explanation:
Given the above, the function of the population of the ants can be modelled thus:
P(x)= 1600x
Where x is the number of weeks and assuming exponential growth 1600 is constant for each week
Assuming average number of ants in week 1,2,3 and 4 are given by 1545,1520,1620 and 1630 respectively, then we would round these numbers to the nearest tenth to get 1500, 1500, 1600 and 1600 respectively. In this case the function above wouldn't apply, as growth values vary for each week and would have to be added without using the function.
On one hand, the function above could be used as an estimate given that 1600 is the average growth of the ants per week hence a reasonable estimate of total ants in x weeks can be made using the function.