Complete question :
There is a competition at the local movie theater for free movie tickets. You must guess all four employees' ages given a few clues. The first clue is when their ages are added together the sum is 106. Kirk is 2 times the quantity of ten years less than the manager's age, Brian is 12 years younger than twice the manager's age, ,and Matt is 6 years older than ½ the manager's age. What are all four of their ages? Be sure to show set up equation work and answer
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following clue :
Let manager's age = m
Kirk's age = k
Brian's age = b
Matt's age = a
Sum of their ages = 106
k = 2(m - 10) = 2m - 20
b = 2m - 12
a = 0.5m + 6
k + b + a + m = 106
Express all their ages in terms of m
2m - 20 + 2m - 12 + 0.5m + 6 + m = 106
5.5m - 20 - 12 + 6 = 106
5.5m - 26 = 106
5.5m = 106 + 26
5.5m = 132
m = 132 / 5.5
m = 24
Manager's age = 24 years
kirk = 2(24 - 10) = 2(14) = 28 years
Brian = 2(24) - 12 = 48 - 12 = 36 years
Matt = 0.5(24) + 6 = 12 + 6 = 18 years
Given :
Rain is falling at 0.5 inches per hour and 1.5 inches have already accumulated.
To Find :
How many hours must have passed if there are 5 inches of rain .
Solution :
Let , after x hours rain accumulated is 5 inches .
We know , general equation of line :
y = mx +c
Here , m = 0.5 and c = 1 .
So , equation of rain accumulated is :
Now , putting value of x = 5 hours .
We get :
Hence , this is the required solution .
Answer:
try and subtract the orgin is 0,0 so maybe it will help
Step-by-step explanation:
The ratio of phelps to mabry is 3:2, meaning for every 5 records, phelps approved 3 and mabry 2. So:
190/5= 38
38 x 2=76 cases approved by mabry
☺☺☺☺
Hello from MrBillDoesMath!
Answer: 500
Discussion:
The idea is to represent p(x) with a squared component...
3 + 4x - 4x^2 =
3 - ( 4x^2 - 4x) =
Add and subtract 1:
(3+1) - (4x^2-4x +1) =
4 - (2x-1)^2
To maximize profit we need to minimize the term (2x-1)^2 as it is always positive (or zero) and subtracts from the number 4. The minimum of (2x -1)^2 occurs when 2x -1 = 0 or x = 1/2. Since x is the number of speakers in thousands, (1/2)x = 500 speakers.
Note: this problem can be more easily addressed in a Calculus course by taking the first derivative of p(x), setting it to zero, and solving for x (which yields x = 1/2 too)
Thank you,
MrB
