Abcdefghijklmnopqrstuvwxy and z now which letter(s) did I repeat ?
5(x + y) - 3(x - y)
5x + 5y - 3x + 3y
5x - 3x + 5y + 3y
2x + 8y
5(x + y) - 3(x - y) = 2x + 8y
Answer:
a)
We know that:
There is a fixed cost of $7
for each mile, you need to pay $0.65
Then if you take the taxi for "m" miles, the total cost is:
c(m) = $0.65*m + $7
Now we know that Gavin also gives a $3 tip, so we need to add this to the cost:
c(m) = ($0.65*m + $7) + $3 = $0.65*m + $10
c(m) = $0.65*m + $10
Now we know that he paid a total of $62.65
Then:
c(m) = $62.65 = $0.65*m + $10
This is the equation we need to solve in order to find m, the number of miles between Gavin's house and the airport.
b)
$62.65 = $0.65*m + $10
We only need to isolate m, we will get:
$62.65 - $10 = $0.65*m
$52.65/$0.65 = m = 81
This means that there are 81 miles between the airport and Gavin's house.
Answer:
a) 
b) 
Step-by-step explanation:
In both parts of the problem y varies directly as x. So, they have the following form:
Where k is the constant of proportionality.
Therefore, you must find k and then write the equations.
a) Solve for k:
Then, the equation is:
b) Solve for k:
Then, the equation is:
A growth rate equation has a general form of:
f(x) = P (1 + r)^x
Where,
P = present value
r = rate of growth
x = number of years
If we write the given equation on that form, it would be:
f(x) = 4 (1 + 3)^x
Therefore we can see that the population’s growth rate is
300% per year. To make this formula to an equivalent of three times a year (3x),
we have to find the new r.
f(x)_3 = 4 (1 + r)^3x
To calculate this, we must take note that the expression or
value of (1 + r)^x must be constant. Therefore equate this with 4^x.
(1 + r)^3x = (4)^x
Taking the logs of both sides:
3x log (1 + r) = x log 4
Cancelling x:
3 log (1 + r) = log 4
3 (1 + r) = 4
1 + r = 4/3
r = 0.33
Therefore the new growth rate is 0.33 or 33%. (ANSWER)
And, the new correct function is:
f(x)_3 = 4 (1 + 0.33)^3x
or
f(x)_3 = 4 (1.33)^3x (ANSWER)
