Answer:


Step-by-step explanation:
We need to simplify

We collect LCM to get;

Therefore:

Also we need to simplify:

We collect LCM to get;

Therefore

To solve this we are going to use the compound interest formula

where:

is the investment

is the interest rate in decimal form

is the number of times the interest is compounded per year

is the time in years

is the amount after

years
First, lets convert the interest rate to decimal dividing it by 100%:

Next, lets find

. Since we know that the interest is compounded every 4 months (quarterly), it will be compounded

times in a year, so

.
We also know that

and

, so lets replace all the quantities into our compound interest formula:


Notice that the the number of years

is in the exponent, so we have to use logarithms to bring it down. But first lets divide both sides by 16000 to isolate the exponential expression:





Now that we know

, the last thing to do is convert 0.43 years to months:

We can conclude that Jimmy's investment will take
6 years and 5 months to reach $25,000.
Rule: (a/b)/(c/d)=(a/b)*(d/c)
(5/14)/(3/4)
(5/14)(4/3)
(5*4)/(14*3)
20/42
10/21
Answer:28.25
Step-by-step explanation:
Equation is: y = - 2x^2 + 113x - 497
In order to find out maximum of X, first step is to take derrivative of the function y = - 2x^2 + 113x -497.
When we do that, derrivative function is:
dy/dx = - 2 * 2 x + 113 * 1 = - 4x +113
At the maximum point derrvative function equals to zero.
So, - 4x + 113 = 0
-4x = -113
x = 28.25
So, the selling price should be 28.25
Step-by-step explanation:
I guess method 1 means to deal with whole factors.
x + 5 = (x - 2)(x + 5)
for (x + 5) <> 0 we can divide both sides by this factor :
1 = x - 2
x = 3
for the second solution we deal with
x + 5 = 0
x = -5
so, for x = -5 and x = 3 both functions deliver the same output, and these are the intersection points.
method 2 : we multiply the expression out and solve it then
x + 5 = (x - 2)(x + 5)
x + 5 = x² + 5x - 2x - 10 = x² + 3x - 10
0 = x² + 2x - 15
the general solution to such a square equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 2
c = -15
x = (-2 ± sqrt(2² - 4×1×-15))/(2×1) =
= (-2 ± sqrt(4 + 60))/2 = (-2 ± sqrt(64))/2 = (-2 ± 8)/2 =
= -1 ± 4
x1 = -1 + 4 = 3
x2 = -1 - 4 = -5
and you get the 2 solutions again. as expected, they are the same as with method 1, of course.