Let

where we assume |r| < 1. Multiplying on both sides by r gives

and subtracting this from
gives

As n → ∞, the exponential term will converge to 0, and the partial sums
will converge to

Now, we're given


We must have |r| < 1 since both sums converge, so


Solving for r by substitution, we have


Recalling the difference of squares identity, we have

We've already confirmed r ≠ 1, so we can simplify this to

It follows that

and so the sum we want is

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?
Answer:
The equation is;
y = 12x-41
Step-by-step explanation:
Mathematically;
slope intercept form is;
y = mx + b
where m is slope and b is intercept
Since we already have the slope , the equation is;
y = 12x + b
To get b which is the y intercept, we simply substitute the value of the points given
Thus;
19 = 5(12) + b
19 = 60+ b
b = 19-60
b = -41
So the equation is;
y = 12x - 41
7x +33 < 26 isolate the term with a variable by subtracting 33
7x < -7 divide by 7
x < -1
Answer:
y=10.1(x)
x=
Step-by-step explanation:
It is said in the problem that y would represent how much money she earns and x represents the number hours she works.
so it also said that the amount of Jessa earns is proportional to the amount of time she works .
finding y will be easy dividing 252.50 by 25 will give you 10.1
so how did we get that equation
y will represent the amount and x will represent the hours