We begin with an unknown initial investment value, which we will call P. This value is what we are solving for.
The amount in the account on January 1st, 2015 before Carol withdraws $1000 is found by the compound interest formula A = P(1+r/n)^(nt) ; where A is the amount in the account after interest, r is the interest rate, t is time (in years), and n is the number of compounding periods per year.
In this problem, the interest compounds annually, so we can simplify the formula to A = P(1+r)^t. We can plug in our values for r and t. r is equal to .025, because that is equal to 2.5%. t is equal to one, so we can just write A = P(1.025).
We then must withdraw 1000 from this amount, and allow it to gain interest for one more year.
The principle in the account at the beginning of 2015 after the withdrawal is equal to 1.025P - 1000. We can plug this into the compound interest formula again, as well as the amount in the account at the beginning of 2016.
23,517.6 = (1.025P - 1000)(1 + .025)^1
23,517.6 = (1.025P - 1000)(1.025)
Divide both sides by 1.025
22,944 = (1.025P - 1000)
Add 1000 to both sides
23,944 = 1.025P
Divide both by 1.025 for the answer
$22,384.39 = P. We now have the value of the initial investment.
Answer:
Step-by-step explanation:
The given points are (-1,0) and (3,0) to find an equation of parabola. Notice that they say or the given points are x-intercepts, which means they make it easier for us to find an equation of parabola using these x-intercepts.
Quick Note:
- x-intercepts are simply the roots or solutions of quadratic equation, so if our root is x = -2 then we can write as (-2,0) and write back to x+2=0.
So what we are going to do is to write the roots’ equation back as 
Our points or roots are given, therefore:
If x = -1 then x+1=0
If x = 3 then x-3=0
Then multiply x+1 with x-3 because if (x-1)(x+3)=0 then x-1=0 or x+3=0:
Convert 0 to y since we want to find a function:
Expand the expressions in and simplify to standard form:
Therefore, the equation is
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Summary
If we are given the points 
and 
with wideness of the graph or a-value = 1 then the parabola equation is:
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Others
If you have any doubts about my answer, explanation or this question, do not hesitate to let me know in the comment!
Answer:
GF = FH
Step-by-step explanation:
GEF & FIH
EF = FI (equal)
GEF = FIH (alternate angle)
EG = HI (parallel sides equal)
GEF & FIH are congruent, under the case of (SAS)
therefore, GF = FH (corresponding angle)
