Answer:
$177.38
Step-by-step explanation:
The first thing you want to do is figure out your variables. In A = Pe^(rt), "A" is the end amount (AKA however much money you have after however much time), "P" is the principle amount (AKA however much you have to start with), "r" is the rate, and "t" is the time. Take all the information they gave you in the problem and try to place it in one of these categories.
Tyler opened a savings account 6 years ago. Ding-ding, we've got a time. The account earns 2% interest, compounded annually. There's our rate. If the current balance is $200.00, how much did he deposit initially?
So, sort these out. t = 6 years. r = 2%, or r = .02. The current balance is $200.00, so is this your end amount or the money you had to start with? Well, since the question is asking you to find how much Tyler deposited initially, you know for sure $200.00 is your end amount ("A"). Let's find out what he started with.
200 = Pe^(.02)(6)
Note that e is not a variable, but a value. You won't ever replace it; it's part of your formula. What you want to solve for here is "P" to get your starting amount. Divide both sides by e^(.02)(6), and you'll see:
P = 200/[e^(.02)(6)] = 177.3840873
Since we're talking money, round that to the nearest cent like your question asked, and you get $177.38. You can check your answer by plugging this value back into A = Pe^(rt) with $177.38 being the principle amount. You get $200 back, so the answer is correct.
Answer:
AB = 14 and BC = 17
Step-by-step explanation:
Congruence is a property that shows an equal relation between sides or angles of a given figure or two figures.
From the question, the given conditions are;
BC = AD, AD = 17, DC = 14, and m< 1 = m<2 .
i. Considering the property of congruence of sides,
BC = 17 (∵ BC = AD and AD has been given to equal 17)
i.e BC = AD = 17
ii. Considering the property of congruent angles and sides,
AB = 14 (∵ m<1 = m<2 and DC is 14)
Therefore, AB = 14 and BC = 17.
Answer:
eqaul to
Step-by-step explanation:
The function given is r(t) = 1 + 4t, where r is the radius in centimeters and t is time in seconds.
So, use the formula of the area: area = π (radius)^2
A(t) = π [r(t) ] ^2
A(t) = π [1 + 4t ]^2 = π [1 + 8t + 16t^2 ]
Answer: π [ 16t^2 + 8t + 1]
Not quite sure what you mean by brackets, but you can get the solution to this equation in a few steps:
<span>(-2x - 1)</span>² <span>= 0 ... square root both sides to eliminate the squared binomial
</span>√(-2x - 1)² = √0 ... simplify; the square is canceled out and the root of 0 brings you back to 0
-2x - 1 = 0 ... solve like a two-step equation
-2x = 1
x = -1/2 is your x-value.