Why do we use variables, and what is the significance of using them in expressions and equations?

1. Tristan Sandino is selling his motorcycle. His friend, Rudy, is offering to pay cash in the amount of $8,800. Another friend,

mina [271]

1. The amortization formula can tell you the present value if the string of payments is made at the end of the month.
A = P(i/n)/(1 -(1 +i/n)^(-nt))
where A is the payment (200), P is the present value, n is the number of compoundings per year (12), and t is the number of years (4).
200 = P(.034/12)/(1 -(1 +.034/12)^-48)
200 = P*0.0223115558
P = 200/0.0223115558 ≈ 8,963.96

This matches the selection ...
a) $8963.96

[Please note that an actual sale would probably require the first payment be made immediately, hence the present value would actually be $8,989.36.]

2. A financial calculator (HP-12c) computes the IRR at 3.889% (per quarter). Hence the annual rate of return is about
4*3.889% ≈ 15.55%

This matches selection ...
a.) 15.55%

8 0

4 years ago

Find an equation of the line passing through the pair of points. Write the equation in the form Ax +By = C.

Alexxandr [17]

9514 1404 393

Answer:

5x -y = -37

Step-by-step explanation:

One way to find the coefficients A and B is to use the differences of the x- and y-coordinates:

A = Δy = y2 -y1 = 2 -(-3) = 5

B = -Δx = -(x2 -x1) = -(-7 -(-8)) = -1

Then the constant C can be found using either point.

5x -y = 5(-7) -2 = -37

The equation of the line is ...

5x -y = -37

_____

<em>Additional comment</em>

This approach comes from the fact that the slope of a line is the same everywhere.

$\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{\Delta y}{\Delta x}\\\\\Delta x(y-y_1)=\Delta y(x-x_1)\qquad\text{cross multiply}\\\\\Delta y(x-x_1)-\Delta x(y-y_1)=0\qquad\text{subtract y term}\\\\\Delta y(x) -\Delta x(y) = \Delta y(x_1)-\Delta x(y_1)\qquad\text{Ax+By=C form}$

The "standard form" requires that A be positive, so we chose point 1 and point 2 to make sure that was the case.

5 0

3 years ago

Kelsey has $100 in an account. The intrest rate is %11 compounded annually. To the nearest cent, how much will she have in 2 yea

postnew [5]

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$100\\ r=rate\to 11\%\to \frac{11}{100}\dotfill &0.11\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A=100\left(1+\frac{0.11}{1}\right)^{1\cdot 2}\implies A=100(1.11)^2\implies A=123.21$