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3 years ago

6

An account is opened with an initial deposit of $5,500 and earns 2.5% interest compounded annually. What will the account be wor

th in 10 years? Round your answer to the nearest cent. Do NOT round until you have calculated the final answer.

1 answer:

vaieri [72.5K]3 years ago

7 0

Answer:3243

Step-by-step explanation:

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A circle passes through points A(7,4), B(10,6), C(12,3). Show that AC must be the diameter of the circle.

Artist 52 [7]

so we have three points, A, B and C, if indeed AC is the diameter of the circle, then half the distance of AC is its radius, and the midpoint of AC is the center of the circle, morever, since B is also on the circle, the distance from B to the center must be the same radius distance.

in short, half the distance of AC must be equals to the distance of B to the midpoint of AC, if indeed AC is the diameter.

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{12}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{12+7}{2}~~,~~\cfrac{3+4}{2} \right)\implies \left( \cfrac{19}{2}~~,~~\cfrac{7}{2} \right)=M\impliedby \textit{center of the circle}$

now, let's check the distance from say A to the center, and check the distance of B to the center, if it's indeed the center, they'll be the same and thus AC its diameter.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AM=\sqrt{\left( \frac{19}{2}-7 \right)^2+\left( \frac{7}{2}-4 \right)^2} \\\\\\ AM=\sqrt{\left( \frac{5}{2}\right)^2+\left( -\frac{1}{2} \right)^2}\implies \boxed{AM\approx 2.549509756796392} \\\\[-0.35em] ~\dotfill$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{10}~,~\stackrel{y_1}{6})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}}) \\\\\\ BM=\sqrt{\left( \frac{19}{2}-10 \right)^2+\left( \frac{7}{2}-6 \right)^2} \\\\\\ BM=\sqrt{\left( -\frac{1}{2}\right)^2+\left( -\frac{5}{2} \right)^2}\implies \boxed{BM\approx 2.549509756796392}$

6 0

3 years ago

A sequence of numbers is formed by the iterative process Xn+1 = (Xn )2 – Xn

xeze [42]

Step-by-step explanation:

X1 = 1

X2 = (X1) 2 - X1

X2 = 2 - 1

X2 = 1. implies that the second term of the sequence is 1.

3 0

3 years ago

Which figure represents the image of trapezoid LMNP

xenn [34]

Answer is C hope this helps

4 0

3 years ago

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everyth

crimeas [40]

The inequality described can be written as:

y < 3x + 2.

<h3>How to get the inequality?</h3>

First, we know that we have a dashed line, and the region to the left of that line is shaded, then we will have:

y < line.

The linear equation is of the form:

y = a*x + b

Where a is the slope and b is the y-intercept.

Remember that if a line passes through the points (x₁, y₁) and (x₂, y₂), then the slope is:

$a = \frac{y_2 - y_1}{x_2 - x_1}$

Here we know that the line passes through (-3, -7) and (0, 2), so the slope is:

$a = \frac{2 - (-7)}{0 - (-3)} = 9/3 = 3$

And because the line passes through (0, 2), the y-intercept is 2, then the inequality is:

y < 3x + 2.

If you want to learn more about inequalities:

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8 0

2 years ago

Solve the Fahrenheit equation for Celsius

horrorfan [7]

The first step you should do is subtract 32 from both sides so your answer will turn out like this -

F = (9/5) C + 32
-
F - 32 = (9/5)

Then we will multiply both sides by 5.

5 ( F - 32 ) = 9 C

Divide both sides by 9 to isolate C.

(5/9) ( F - 32 ) = C

So the answer is :

C = (5/9) ( F - 32 )

Hope this helps :)

7 0

3 years ago

Read 2 more answers