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2 years ago

Find the distance between two points (-8, 4) and (9, 8)

Mathematics

1 answer:

RoseWind [281]2 years ago

8 0

Answer:

Length between two points:

${ \bf{length = \sqrt{ {9}^{2} - {( - 8)}^{2} + {8}^{2} - {4}^{2} } }} \\ = \sqrt{65}$

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2865 students participated in a competitive exam. There were 60 rooms in the

sladkih [1.3K]

47 students per room, 45 weren’t in a room

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3 years ago

Find the slope of the line.

lorasvet [3.4K]

<h3>Given ↓</h3>

Two points that a line goes through

The line's slope

<h3>Calculations ↓</h3>

When we have two points that a line passes through and asked to determine the slope of the line, the slope formula is going to come in handy.

This is the formula :

$\boxed{\\\begin{minipage}{3cm}slope~formula~: \\ $\displaystyle\frac{y2-y1}{x2-x1}$ \\ \end{minipage}}$

y2 and y1 are y-coordinates, and x2 and x1 are x coordinates

Plug in the values :

$\boxed{\\\begin{minipage}{3cm}$\displaystyle\frac{0-(-7)}{7-0} $\end{minipage}}$

$\boxed{\\\begin{minipage}{3cm}$\displaystyle\frac{0+7}{7} \end{minipage}}$

Which simplifies to $^7/_7$ , or 1

<h3>Slope ↓</h3>

1 (Option D.)

hope helpful ~

5 0

2 years ago

If a rectangular prism is sliced vertically by a plane, what is the shape of the resulting two dimensional figure?

Romashka [77]

I think 2 triangular prisms.

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3 years ago

Determine whether the following series converge or diverge

Mars2501 [29]

An alternating series $\sum\limits_n(-1)^na_n$ converges if $|(-1)^na_n|=|a_n|$ is monotonic and $a_n\to0$ as $n\to\infty$ . Here $a_n=\dfrac1{\ln(n+1)}$ .

Let $f(x)=\ln(x+1)$ . Then $f'(x)=\dfrac1{x+1}$ , which is positive for all $x>-1$ , so $\ln(x+1)$ is monotonically increasing for $x>-1$ . This would mean $\dfrac1{\ln(x+1)}$ must be a monotonically decreasing sequence over the same interval, and so must $a_n$ .

Because $a_n$ is monotonically increasing, but will still always be positive, it follows that $a_n\to0$ as $n\to\infty$ .

So, $\sum\limits_n(-1)^na_n$ converges.

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3 years ago

Students collected $441 for a donation camp. Each student have as many dollars as there were students. How many students are the

Alexandra [31]

Answer:

There are 21 students.

Step-by-step explanation:

If there are 21 students, and each of them had $21 then this would equal a total of $441 because 21 multiplied by 21 equals 441.

Hope this helps,

Trey

6 0

2 years ago