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3 years ago

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A quadrilateral has congruent side lengths. 2 opposite angles have measures of 100 degrees. The other 2 opposite angles have mea

sures of 70 degrees and (5 x) degrees. What is the value of x? 14 15 16 17

2 answers:

Burka [1]3 years ago

6 0

Answer:

x = 14.

Step-by-step explanation:

The other 2 opposite angle are both equal to 70 degrees.

So 5x = 70

x = 70/5

= 14 degrees.

romanna [79]3 years ago

5 0

Answer:

Option A.

Step-by-step explanation:

It is given that a quadrilateral has congruent side lengths. It means the quadrilateral is either square of rhombus.

Each interior angles of a square is a right angle.

2 opposite angles have measures of 100 degrees. The other 2 opposite angles have measures of 70 degrees and (5 x) degrees.

Since the interior angles of the given quadrilateral are not right angles, therefore it must be a rhombus.

Opposite angles of a rhombus are congruent.

$5x=70$

Divide both sides by 5.

$x=\frac{70}{5}$

$x=14$

The value of x is 14.

Therefore, the correct option is A.

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What is the equation of the line which includes points (-3, 2) and (1, 6)?

olchik [2.2K]

Answer:

required equation of line is y=x+5

Step-by-step explanation:

equation of line passing through points $(x_1,y_1)$ and ${ x_2,y_2)$

$y-y_1$ = $\frac{y_2-y_1}{x_2-x_1}$ \times{x-x_1}

put the co-ordinate (-3,2) and(1,6)

y-2= $\frac{6-2}{1+3}$ \times{x+3}

y-2=x+3

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2 years ago

A committee must be formed with 4 teachers and 5 students. If there are 7 teachers to choose from, and 15 students, how many dif

nikitadnepr [17]

Answer:

Step-by-step explanation:

There are a total of 10 persons (6 teachers + 4 students) from which a committee of 5 is to be formed. This can be done in 10C5 ways.

The number of ways that a committee can be formed with no students in it is to select 5 teachers out of the pool of 6 teachers available. This can be done in 6C5 ways.

Therefore the total number of ways that the committee can be formed with at least one student in it is 10C5 - 6C5.

10C5 = 252

6C5 = 6

Therefore the required number of ways = 246

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2 years ago

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Nataly [62]

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Step-by-step explanation:

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2 years ago

How to make 3 dimensional object become 4 dimensional object

NISA [10]

Using Hinton's method;

Draw two ordinary 3D cubes in 2D space, one encompassing the other, separated by an "unseen" distance
Then draw lines between their equivalent vertices.
The eight lines connecting the vertices of the two cubes in this case represent a single direction in the "unseen" fourth dimension.

<h3>What is a 4 dimensional shape?</h3>

A four-dimensional shape (4D) is a mathematical extension of a three-dimensional or 3D space.

Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called dimensions, to describe the sizes or locations of objects.

Using Hinton's method;

Draw two ordinary 3D cubes in 2D space, one encompassing the other, separated by an "unseen" distance
Then draw lines between their equivalent vertices.
The eight lines connecting the vertices of the two cubes in this case represent a single direction in the "unseen" fourth dimension.

Learn more about dimensional shapes here:

brainly.com/question/12280037

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1 year ago

Use the Limit Comparison Test to determine whether the series converges.

lianna [129]

Answer:

The infinite series $\displaystyle \sum\limits_{k = 1}^{\infty} \frac{8/k}{\sqrt{k + 7}}$ indeed converges.

Step-by-step explanation:

The limit comparison test for infinite series of positive terms compares the convergence of an infinite sequence (where all terms are greater than zero) to that of a similar-looking and better-known sequence (for example, a power series.)

For example, assume that it is known whether $\displaystyle \sum\limits_{k = 1}^{\infty} b_k$ converges or not. Compute the following limit to study whether $\displaystyle \sum\limits_{k = 1}^{\infty} a_k$ converges:

$\displaystyle \lim\limits_{k \to \infty} \frac{a_k}{b_k}\; \begin{tabular}{l}\\ $\leftarrow$ Series whose convergence is known\end{tabular}$ .

If that limit is a finite positive number, then the convergence of the these two series are supposed to be the same.
If that limit is equal to zero while $a_k$ converges, then $b_k$ is supposed to converge, as well.
If that limit approaches infinity while $a_k$ does not converge, then $b_k$ won't converge, either.

Let $a_k$ denote each term of this infinite Rewrite the infinite sequence in this question:

$\begin{aligned}a_k &= \frac{8/k}{\sqrt{k + 7}}\\ &= \frac{8}{k\cdot \sqrt{k + 7}} = \frac{8}{\sqrt{k^2\, (k + 7)}} = \frac{8}{\sqrt{k^3 + 7\, k^2}} \end{aligned}$ .

Compare that to the power series $\displaystyle \sum\limits_{k = 1}^{\infty} b_k$ where $\displaystyle b_k = \frac{1}{\sqrt{k^3}} = \frac{1}{k^{3/2}} = k^{-3/2}$ . Note that this

Verify that all terms of $a_k$ are indeed greater than zero. Apply the limit comparison test:

$\begin{aligned}& \lim\limits_{k \to \infty} \frac{a_k}{b_k}\; \begin{tabular}{l}\\ $\leftarrow$ Series whose convergence is known\end{tabular}\\ &= \lim\limits_{k \to \infty} \frac{\displaystyle \frac{8}{\sqrt{k^3 + 7\, k^2}}}{\displaystyle \frac{1}{{\sqrt{k^3}}}}\\ &= 8\left(\lim\limits_{k \to \infty} \sqrt{\frac{k^3}{k^3 + 7\, k^2}}\right) = 8\left(\lim\limits_{k \to \infty} \sqrt{\frac{1}{\displaystyle 1 + (7/k)}}\right)\end{aligned}$ .

Note, that both the square root function and fractions are continuous over all real numbers. Therefore, it is possible to move the limit inside these two functions. That is:

$\begin{aligned}& \lim\limits_{k \to \infty} \frac{a_k}{b_k}\\ &= \cdots \\ &= 8\left(\lim\limits_{k \to \infty} \sqrt{\frac{1}{\displaystyle 1 + (7/k)}}\right)\\ &= 8\left(\sqrt{\frac{1}{\displaystyle 1 + \lim\limits_{k \to \infty} (7/k)}}\right) \\ &= 8\left(\sqrt{\frac{1}{1 + 0}}\right) \\ &= 8 \end{aligned}$ .

Because the limit of this ratio is a finite positive number, it can be concluded that the convergence of $\displaystyle a_k &= \frac{8/k}{\sqrt{k + 7}}$ and $\displaystyle b_k = \frac{1}{\sqrt{k^3}}$ are the same. Because the power series $\displaystyle \sum\limits_{k = 1}^{\infty} b_k$ converges, (by the limit comparison test) the infinite series $\displaystyle \sum\limits_{k = 1}^{\infty} a_k$ should also converge.

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3 years ago