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2 years ago

What is the value of y? 18+2y+4+10+2x+10

Mathematics

1 answer:

Rus_ich [418]2 years ago

3 0

Answer:

1) 18+2y+4+10+2x+10

2) 42+2y+2x

3) 42+2x=-2y

4) -1(42-2x=2y)

5) (42-2x=2y)/2

y=21-x

Step-by-step explanation:

1) Original equation

2) Combine like terms

3) Since the problem is asking to find the value of Y, Isolate it

4) Multiply by a negative to make Y positive

5) Since what we have left isn't in simplest form, divide by 2

What is left is y=21-x or y=-x+21

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2 years ago

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Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the co

jeka57 [31]

Answer:

<h2>A. The series CONVERGES</h2>

Step-by-step explanation:

If $\sum a_n$ is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

$\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho$

If $\rho$ < 1, the series converges absolutely

If $\rho > 1$ , the series diverges

If $\rho = 1$ , the test fails.

Given the series $\sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}$

To test for convergence or divergence using ratio test, we will use the condition above.

$a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}$

$\frac{a_n_+_1}{a_n} = \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\$

$\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\$

aₙ₊₁/aₙ =

$\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\$

note that any constant dividing infinity is equal to zero

$|\frac{1+2/\infty+1/\infty^2}{5}|\\\\$

$\frac{1+0+0}{5}\\ = 1/5$

$\rho = 1/5$

Since The limit of the sequence given is less than 1, hence the series converges.

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2 years ago

yawa3891 [41]

Answer:

Step-by-step explanation:

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2 years ago

What is true of a sequence of transformations that rotates an image and then translates it in order to map it onto another image

joja [24]

The true statement about the sequence of transformations is it includes exactly two rigid transformations.

<h3>How to determine the true statement?</h3>

The transformation statement is given as:

a sequence of transformations that rotates an image and then translates it in order to map it onto another image

This can be split as follows:

A sequence of transformations that rotates an image
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Translation and rotation are rigid transformations

This means that the size and the angle of the shape that is transformed will remain the same

Hence, the true statement about the sequence of transformations is it includes exactly two rigid transformations.