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3 years ago

X+3

Mathematics

2 answers:

Anna007 [38]3 years ago

8 0

$\\ \sf\longmapsto y=\left(\dfrac{1}{2}\right)^{x-3}+1$

Graph attached

Nitella [24]3 years ago

3 0

$▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪$

The Correct choice is ~

$\boxed{y = \bigg({\dfrac{1}{2} \bigg) }^{x - 3} + 1}$

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Which sequences are geometric sequences? Check all that apply. 4, 2, 1, One-half,One-fourth,... −2, 3, −4, 5, −6, … 2, 6, 18, 54

hjlf

Answer:

(1)We get that all terms have same $(r)$ then It is a Geometric Sequence.

(2)We get Common ratio of given sequence is not same. It is not an geometric sequence.

(3)We get the common ratio is same then it is a Geometric Sequence

(4)We get the common ratio is same then it is a Geometric Sequence.

(5)We get Common ratio of given sequence is not same. It is not an geometric sequence.

Step-by-step explanation:

Here, The Geometric Progression in the form:

$G.P: a, ar, ar^{2}, ar^{3}, ar^{4}, ar^{5}........................................., ar^{n-1}, ar^{n}.$

Where $a - First\ term\\r - Common \ ratio\\n - Number\ of\ terms\ of\ an\ progression$

So, Check all that apply.

(1) $4,2,1,\frac{1}{2},\frac{1}{4}$

For the geometric Sequence Common ratio $(r)$ must be same.

⇒ $r= \frac{ar^{n} }{ar^{n-1} }$

Then, Finding $(r)$ for given sequence

$r=\frac{a_{2} }{a_{1} } =\frac{a_{3} }{a_{2} } =\frac{a_{4} }{a_{3} }............................\frac{ar^{n} }{ar^{n-1} } .$

∴ $r= \frac{2}{4}=\frac{1}{2}=\frac{\frac{1}{2} }{1} =\frac{\frac{1}{4} }{\frac{1}{2} }$

⇒ $r= \frac{1}{2}=\frac{1}{2}=\frac{1}{2} } = \frac{1}{2} }$

Clearly,

We get that all terms have same $(r)$ then It is a Geometric Sequence.

(2) $-2, 3,-4,5,-6.........$

Same as above we will check the common ratio

⇒ $r=\frac{3}{-2} =\frac{-4}{3} =\frac{5}{-4}=\frac{-6}{5}$

⇒ $r=\frac{3}{-2} \neq \frac{-4}{3} \neq \frac{5}{-4}\neq \frac{-6}{5}$

Clearly,

We get Common ratio of given sequence is not same. It is not an geometric sequence.

(3) $2,6,18,54,162.................$

Now checking common Ratio $(r)$

⇒ $r=\frac{6}{2} =\frac{18}{6} =\frac{54}{18}=\frac{162}{54}$

⇒ $r=3=3=3=3$

Therefore,

We get the common ratio is same then it is a Geometric Sequence.

(4) $-4,-16,-64,-256.........$

Now checking common Ratio $(r)$

⇒ $r=\frac{-16}{-4} =\frac{-64}{-16} =\frac{-256}{-64}$

⇒ $r=4=4=4$

Therefore,

We get the common ratio is same then it is a Geometric Sequence.

(5) $-2,-4,-12,-48,-240............................$

Now checking common Ratio $(r)$

⇒ $r=\frac{-4}{-2} =\frac{-12}{-4} =\frac{-48}{-12}=\frac{-240}{-48}$

⇒ $r= 2\neq 3\neq 4\neq 5$

Clearly,

We get Common ratio of given sequence is not same. It is not an geometric sequence.

8 0

3 years ago

Read 2 more answers

Simplify the expression: 10h2+h–6h2

cupoosta [38]

Answer:

The answer is 4h^2 + h

Step-by-step explanation:

Subtract 6h^2 from 10h^2

~Hoped this helped~

4 0

3 years ago

Read 2 more answers

In a parallelogram a diagonal of the length 20 cm is perpendicular to one of the sides. Find the longer side of parallelogram if

Ivan

Hello,
Please, see the attached file.
Thanks.

4 0

3 years ago

A number added by 7 is the same as that

boyakko [2]

Answer:

$x+7=4x-11$

Step-by-step explanation:

Hi there!

Let $x$ represent "the number".

A number added by 7 is the same as that number times four minus eleven.

A number added by 7 ⇒ $x+7$

Is the same as ⇒ $x+7=$

The number times four ⇒ $x+7=4x$

Minus eleven ⇒ $x+7=4x-11$

I hope this helps!

4 0

3 years ago

Two dice are thrown simultaneously. Given that sum of the numbers is NOT more than 5, what is the probability that sum is more t

defon

A method to know the probability is to list down all of the possible combinations that would present an outcome of not more than 5. This is listed below:

1 + 4
4 + 1
2 + 3
3 + 2
1 + 1
2 + 2
1 + 2
2 + 1
1 + 3
3 + 1

There are 10 possible outcomes. But among these, the only ones that can have a sum more than 3 are:

1 + 4
4 + 1
2 + 3
3 + 2
2 + 2
1 + 3
3 + 1

There are only 7 possible outcomes that meet both requirements. Given that there are 7 outcomes within the total of 10, the probability would be 7/10, or 0.7.

3 0

3 years ago