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2 years ago

Add: 5/7 + 9/11 + 21/77

Mathematics

1 answer:

Vsevolod [243]2 years ago

4 0

Answer:

Step-by-step explanation:

You want to begin by making each fraction have the same common denominator. The LCF (least common factor) is 77. So, knowing this, we can now multiply the fractions that need to have a denominator of 77.

1. 5/7*11/11=55/77

2. 9/11 * 7/7 =63/77

Now we can add

55/77 + 63/77 + 21/77 = 139/77 or 1.805194805

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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

The ratio of the side lengths for a triangle is exactly 7:11:13. in a second triangle similar to the first, the shortest side is

topjm [15]

9 / 7 = 1.285
1.285 × 13 = 16.71 inch

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3 years ago

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almond37 [142]

Answer:

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3 years ago

The perimeter of a regulation singles tennis court is 210 feet and the length is 57 feet less than five times the width.

Marianna [84]

Answer:

Length = 24 and Width = 81

Step-by-step explanation:

Let Width be W

then Length = W-57

Perimeter of rectangle = 2(Length + Width)

=2 (W-57+W)= 210

4W- 114= 210

4W= 324

W= 81

Then Length = 81-57 = 24

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3 years ago

Resuelve los siguientesTriángulos semejantes, Obteniendo el valor de la incógnita faltante en cada caso

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Answer:

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Step-by-step explanation:

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3 years ago