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3 years ago

The sketch shows two parallel lines cut by a transversal. Angle 2 is 36°. What is the measure of angle 8?

Mathematics

1 answer:

erastova [34]3 years ago

6 0

∠8 = 144°

∠6 = ∠2 = 36° ( corresponding angles are congruent )

∠8 + ∠6 = 180° ( sum of angles in a straight angle )

∠8 = 180° - 36° = 144°

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Homework

Zolol [24]

Note: As you have missed to mention the first four terms of the Arithmetic sequence. So, I am randomly assuming that first four terms of the arithmetic sequence be 1, 3, 5, 7... This would anyhow make you understand the concept. So, I am solving your query based on assuming the first four terms of an Arithmetic sequence as 1, 3, 5, 7...

Part A)

What is the next term of this sequence?

Answer:

${\displaystyle \ a_{5}=9$ is the next term i.e. 5th term of the arithmetic sequence 1, 3, 5, 7...

Step-by-step explanation:

Considering the Arithmetic sequence with fist four terms

1, 3, 5, 7...

As we know that a sequence is termed as arithmetic sequence of numbers if the difference of any two consecutive terms of the sequence remains constant.

For instance, 1, 3, 5, 7... will be an arithmetic sequence having the common difference 2. Common difference is denoted by 'd'.

So,

Given the sequence

1, 3, 5, 7...

$d=3-1=2,d=5-3=2$

As $a_{1} = 1$ and $d = 2$

The next term i.e. 5th term can be found by using the $nth$ term of the sequence.

So, consider the nth term of the sequence $a_{n$

$\ a_{n}=a_{1}+(n-1)d$

Putting $n=5$ in, $a_{1} = 1$ and $d = 2$ in $\ a_{n}=a_{1}+(n-1)d$ to find the 5th term.

$\ a_{n}=a_{1}+(n-1)d$

$\ a_{5}=1+(5-1)2$

$\ a_{5}=1+(4)2$

${\displaystyle \ a_{5}=9$

So, ${\displaystyle \ a_{5}=9$ is the next term i.e. 5th term of the arithmetic sequence 1, 3, 5, 7...

Part B)

Writing down an expression, in terms of n for the nth term of the sequence

consider the nth term of the sequence $a_{n$

$\ a_{n}=a_{1}+(n-1)d$

Here, $a_{1}$ is the first term, $d$ is the common difference.

For example,

Given the sequence

1, 3, 5, 7...

$d=3-1=2,d=5-3=2$

As $a_{1} = 1$ and $d = 2$

The next term i.e. 5th term can be found by using the $nth$ term of the sequence.

So, consider the nth term of the sequence $a_{n$

$\ a_{n}=a_{1}+(n-1)d$

Putting $n=5$ in, $a_{1} = 1$ and $d = 2$ in $\ a_{n}=a_{1}+(n-1)d$ to find the 5th term.

$\ a_{n}=a_{1}+(n-1)d$

$\ a_{5}=1+(5-1)2$

$\ a_{5}=1+(4)2$

${\displaystyle \ a_{5}=9$

Keywords: arithmetic sequence, nth term, common difference

Learn more abut arithmetic sequence, nth term and common difference from brainly.com/question/12227567

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7 0

4 years ago

What is the sum of 6 5/3 +5 1/7

madreJ [45]

12 17/21 is the sum

8 0

3 years ago

Please help me do this

Kobotan [32]

For #1 I think maybe 5 qts

6 0

3 years ago

Read 2 more answers

the ratio of the areas of two similar polygons is 81:64. If the perimeter of the first polygon is 32 cm, what is the perimeter o

marta [7]

In two similar polygons, the ratio of their areas is the square of the ratio of their sides. If the sides of any polygon are a and b then :

Ratio of area = $a^{2} :b^{2}$

Given ratio of area =81:64

Or 81:64= $a^{2} :b^{2}$

Taking root of both sides

9:8=a:b

The ratio of perimeter of any two similar polygon is equal to the ratio of sides.

Ratio of perimeter = a:b

Perimeter of first polygon is 32 cm.

Let the perimeter of second polygon be x.

32:x=a:b

Or, 32:x=9:8

$\frac{32}{x} =\frac{9}{8}$

Cross multiplying

9x= (32)(8)

9x=256

Dividing both sides by 9

x=28.4.

The perimeter of second polygon is 28.4cm.

5 0

4 years ago

PLEASE HELP ME!!

Mamont248 [21]

The exact height of the triangle is 20.8ft

The area of the right tringle in radical form is 72√3 ft²

The area of the triangle in decimal form is 124.7 ft²

<h3>How to find the side and area of a right angle triangle?</h3>

The side XY or height of the triangle can be found as follows:

Using trigonometric ratios,

tan 60° = XY / 12

XY = 12 tan 60°

XY = 12 × 1.73205080757

XY = 20.7846096908

height = 20.8ft

The area of XYZ = 1 / 2 bh

where

b = base
h = height

Therefore,

The area of XYZ = 1 / 2 × 12 × 20.8 = 124.707658145 = 124.7 ft²

The area in radical form = 1 / 2 × 12 × 12 tan 60°

The area in radical form = 1 / 2 × 12 × 12 × √3 = 144√3 / 2 = 72√3 ft²

learn more on triangles here: brainly.com/question/2773823

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4 0

2 years ago