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3 years ago

A trapezoid was broken into a rectangle and two equal

Mathematics

2 answers:

love history [14]3 years ago

5 0

Step-by-step explanation:

For the base of the triangles, we just have to remove the 1m and divide the remaining measurement into two since they are symmetrical.

$5m - 1m = 4m \\ \frac{4m}{2} = 2m \: each$

For the area of the rectangle:

$base \times height = 1m \times 4m = 4 {m}^{2}$

For the area of each triangle:

$\frac{1}{2} base \times height = \frac{1}{2} (2m)(4m) = 4m^{2}$

For the area of the trapezoid, just combine the two areas:

4m² + 4m² = 8m²

Yuki888 [10]3 years ago

5 0

Answer:

For the base of the triangles, we just have to remove the 1m and divide the remaining measurement into two since they are symmetrical.

For the area of the rectangle:

Step-by-step explanation:

For the area of each triangle:

For the area of the trapezoid, just combine the two areas:

4m² + 4m² = 8m²

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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

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7 0

4 years ago

Plz help me who can answer in 2 mins

wariber [46]

Express incrase as percent of original
incrase=new-original=680-500=180

percent increase=increase/original times 100=180/500 times 100=0.36 times 100=36

36% increase

8 0

3 years ago

Read 2 more answers

What are parallel lines

tankabanditka [31]

Answer:

Parallel lines are lines in the same plane that do not intersect, like lines on notebook paper.

The "in the same plane" requirement is important! Take a look at the attached image. Lines AD and DC don't intersect, but they are not in the same plane (face of the rectangular solid). We don't call those parallel, we call them skew lines.