L –3 | A. 3 B. -3 C. 0.30 D. 30

In circle E shown below, the measure of ∠AED is 98°:

ElenaW [278]

We know that
m Arc DC = 32°

if ∠AED = 98°
then
m Arc AD = 98°-----> by central angle

therefore
m Arc ABC=360°-[m Arc AD+m Arc ]----> 360°- [98°+32°]---> 230°

the answer is
m Arc ABC = 230°

3 0

4 years ago

Read 2 more answers

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

A customer placed an order with a bakery for cupcakes. The baker has completed 37.5% of the order 81 cupcakes. How many cupcakes

Paul [167]

Answer:

The total number of cupcakes ordered=216

Step-by-step explanation:

The total number of cupcakes ordered that the baker completed can be expressed as;

C=P×t

where;

C=Total number of completed order of cupcakes

P=percentage of order completed

t=total number of ordered cupcakes

In our case;

C=81

P=37.5%

t=t

replacing in the above expression;

81=37.5%×t

(37.5/100)×t=81

t=81×100/37.5

t=216

The total number of cupcakes ordered=216

3 0

3 years ago

What is the length of the diagonal, d, of the rectangular prism shown below?

vodomira [7]

Answer:

<h2>The diagonal of the volumetric figure is 7 units long.</h2>

Step-by-step explanation:

The figure is attached.

Notice that the dimensions of the prism are

$w=2\\l=3\\h=6$

First, we need to find the diagonal of the rectangular face on the base, this diagonal of the base is part of the right triangle formed by the diagonal of the volume, that's why we need it.

Let's use the Pythagorean's Theorem

$d_{base}=\sqrt{2^{2} +3^{2} }=\sqrt{4+9}=\sqrt{13}$