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Marizza181 [45]

1 year ago

9

What are the coordinates of the point on the directed line segment from (-7,-9) to (-2,4) that partitions the segment into a rat

io of 1 to 4?

1 answer:

Mrac [35]1 year ago

4 0

P1 = (-7, -9)

P2 = (-2, 4)

ratio = 1/4

x = (-7 + 0.25(-2))/(1 + 0.25)

= (-7 - 0.5) / 1.25

= -7.5/1.25

= -6

y = (-9 + 0.25(4)) / (1 + 0.25)

y = (-9 + 1) / 1.25

y = -8/1.25

y = 6.4

The coordinate sof the point are (-6, 6.4)

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9x > 72
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6 0

4 years ago

Zolol [24]

<u><em>Note:</em></u><em> 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...</em>

Part A)

<em><u>What is the next term of this sequence?</u></em>

Answer:

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

Step-by-step explanation:

Considering the Arithmetic sequence with fist four terms

<em> 1, 3, 5, 7...</em>

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, <em> 1, 3, 5, 7... </em>will be an arithmetic sequence having the common difference 2. Common difference is denoted by 'd'.

So,

Given the sequence

<em>1, 3, 5, 7...</em>

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

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 <em>1, 3, 5, 7...</em>

Part B)

<u><em>Writing down an expression, in terms of n for the nth term of the sequence</em></u>

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

<em>1, 3, 5, 7...</em>

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

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

#learnwithBrainly

7 0

3 years ago

3/4 of a number is 24. What's the number?

Lady_Fox [76]

Hi

3x/4 = 24
3x = 24·(4)
3x = 96
x = 96/3
x = 32

3/4 of 32 is 24

4 0

3 years ago

Please help me I need N<br><br> Please help please I'm begging

Bad White [126]

58 degrees

Explanation
If you have a triangle with the angle measures of abc as 58 degrees, 102 degrees and 20 degrees you can multiply them in order of abc so 58 degrees is angle a, 102 degrees is angle b and 20 degrees is angle c. Then you just put in angle a for d which would be 58 degrees and angle e for b 102 degrees and angle f for c which would be 20 degrees

3 0

2 years ago

If someone flips switches on the selection in a completely random fashion, what is the probability that the system selected cont

DiKsa [7]

Given that a display allows a customer to hook together any selection of components, one of each type. These are the types:
Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood
CD player: Onkyo, Pioneer, Sony, Technics
Speakers: Boston, Infinity, Polk
Cassette: Onkyo, Sony, Teac, Technics:

Part (a):
In how many ways can one component of each type be selected?

The number of ways one type of receiver will be selected is given by 5C1 = 5
The number of ways one type of CD player will be selected is given by 4C1 = 4
The number of ways one type of speakers will be selected is given by 3C1 = 3
The number of ways one type of cassette will be selected is given by 4C1 = 4

Therefore, the number of ways one component of each type can be selected is given by 5 x 4 x 3 x 4 = 240 ways

Part (b):
In how many ways can components be selected if both the receiver and the compact disc player are to be Sony?

The number of ways of selecting a Sony receiver is 1
The number of ways of selecting a Sony CD player is 1
The number of ways one type of speakers will be selected is given by 3C1 = 3
The number of ways one type of cassette will be selected is given by 4C1 = 4

Therefore, the number of ways components can be selected if both the receiver and the compact disc player are to be Sony is given by 1 x 1 x 3 x 4 = 12

Part (c)
In how many ways can components be selected if none of them are Sony?

The number of ways one type of receiver that is not Sony will be selected is given by 4C1 = 4
The number of ways one type of CD player that is not Sony will be selected is given by 3C1 = 3
The number of ways one type of speakers that is not Sony will be selected is given by 3C1 = 3
The number of ways one type of cassette that is not Sony will be selected is given by 3C1 = 3

Therefore, the number of ways that components can be selected if none of them are Sony is given by 4 x 3 x 3 x 3 = 108

Part (d):
In how many ways can a selection be made if at least one Sony component is to be included?

The total number of ways of selecting one component of each type is 240
The number of ways that components can be selected if none of them are Sony is 108

Therefore, the number of ways of selecting at least one Sony component is given by 240 - 108 = 132

Part (e):
If someone flips switches on the selection in a completely random fashion, what is the probability that the system selected contains at least one Sony component?

The total number of ways of selecting one component of each type is 240
The number of ways of selecting at least one Sony component is 132

Therefore, the probability that a system selected at random contains at least one Sony component is given by 132 / 240 = 0.55

Part (f):
If someone flips switches on the selection in a completely random fashion, what is the probability that the system selected contains exactly one Sony component? (Round your answer to three decimal places.)

The number of ways of selecting only a Sony receiver is given by 1 x 3 x 3 x 3 = 27
The number of ways of selecting only a Sony CD player is given by 4 x 1 x 3 x 3 = 36
The number of ways of selecting only a Sony cassette is given by 4 x 3 x 3 x 1 = 36

Thus, the number of ways of selecting exactly one Sony component is given by 27 + 36 + 36 = 99

Therefore, the probability that a system selected at random contains exactly one Sony component is given by 99 / 240 = 0.413

5 0

4 years ago