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Pavel [41]
3 years ago
9

For what value of k will k+9,2k-1 and 2k+7 are the consecutive terms of an A.P

Mathematics
1 answer:
Stolb23 [73]3 years ago
8 0

k = 18

the common difference d of an arithmetic sequence is

d = a₂ - a₁ = a₃ - a₂ = ....

a₂ - a₁ = 2k - 1 - k - 9 = k - 10 and

a₃ - a₂ = 2k + 7 - (2k - 1) = 2k + 7 - 2k + 1 = 8, hence

k - 10 = 8 ⇒ k = 8 + 10 = 18

the 3 consecutive terms are

27, 35, 43


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REALLY IMPORTANT
Mashutka [201]

Answer:

we choose (3,4)

Step-by-step explanation:

Given the coordinates:

  • A (5, 2)
  • B (5, -2)
  • C  (2,1)
  • L (-5, 6)
  • M (-5, -6)

To find a distance between two points or the length of the segment, we use the following formula:

\sqrt{(x2-x1)^2+(y2-y1)^2}

  • Because A and B are located in the same line x =5

=> the lenght of AB = \sqrt{(-2-2)^{2} } =\sqrt{-4^{2} } =4

  • Because A and B are located in the same line x =-5

=>  the lenght LM = \sqrt{(-6-6)^{2} } =\sqrt{-12^{2} } =12

  • Because ABC is similar to LMN

=> the ratio of LM : AB = 12:4 = 3:1

<=> the ratio LN : CA = 3:1

We need to find the lenght of CA

= \sqrt{(2-5)^2+(1-2)^2} = \sqrt{-3^{2} + -1^{2} } = \sqrt{10}

=> the lenght of LN = 3CA = 3\sqrt{10}

Let (x, y) is the coordinate of N, we have:

The length of LN: \sqrt{(x+5)^2+(y-6)^2} = 3\sqrt{10} = \sqrt{90}

Let try all the possible answer;

(3,4) => \sqrt{(3+5)^2+(4-6)^2} = \sqrt{8^{2} + -2^{2} } = \sqrt{90} True

So we choose (3,4)

7 0
3 years ago
Here is a list of numbers:
ehidna [41]

Answer:

put the numbers in order from least to greatest and then cross them out til you get to the center number

3 0
3 years ago
Read 2 more answers
The table below describes the smoking habits of a group of asthma sufferers. If one of the 1156 people is randomly selected, fin
Rashid [163]

Answer:

0.554

Step-by-step explanation:

In the figure attached, the table is shown

Total people: 1156

Nonsmoker men + occasional smoker men + regular smoker men + heavy smoker men + heavy smoker women = men + heavy smoker women = 601 + 39 = 640

Probability that the person is a  man or a heavy smoker = 640/1156 = 0.554

(Notice that if you directly add heavy smoker and total men you will count twice heavy smoker men)

8 0
3 years ago
What is the scale factor? ( the answer must be a fraction).
MrRissso [65]
Since these are similar triangles you can use any two corresponding sides to figure out the scale factor.

Use the bottom side. Going from the first triangle to the second the scale factor is:
15/9 = 5/3
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Which ordered pair is a solution of the equations y=-5/4x-2
sashaice [31]
The answer is C. That would be ur answer
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