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True [87]
3 years ago
14

The first two terms of an arithmetic progression are 27 and 24 respectively. How many terms of the progression are to be added t

o get - 30?
Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
4 0

Answer:

20 terms

Step-by-step explanation:

<u>Given AP with the first two terms:</u>

  • a₁= 27 and a₂=24

<u>Common difference: </u>

  • d= 24-27 = -3

<u>To find </u>

  • n for which Sₙ= -30
<h3>Solution</h3>
  • Sₙ = 1/2*n*(a₁+aₙ) =
  • 1/2n(a₁+a₁+(n-1)d) =
  • 1/2n(27+27+(n-1)(-3))=
  • 1/2n(54 - 3n + 3) =
  • 1/2n(57 - 3n)

<u>Since Sₙ = -30</u>

  • 1/2n(57 - 3n) = -30
  • 57n - 3n² = -60
  • 19n - n²- 20 = 0
  • n² -19 n -20= 0

<u>Solving the quadratic equation we get:</u>

  • n =20

So the sum of 20 terms will add up - 30

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5 0
3 years ago
Sunday by 11:59pm
beks73 [17]

Answer:

The amount of markup is 88 dollars.

Step-by-step explanation:

Given that the whole sale price of bicycle is: $400

P = \$400

Mark up is the profit that the seller of the product makes after selling the product more in price more than its cost or buying price.

Given that mark up percentage is 22%

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Mark\ up = 22\%\ of\ Price\\Mark\ up = 0.22 * P\\Mark\ up = 0.22 * 400\\= \$88

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7 0
3 years ago
The graph of a trigonometric function oscillates between y=1 and y=-7. It reaches its
madam [21]

Answer:

y = 4 sin(½ x) − 3

Step-by-step explanation:

The function is either sine or cosine:

y = A sin(2π/T x) + C

y = A cos(2π/T x) + C

where A is the amplitude, T is the period, and C is the midline.

The midline is the average of the min and max:

C = (1 + -7) / 2

C = -3

The amplitude is half the difference between the min and max:

A = (1 − -7) / 2

A = 4

The maximum is at x = π, and the minimum is at x = 3π.  The difference, 2π, is half the period.  So T = 4π.

Plugging in, the options are:

y = 4 sin(½ x) − 3

y = 4 cos(½ x) − 3

Since the maximum is at x = π, this must be a sine wave.

y = 4 sin(½ x) − 3

4 0
3 years ago
Can a Right Triangle be a(n)<br> A.Obtuse<br> B.Scalene
Blizzard [7]
Your answer is B hope i helped
4 0
3 years ago
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I need someone to explain on how to do this problem.​
weqwewe [10]

Answer:

I think it's x=-12 for the buttom one

Step-by-step explanation:

I think when you get open equations like these you would asume 1 is there so rewrite it as 2x + 25 = 1

so take the 25 away from 1. to do that we need to do the opisite of +

2x + 25 = 1

1 - 25 = -24

rewrite

2x = -24

take the 2 away. oppisite of mulitplication is division. so divide 2 by -24

-24 divided by 2 = -12

Hope this helps! Please mark as brainliest! Thanks! If you need me to solve the top one too, I'll do it! Just comment bellow. :D

5 0
3 years ago
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