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RideAnS [48]
1 year ago
7

H2 Worksheet #8

Mathematics
1 answer:
ohaa [14]1 year ago
3 0

Answer:

It's easy to solve the problem.

let's start...

given equation:- y = 2x+2

X y

1 (2× 1 )+ 2 = 4 .

3 (3×2)+2 = 8 .

9 (9×2) + 2 = 20 .

10. (10× 2)+2 = 22 .( table completed)

just put the value of X in the expression.

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Minchanka [31]

Answer:

3/4

Step-by-step explanation:

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3 years ago
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The first, third and thirteenth terms of an arithmetic sequence are the first 3 terms of a geometric sequence. If the first term
Salsk061 [2.6K]

Answer:

The first three terms of the geometry sequence would be 1, 5, and 25.

The sum of the first seven terms of the geometric sequence would be 127.

Step-by-step explanation:

<h3>1.</h3>

Let d denote the common difference of the arithmetic sequence.

Let a_1 denote the first term of the arithmetic sequence. The expression for the nth term of this sequence (where n\! is a positive whole number) would be (a_1 + (n - 1)\, d).

The question states that the first term of this arithmetic sequence is a_1 = 1. Hence:

  • The third term of this arithmetic sequence would be a_1 + (3 - 1)\, d = 1 + 2\, d.
  • The thirteenth term of would be a_1 + (13 - 1)\, d = 1 + 12\, d.

The common ratio of a geometric sequence is ratio between consecutive terms of that sequence. Let r denote the ratio of the geometric sequence in this question.

Ratio between the second term and the first term of the geometric sequence:

\displaystyle r = \frac{1 + 2\, d}{1} = 1 + 2\, d.

Ratio between the third term and the second term of the geometric sequence:

\displaystyle r = \frac{1 + 12\, d}{1 + 2\, d}.

Both (1 + 2\, d) and \left(\displaystyle \frac{1 + 12\, d}{1 + 2\, d}\right) are expressions for r, the common ratio of this geometric sequence. Hence, equate these two expressions and solve for d, the common difference of this arithmetic sequence.

\displaystyle 1 + 2\, d = \frac{1 + 12\, d}{1 + 2\, d}.

(1 + 2\, d)^{2} = 1 + 12\, d.

d = 2.

Hence, the first term, the third term, and the thirteenth term of the arithmetic sequence would be 1, (1 + (3 - 1) \times 2) = 5, and (1 + (13 - 1) \times 2) = 25, respectively.

These three terms (1, 5, and 25, respectively) would correspond to the first three terms of the geometric sequence. Hence, the common ratio of this geometric sequence would be r = 25 /5 = 5.

<h3>2.</h3>

Let a_1 and r denote the first term and the common ratio of a geometric sequence. The sum of the first n terms would be:

\displaystyle \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}.

For the geometric sequence in this question, a_1 = 1 and r = 25 / 5 = 5.

Hence, the sum of the first n = 7 terms of this geometric sequence would be:

\begin{aligned} & \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}\\ &= \frac{1 \times \left(1 - 2^{7}\right)}{1 - 2} \\ &= \frac{(1 - 128)}{(-1)} = 127 \end{aligned}.

7 0
2 years ago
What is the slope and y intercept?​
natka813 [3]
The y intercept is -2.
4 0
2 years ago
Find the area of the blue sector. Use 3.14 for pi and round to the nearest hundredth.
Anni [7]
Answer:

25.64 in^2

Explanation:

<span><span>60360</span>⋅π<span>r2</span></span>, where <span>r=7</span>

<span>=<span>16</span>⋅3.14⋅<span>72</span>=<span>16</span>⋅3.14⋅49=25.64</span> in^2

4 0
3 years ago
David's bowling score is 6 less than 2 times Aaron's score. The sum of their scores is 84. Find the score of each student. Use t
Y_Kistochka [10]

Answer:

Aaron's bowling score is 30

David's bowling score is 54

Step-by-step explanation:

The variable representing Aaron's score is = a

The variable representing David's bowling score = d

The sum of their scores is 84.

= a + d = 84...... Equation 1

David's bowling score is 6 less than 2 times Aaron's score.

d = 2a - 6

Substituting 2a - 6 for d in Equation 1

a + 2a - 6 = 84

3a - 6 = 84

3a = 84 + 6

3a = 90

a = 90/3

a = 30

Hence, Aaron's bowling score is 30

d = 2a - 6

d = 2(30) - 6

d = 60 - 6

d = 54

David's bowling score is 54

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2 years ago
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