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3 years ago

Write them least to greatest...

1 answer:

3 0

1. 0.2,0.4,0.54,0.61
2.0.02,0.11,0.3,0.45
3.1.02,1.24,1.33,1.7
4.1.01,1.06,1.2,1.42
5.0.87,0.9,0.98,1.23
6.0.06,0.5,1.4,1.23
7.0.003,0.031,0.033.0.03
8.0.002.0.022.0.02.0.2

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What is the nth term rule of the quadratic sequence below?

Vladimir [108]

Answer:

3n² + 5n - 2

Step-by-step explanation:

Given sequence:

6, 20, 40, 66, 98, 136, ...

Calculate the first differences between the terms:

$6 \underset{+14}{\longrightarrow} 20 \underset{+20}{\longrightarrow} 40 \underset{+26}{\longrightarrow} 66 \underset{+32}{\longrightarrow} 98 \underset{+38}{\longrightarrow} 136$

As the first differences are not the same, calculate the second differences:

$14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38$

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of the n² term is half of the second difference.

Therefore, the n² term is: 3n²

Compare 3n² with the given sequence:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

The second operations are different, therefore calculate the differences between the second operations:

$3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18$

As the differences are the same, we need to add 5n as the second operation:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2 &-2 & -2 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.

Therefore, the nth term of the quadratic sequence is:

3n² + 5n - 2

6 0

2 years ago

2x + 4y = 14 3x - 4y = -39

cestrela7 [59]

Answer:

2x + 4y = 14 = x= −2y+7

3x - 4y = -39= x= 4=3 y−13

Step-by-step explanation:

5 0

3 years ago

A line representing Car B would have a parallel slope if:

Lerok [7]

Answer:

you add an image

Step-by-step explanation:

6 0

3 years ago

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The length of the sides of a square is 10 meters. Find the length of the diagonals of the square

BaLLatris [955]

｡☆✼★ ━━━━━━━━━━━━━━ ☾

Use Pythagoras' theorem:

a^2 + b^2 = c^2

Sub the values in:

10^2 + 10^2 = c^2

200 = c^2

Square root to find the answer:

c = 14.14

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- Ally ✧

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3 years ago

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What paces back and forth on the ocean floor

eduard

the answer is A nervous wreck

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3 years ago