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1 year ago

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A pet store has three fish tanks each holding a different volume of water in a different number of fish to a holds 4 L and five

fish tank bee holds 100 L in office tanks tea or 108 L and 23 fish. order the tanks by volume per fish from least to greatest.

1 answer:

Karolina [17]1 year ago

7 0

4l would be the least and 100l would be nect and then 108l

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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:

<u>Given sequence</u>:

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

Calculate the <u>first differences</u> 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 <u>second differences:</u>

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

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

The <u>coefficient</u> of the n² term is <u>half of the second difference</u>.

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 <em>between</em> 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

1 year ago

How many ounces are in 4 pounds and 7 ounces?

hram777 [196]

Answer:

4*16=64. 64+7=71. 71 is the answer

7 0

3 years ago

Can someone plz help me with this one problem plz!!!

Archy [21]

It’s doesn’t satisfy the equation

6 0

2 years ago

Read 2 more answers

These equations take their y-values from the set (4, 5, 6, 7, 8). Arrange the equations in decreasing order of the values of y t

Advocard [28]

9514 1404 393

Answer:

a, c, b

Step-by-step explanation:

Collect terms, subtract the constant, divide by the y-coefficient.

(a) 4y + (y - 1) = 29 ⇒ y = 6

(c) (2y + 3) - 4 = 9 ⇒ y = 5

(b) 4y - y + 1 = 13 ⇒ y = 4 . . . . . this equation is not what you have written

__

<em>Additional comment</em>

The second equation suffers from a typo, so your answer may vary.

3 0

2 years ago

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Which of the following represents the zeros of f(x) = 6x3 + 25x2 − 24x + 5?

cestrela7 [59]

F(-5) = 6(-5)^3 + 24(-5)^2 - 24(-5) + 5 = 0
so x = -5 is one zero.

7 0

3 years ago