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Masteriza [31]
3 years ago
11

Mrs. Clever mixes 1.24 liters of red paint with 3 times as much blue paint to make purple paint. She pours the paint equally int

o 5 containers. How much blue paint is in each container? Give your sender in liters
Mathematics
1 answer:
Contact [7]3 years ago
7 0
Amount of blue paint = 1.24 x 3
= 3.72
amount of blue paint in each container = 3.72/5
= 0.744

0.744 litres of blue paint is in each container.
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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
Troy's family is going to the beach for vacation. They plan to drive at the posted speed limit of 65 miles per hour and drive 5
Elena-2011 [213]
The answer is A) the number of miles
4 0
3 years ago
What is x?<br>(4/5)^x=64/125​
ankoles [38]

Answer:

x = 3

Step-by-step explanation:

(4/5)^x = 64/125​ means that 4^x / 5^x = 64/125

x can only be 3 because 4^3 = 64 and 5^3 = 125

Please mark Brainliest :)

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3 years ago
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aalyn [17]
To get the answer, multiply 9.99 x 17.4 yards. That will give you the answer 173.826. That rounds to 173.83
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Write the polynomial in standard form. 4g-g^3+3g^2-2
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