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dlinn [17]
3 years ago
6

Simplify the expression. Write your answer as a complex number. please help

Mathematics
1 answer:
tia_tia [17]3 years ago
8 0
The answer is
=15-8i
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Find the 21st term in the arithmetic sequence.<br> 3, 7, 11, 15, 19, ...
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The 21st term of the given arithmetic sequence is 83. The nth term of an arithmetic sequence is applied to find the required value where n = 21.

<h3>What is the nth term of an arithmetic series?</h3>

The nth term of an arithmetic sequence is calculated by the formula

aₙ = a + (n - 1) · d

Here the first term is 'a' and the common difference is 'd'.

<h3>Calculation:</h3>

The given sequence is an arithmetic sequence.

3, 7, 11, 15, 19, ....

So, the first term in the sequence is a = 3 and the common difference between the terms of the given sequence is d = 7 - 3 = 4.

Thus, the required 21st term in the sequence is

a₂₁ = 3 + (21 - 1) × 4

⇒ a₂₁ = 3 + 20 × 4

⇒ a₂₁  = 3 + 80

∴ a₂₁  = 83

So, the 21st term in the given arithmetic sequence is 83.

Learn more about the arithmetic sequence here:

brainly.com/question/6561461

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A protein mix claims to contain a bonus of 20% more mix than the usual size container. If the bonus size contains 18 ounces of m
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Answer:

The usual size of the container is 15 ounces.

Step-by-step explanation:

Consider the provided information.

A protein mix claims to contain a bonus of 20% more mix than the usual size container.

Let the usual size of the container was x ounces.

They increase 20% of usual size and the bonus size is 18 ounces.

Therefore, the new size should be:

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x(1+0.20)=18 (∴20%=\frac{20}{100}=0.20)

x(1.20)=18

x=\frac{18}{1.20}

x=15

Hence, the usual size of the container is 15 ounces.

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Step-by-step explanation:


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