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3 years ago

Find the additive inverse of -7+5i.

Mathematics

1 answer:

Deffense [45]3 years ago

4 0

Answer:

Required additive inverse is $-7-5i$ .

Step-by-step explanation:

Given number is $-7+5i$ .

Now we need to find about what is that additive inverse of the given number $-7+5i$ .

We know that if complex number is $a+bi$ then it's additive inverse is given by $a-bi$ .

Basically we need to change the sign of imaginary term.

imaginary term in given number $-7+5i$ is +5i.

Changing sign of +5i gives -5i.

Hence required additive inverse is $-7-5i$ .

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Can you help on question 22?!

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Answer:

I think it may be B (d-$5 )

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3 years ago

Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

$b_n = a_{n+1} - a_n$

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

$2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)$

Then

$a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)$

$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

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2 years ago

A.) which of these expressions is equivalent to 4 x x

Law Incorporation [45]

Answer:

a) The correct option is C: 4x

b) The correct option is B: 2x

Step-by-step explanation:

a) Usually when we have a real number multiplying a variable, we do not need to write the multiplication symbol.

So instead of writing:

4×x

We can write:

And this will be equivalent.

Then in this case the correct option is C.

b) We know that if we have the multiplication of A by n, this will be equivalent to add A n times.

Then if we have the sum of A, for example, 4 times, we have:

A + A + A + A

And this can be written as 4*A

In this case, we have the expression x + x.

So we are adding x two times, then this can be written as: 2*x, or, as we said earlier, this also can be written as 2x.

Then the correct option is option B.

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3 years ago

Use synthetic division to solve (2x^3+4x^2-35x+15) divided by (x-3) What is the quotient?

Salsk061 [2.6K]

Answer:

Step-by-step explanation:

The only thing you need to watch carefully is the divisor which in this case is x - 3. The divisor, in synthetic division, is the number that will make the binomial go to 0.

x - 3 =0

x = 3

So the divisor is 3.

3 || 2 4 -35 15

6 30 -15

======================

2 10 -5 0

So the quotient is

2x^2 + 10x - 5 with no remainder

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3 years ago

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12.5% is what in fraction form?

Serggg [28]

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3 years ago

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