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3 years ago

Operations with Complex NumbersSimplify.1) 1 + 6i3) 3i + i5) -1 – 8i- 4 - i

Mathematics

1 answer:

kogti [31]3 years ago

7 0

1. The answer is already in its simplest form.
3. 3i + i is equal to 4i.
5. Combining like terms results in -5 - 9i.

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umka21 [38]

Answer:

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2 years ago

The function f(x) = x2 + 6x + 3 is transformed such that g(x) = f(x − 2). Find the vertex of g(x).

garri49 [273]

Answer:

(-1,-6)

Step-by-step explanation:

$f(x)=x^2+6x+3$

$g(x)=f(x-2)$

$g(x)=(x-2)^2+6(x-2)+3$ (Replaced x in f with (x-2))

$g(x)=x^2-4x+4+6x-12+3$ (Used $(x+b)^2=x^2+2bx+b^2$ and distributive property)

$g(x)=x^2-4x+6x+4-12+3$ (Gathered like terms)

$g(x)=x^2+2x-5$ (Simplified)

The vertex of a parabola occurs at $(\frac{-b}{2a},g(\frac{-b}{2a})$ .

Let's find $\frac{-b}{2a}$ first.

$\frac{-2}{2(1)}=-1$

Now we can obtain $g(\frac{-b}{2a})$ which is $g(-1)$ in this case:

$g(x)=x^2+2x-5$

$g(-1)=(-1)^2+2(-1)-5$

$g(-1)=1-2-5$

$g(-1)=-1-5$

$g(-1)=-6$ .

The vertex is (-1,-6).

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3 years ago

How can $54,000 be invested part at 8% annual simple Interest and the remainder at 10% annual simple interest so that the intere

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Answer:

0.08x = $5400-0.1x Add 0.1x to both sides of the equation.

0.18x = $5400 Divide both sides by 0.18

x = $3000 and $54000-$3000 = $24000

$3,000 is invested at 8%

$2,400 is invested at 10%

Step-by-step explanation:

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In order to match each of the pairs you need to divide the numerator by the denominator to make it into a decimal.

Below are the pairs:

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13/20 = 65%

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3/4 = 75%

3/5 = 60%

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2 years ago

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Minutes. Because you cannot concert minutes to hours.

1 hour= 60 Minutes
2 hours= 120 Minutes

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3 years ago

Read 2 more answers

Operations with Complex NumbersSimplify.1) 1 + 6i3) 3i + i5) -1 – 8i- 4 - i​

Operations with Complex NumbersSimplify.1) 1 + 6i3) 3i + i5) -1 – 8i- 4 - i