Select the correct answer.
What is the standard form of this complex number?
3i + ( + 2i ) – (3 + 3i)

Answer: B

Step-by-step explanation:

It has to be B. None of the other answers make sense.

Answer:

30.06 kg

Step-by-step explanation:

480kg  960g = 480969g.

480960 / 16 = 3060g

30060g

30060g = 30.06kg.

Answer:

(b)

[tex]\displaystyle \frac{2005}{2006}[/tex]

Step-by-step explanation:

(a)

First, we have to prove that:

[tex]\displaystyle \frac{1}{x}-\frac{1}{x+1}=\frac{1}{x(x+1)}[/tex]

Operate:

[tex]\displaystyle \frac{1}{x}-\frac{1}{x+1}=\frac{x+1-x}{x(x+1)}[/tex]

Simplifying:

[tex]\displaystyle \frac{1}{x}-\frac{1}{x+1}=\frac{1}{x(x+1)} [1][/tex]

(b)

Now we use the above expression to find the sum:

[tex]\displaystyle S=\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+...+\frac{1}{2005\times 2006}[/tex]

Let's use [1] for each term of the sum:

[tex]\displaystyle \frac{1}{1\times 2}=\frac{1}{1}-\frac{1}{2}[/tex]

[tex]\displaystyle \frac{1}{2\times 2}=\frac{1}{2}-\frac{1}{3}[/tex]

[tex]\displaystyle \frac{1}{3\times 4}=\frac{1}{3}-\frac{1}{4}[/tex]

[tex]\displaystyle \frac{1}{2005\times 2006}=\frac{1}{2005}-\frac{1}{2006}[/tex]

Substituting:

[tex]\displaystyle S=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{2005}-\frac{1}{2006}[/tex]

Note the terms 1/2 and -1/2, 1/3 and -1/3, etc. are canceled out, leaving only the first and last terms:

[tex]\displaystyle S=\frac{1}{1}-\frac{1}{2006}=\frac{2006-1}{2006}[/tex]

[tex]\boxed{\displaystyle S=\frac{2005}{2006}}[/tex]

Answer:

[tex]\frac{3\sqrt{2} }{2}[/tex]

Step-by-step explanation:

Given

[tex]\frac{\sqrt{2} }{2}[/tex] + [tex]\frac{2}{\sqrt{2} }[/tex] ← rationalise the denominator by multiplying by [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex]

= [tex]\frac{\sqrt{2} }{2}[/tex] + ( [tex]\frac{2}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex] )

= [tex]\frac{\sqrt{2} }{2}[/tex] + [tex]\frac{2\sqrt{2} }{2}[/tex]

= [tex]\frac{3\sqrt{2} }{2}[/tex]

Answer:

what?

Step-by-step explanation:

karma

Answer:

x = 816 kilometers per hour.

Step-by-step explanation:

Given the following data;

Distance traveled by Kirk = 450km

Distance traveled by Thor = 408 km

Let the average driving speed of Thor be x.

Translating the word problem into an algebraic equation;

k = x + 6

We know that the time taken to cover a distance by an object with speed is given by the formula;

Time = distance/speed

Substituting into the equation, we have;

408/x = 405/x + 6

Cross-multiplying, we have;

408*(x + 6) = 405*x

408x + 2448 = 405x

408x - 405x = 2448

3x = 2448

x = 2448/3

x = 816 kilometers per hour.

Here are the steps, hope it helps!

Answer:

true

Step-by-step explanation:

hope you have a wonderful new year

Answer:

(2,3)

Step-by-step explanation:

it's the point of intersection

hope this helps, pls mark brainliest :D

Answer:

2,3 i believe 2 on the x axis and 3 on the y

Step-by-step explanation:

___________________________________________________________

Answer:

no. i*i = -1

2i*3i=-6

now if they meant complex numbers the answer is still no

(2+4i)(2-4i) = 4-8i+8i-16 = -12

___________________________________________________________

Answer: NA and Rb and there are 20 protons in calcium!

Step-by-step explanation:

Answer:

No. of protons = 20

No. of electrons = 20

No. of neutrons = 20

Step-by-step explanation:

Part 1 :

Na, K and Rb are in the same group.

So, K and Rb are the two elements that have the same properties as sodium ( Na ).

Part 2 :

Atomic Number of Calcium = 20

Note :

Atomic Number = No. of protons

Therefore,

No. of protons = 20

Note :

No. of neutrons = No. of protons.

Therefore,

No. of neutrons = 20

Calcium is the 20th element, with 20 protons. Since a stable atom has a net charge of 0, it must have 20 electrons.

Answer:

11+p-3 or 3+p-11

Step-by-step explanation:

depending if the p is negative or positive

Answer: x = 7

Step-by-step explanation: In order for a parallelogram to be a square, the angles at the corners must be 90 degrees, and the diagonals that bisect the corner angles must be 45 degrees.

4x + 17 = 45  Subtract 17 from both sides.

4x = 28   Divide both sides by 4

x = 7

Answer:

44

Step-by-step explanation:

(50+5)=55x.08= 4.4

55+4.4= 59.4

Answer:

$59.40

Step-by-step explanation:

$55 + $4.40 (8% tax) = $59.40

Answer:

1 is 3.5

2 is 480

3 is 15

4 is 2.5

5 is B and D

Answer:

1/2x + 5

Step-by-step explanation:

The y intercept is 5 & the slope is already given!

Answer:

350/ 10 = 35

Step-by-step explanation:

hope it helps!

........

Answer:

mean= 32+41+28+54+35+26+23+33+38+40/10

mean=350/10

mean= 35

Answer:

x is greater than or equal to 8.75 or 8 3/4

Step-by-step explanation:

So we first write the inequality 3 + 1.2c "is greater than or equal to sign" 13.5. Then we subtract 3, then divide both sides by 1.2 to isolate c. We get x "is greater than or equal to" 8.75.

Answer:

1. polynomial

2. equation

I hope it will be useful.

Probability theory, a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance.

Answer:

6%

Step-by-step explanation:

Interest = Principal x Rate x Time (in years)

30 = 500r

r = 3/50 or 6/100 which is 6%

Answer:

4 inches

Step-by-step explanation:

1 inch * 10 feet / 2.5 feet = 4 inches

Answer:

Lo: - 94o F

Step-by-step explanation:

Hi: 98oF

Difference: 192 degrees lower

Low: ?

Formula

98 - 192 = -94

That seems incredibly cold. I've lived through a day that was - 60oF and that was enough. (about - 51o C)

If you think in Celcius

The formula is

C =   5/9(F - 32)

C =  5/9 (-94 - 32)

C = 5/9 (-126)

C = -60

I think Siberia must be much colder than -60.

Answer:

A) Domain: All real numbers, excluding zero        (-∞, 0) ∪ (0, ∞)

Range: All real numbers, excluding zero      (-∞, 0) ∪ (0, ∞)

Step-by-step explanation:

Given:

The graph of the function [tex]f(x)=\dfrac{1}{x}[/tex].

To find:

The value of the function f(x), when x is close to zero.

Solution:

From the given graph it is clear that, f(x) approaches towards infinity and negative infinity as x approaches towards 0.

[tex]f(x)\to \infty[/tex] as [tex]x\to 0^+[/tex]

[tex]f(x)\to -\infty[/tex] as [tex]x\to 0^-[/tex]

In means, the value of must be very large positive value or very large negative if x is close to zero.

From the given options -10,000 is very large negative value.

So, the possible value of f(x) could be -10000 if x is close to 0.

Therefore, the correct option is A.

Answer:

When the temperature is 70° above freezing, the temperature is 70°C.

A temperature of –16°C is colder than –12°C.  

When the temperature is 7° below freezing, the temperature is –7°C.

A temperature of 10°C is colder than –12°C.

When the temperature is 70° above freezing, the temperature is 70°C.

A temperature of –8°C is colder than –12°C.

When the temperature is 7° below freezing, the temperature is –7°C.