Which model represents the product 6×34?

Answer:

Correct answer: a) -8

Step-by-step explanation:

Complex Numbers

A complex number z in polar form is expressed as

[tex]z=r(\cos\theta+\mathbf{i}\sin\theta)[/tex]

The nth power of a complex number in polar form is:

[tex]z^n=r^n(\cos(n\theta)+\mathbf{i}\sin(n\theta))[/tex]

If the complex number is given in rectangular form

[tex]z=x+\mathbf{i}y[/tex]

then the values of r and θ are given by:

[tex]r=\sqrt{x^2+y^2}[/tex]

[tex]\displaystyle \theta=\arctan\left(\frac{y}{x}\right)[/tex]

The given complex number is:

[tex]z=1-\mathbf{i}\sqrt{3}[/tex]

The value of r is:

[tex]r=\sqrt{1^2+(-\sqrt{3})^2}[/tex]

[tex]r=\sqrt{1+3}=2[/tex]

r=2

Calculating the angle:

[tex]\displaystyle \theta=\arctan\left(\frac{-\sqrt{3}}{1}\right)[/tex]

[tex]\displaystyle \theta=\arctan(-\sqrt{3})[/tex]

Since the number is in the quadrant IV, the angle is:

[tex]\theta=-60^\circ[/tex]

Thus, z is expressed in polar form as:

[tex]z=2(\cos(-60^\circ)+\mathbf{i}\sin(-60^\circ))[/tex]

Calculating:

[tex]z^3=2^3(\cos(-180^\circ)+\mathbf{i}\sin(-180^\circ))[/tex]

Given cos 180°=-1 and sin(-180°)=0

[tex]z^3=8(-1+0)[/tex]

[tex]z^3=-8[/tex]

Correct answer: a) -8

Answer:

A

Step-by-step explanation:

just finished test

Answer: its the third one

Step-by-step explanation:

:)

Answer:

A shape can have more than one line of symmetry. Thus a rectangle has two lines of symmetry, an equilateral triangle has three lines of symmetry, and a square has four. A circle has an infinite number of lines of symmetry since it can be folded about any diameter.

Step-by-step explanation:

Answer: E

Step-by-step explanation: All of the sides are the same length

Answer:

the answers is 3 over 2 in fraction form

Answer:

1 1/2 or 3/2

Steps:

As we know .5 = 1/2

If we take one the 1 out of 1.5 we can use it to connect 1 and 1/2

Answer:

37.5 miles

Step-by-step explanation:

We can find the rate of conversion by dividing kilometers by miles. 5÷8=1.6, so 1.6 km = 1 mile. Now we can divide 60 by 1.6 to find miles.

[tex]60/1.6=37.5[/tex]

Hope this helped!

Answer:

96 km

Step-by-step explanation:

I try it its 96 km

Trust me

Answer:

x = 2

y = -3

z = 4

( 2 , -3, 4 )

Step-by-step explanation:

x + y + z = 3 ---- i

x – y =5 ---- ii

y - z = -7 ---- iii

ii + iii

x - z = -2 ---- iv

i + ii

2x + z = 8 --- v

iv + v

3x = 6

x = 2

x=2 substitute for v

z = 4

x =2 substitute for ii

y = -3

Answer:

second option :)

Step-by-step explanation:

Answer:

B.

StartLayout Enlarged left-brace 1st Row 3 x squared minus 4 y squared = 25 2nd row negative 12 x squared + 4 y squared = 22 EndLayout

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

8 x 9 = 72

72 ÷ 2 = 36

Find the measurements of the height and length then multiply them together.

Now, divide the sum by two because a triangle has half the area of a square's area.

Answer:

there are 30 right-handed players on the team

Answer:

3x - y = -1

Step-by-step explanation:

y - y₁ = m(x - x₁)

substitute (1,4) in for (x₁, y₁) respectively and the slope of 3 in for m

y -4 = 3(x - 1)

distribute 3 to (x - 1)

y - 4 = 3x -3

isolate 3x by itself by adding 3 to both sides

y - 1 = 3x

subtract y from each side

-1 = 3x - y

and just flip around the equation to make it look nicer

3x - y = -1

Answer:

180 boys

Step-by-step explanation:

If there is a ratio of 9 boys : 11 girls

9 + 11 = 20 total

And if there are 400 students total in the school

400/20 = 20.

9 * 20 = 180

11 * 20 = 220

So the ratio of 400 pupils would now be 180 boys: 220 girls

Answer: m∠EFG = 70

Step-by-step explanation:

m∠EFG = 2x35

m∠EFG = 70

In conclusion the answer is 70

Answer:

no

Step-by-step explanation:

Answer:

No

Because 5 and 1 have the same output as 1.

Answer:

a

Step-by-step explanation:

Answer:

Well it seems like you figured it out, thanks for the points :)

Answer:

-11

Step-by-step explanation:

Triangles have 180 degrees

using the vertical angle theory we know that 80 and 60 are angles

We can subtract them from 180 to get 40 left

this minus 51 is -11

x is -11

Answer:

x − 9 x ^2 − 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

We want to reduce the radical. In order to do that, we want to find the factors of 96 that are square numbers

The factors of 96 are:

[tex]1, 96, 2, 48, 3, 32, 4, 24, 6, 16...[/tex]

16 is a square number, so we can rewrite

[tex]\sqrt{96} = \sqrt{16*6} = \sqrt{16} * \sqrt{6} = 4\sqrt{6}[/tex]

Answer:

= -32a+64b

Step-by-step explanation:

thats the answer

Answer: 0.555... miles per hour.

Step-by-step explanation: 5/9 = 0.555...

Answer: $7.25 at part-time job

$9.00 every time lawn mowed

so he would get 33.33 day so we will just say 33 times to get 300 dollars if he gets $9 for mowing. And 41.37 hours to get $300 and he would have to use x and y graph to find the boundary line.

Step-by-step explanation:

divide

Step-by-step explanation:

But i think I know what you need to do so first count the graph like see where it is pointed at then divide and u get ur answer Again im not sure but maybe

Answer: 12 is the square root of 144

Step-by-step explanation:

Answer:

Just getting points i hope u find the answer tho :))

Step-by-step explanation: