Question 1 Imaginary & Complex Numbers-Addition & Subtraction Solve the following: (7 – 21) – (2+61) = O 9 +82 O 5 - 42 0 5 - 82 0 5+ 8i​

Answer:

$67.50

Step-by-step explanation:

You would just multiply 4.5x15

Hope this helps!

-AxekickNebulite

Answer:

We kindly invite you to see the result in the image attached below.

The number in polar form is [tex]z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}[/tex].

Step-by-step explanation:

A complex number is represented by elements of the form [tex]a + i\,b[/tex], for all [tex]a[/tex], [tex]b[/tex] [tex]\in \mathbb{R}[/tex]. The first part of the sum is the real component of the complex number, whereas the second part of the sum is the imaginary component of the complex number. The real component is located on the horizontal axis and the imaginary component on the vertical axis.

Now we proceed to present the point on the graph: ([tex]a = 6[/tex], [tex]b = 3[/tex])  We kindly invite you to see the result in the image attached below.

The polar form of the complex number is defined by:

[tex]z = r\cdot e^{i\cdot \theta}[/tex] (1)

Where:

[tex]r[/tex] - Magnitude of the complex number, dimensionless.

[tex]\theta[/tex] - Direction of the complex number, measured in radians.

The magnitude and the direction of the complex number are defined by the following formulas:

Magnitude

[tex]r =\sqrt{a^{2}+b^{2}}[/tex] (2)

Direction

[tex]\theta = \tan^{-1} \frac{b}{a}[/tex] (3)

If we know that [tex]a = 6[/tex] and [tex]b = 3[/tex], then the polar form of the number is:

[tex]r =\sqrt{6^{2}+3^{2}}[/tex]

[tex]r = 3\sqrt{5}[/tex]

[tex]\theta = \tan^{-1} \frac{6}{3}[/tex]

[tex]\theta \approx 0.352\pi \, rad[/tex]

[tex]z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}[/tex]

The number in polar form is [tex]z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}[/tex].

Answer:[tex]\frac{11}{-2}[/tex]

Step-by-step explanation:

ok so I'm going to try to show it the best c an

m = slope

the equation you use is

[tex]\frac{y2-y1}{x2-x1} =[/tex] m

so when using that formula with the cords, you get

[tex]\frac{4-(-7)}{-6-(-4)}[/tex]

and then subtract everything and you'll get

[tex]\frac{11}{-2}[/tex]

Answer:

C would  be your answer

Step-by-step explanation:

Answer:

[tex]\displaystyle \frac{d}{dx}[(4x + 1)^2] = 8(4x + 1)[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = (4x + 1)^2[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

x=17. I think.....

Step-by-step explanation:

Answer:

x = 17

Step-by-step explanation:

Since the two angles are vertical to each other they have the same measure.

x + 35 = 3x + 1 (subtract 1 on both sides)

x + 34 = 3x (subtract x on both sides)

34 = 2x (divide by 2 on both sides)

17 = x

Hope this helps ya!!

Answer:

A.

Step-by-step explanation:

I believe the answer is A. (Line JK and line LM will be parallel) because lines EF and GH are parallel. Therefore if the are just reflected, the new set of lines will also be parallel.

EF: (-9,1) (-4,9)

[tex]\frac{1-9}{-9+4}[/tex] = [tex]\frac{-8}{-5}[/tex] = [tex]\frac{8}{5}[/tex] or 1.6

GH: (-5,-2) (0,6)

[tex]\frac{-2 - 6}{-5-0}[/tex] = [tex]\frac{-8}{-5}[/tex] = [tex]\frac{8}{5}[/tex] or 1.6

Same slope and different y-intercept means the lines a parallel

Answer:

4

Step-by-step explanation:

If the sum is 10 and 6 is one of the numbers that makes up 10, all you have to do is subtract 6 from 10 and you get 4.

hope this helps

sorry if it wrong

Answer:

Step-by-step explanation:

YESS

Because these are f r e e points

The distance between (-8,0) and (-5,3) in the coordinate plane is 9 units.

Given that the coordinates of points in the coordinate plane are (-8,0) and (-5,3).

We are required to find the distance between the given points.

Distance is basically a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to physical length or an estimation based on other criteria.

Distance between (-8,0) and (-5,3)=[tex]\sqrt{(-5+8)^{2} +(3-0)^{2} }[/tex]

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

=[tex]\sqrt{9+9}[/tex]

=[tex]\sqrt{81}[/tex]

=9 units

Hence the distance between (-8,0) and (-5,3) in the coordinate plane is 9 units.

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Answer:

b

Step-by-step explanation:

it b yeah ddddddddddddddddddd

Answer:

-6

Step-by-step explanation:

The slope of a perpendicular line has the slope of the opposite and reciprocal of the current line. We would get -1/6 and then -6.

Answer:

a = 10 and b = 6

Step-by-step explanation:

I am having a little trouble reading the numbers, but I think that I see

[tex]\frac{7^{2} 7^{8} }{7^{4} }[/tex]

If we wrote this in expanded form, it would look like:

[tex]\frac{7x7x7x7x7x7x7x7x7x7}{7x7x7x7}[/tex]  How many 7s are on the top?  10  That is the answer to a.  The product of powers principle tells us that if we are multiplying powers with the same bases we add the exponents 2 + 8 = 10

[tex]\frac{^{10} }{7^{4} }[/tex]

Now it looks like

[tex]\frac{7x7x7x7x7x7x7x7x7x7}{7x7x7x7}[/tex]  if we cross the 7's out in the top and the bottom, we are left with 6 7's on the top.  That is the answer to b.

The quotient of powers principle tells us that if we are dividing powers with the same bases, we can subtract the exponents (10 -4 = 6)

Answer:

$427

Step-by-step explanation:

6.10 x 70 (the weight of both steaks combined) = 427

Answer:

the amount after 5 years using compound continuously is $135.03

Step-by-step explanation:

The computation of the amount after 5 years using compound continuously is as follows

= Principal × e^(rate × time period)

= $110 × e^(4.2% × 5)

= $110 × 1.227525065

= $135.03

Hence, the amount after 5 years using compound continuously is $135.03

We simply applied the above formula so that the correct value could come

And, the same is to be considered  

Answer:

5 weeks

Step-by-step explanation:

To find the answer to this question we have to write an equation for both situation and put them equal to each other.

Let's write an equation for Joe:

12x + 100

Now, for Jessica

6x + 130

Next, put them equal to each other:

12x + 100 = 6x + 130

Solve:

12x + 100 = 6x + 130

6x + 100 = 130

6x = 30

x = 5

Therefore, it will take 5 weeks for Joe and Jessica to have the same amount of cards.

Check:

12(5) + 100 = 6(5) + 130

60 + 100 = 30 + 130

160 = 160

I hope this helps!!

- Kay :)

Answer:

$43.74

Step-by-step explanation:

will pay= $45

10% of =$45×10/100=$4.5

so, $45-$4.5= $40.5

8% tax= $40.5×8/100 =$3.24

total= $43.74

Answer:

id say 10 but im dumn if get wrong do not star me 5 only one star

Step-by-step explanation:

Answer: 6 of the flowers are pink

Step-by-step explanation:

If 3/5 of the flowers are yellow you would convert the 3/5 into a 9 because 1/5 of 15 is 3 so you would multiply 3 by 3 to get nine. By doing this you will find out the 2/5 or the remaining flowers are pink which makes 6 pink flowers.

Answer:

1/2

Step-by-step explanation:

parallel slopes are exactly the same

Answer:

slope is 1/2

Step-by-step explanation:

the function y = 1/2 x+4 has the slope 1/2 because y=mx+b where m is slope

Tne slope of a parallel line to this function is the same m=1/2 because parallel lines have same slope

Answer:

C. 574.53

Step-by-step explanation:

Option C) is correct work done = 574.53.

Force = 15 pounds
distance = 50 feet
Ф = 40°

work done is product of force and cosine of displacement.

work done = force x displacement x cosФ
= 15 x 50 x cos40
= 15 x 50 x 0.76
= 574.53

Thus the required work done is 574.53 to pull the wagon.

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Answer:

c = 10

Step-by-step explanation:

Hypotnuse² = base²+height²

c²= 8²+6²

c²=64+36

= 100

100 = 10²

c = 10

Answer:

The answer is 1

Step-by-step explanation:

1/5 + 4/5 = 5/5

5/5 = 1

Answer:

20 hours

Step-by-step explanation:

Answer:

I think it is 90 and 100

Step-by-step explanation:

I used this equation: x is the speed of the slower train

910 = (5x + 10) + 5x

Answer:

The answer is 86 and 96 mph

Step-by-step explanation:

Givens

Train A

Distance traveled = d

time taken = 5 hours

rate traveled = r

Train B

Distance traveled = 910 - d

time taken = 5 hours

rate = r + 10

Formula

basically d = r * t

Solution

Train A: d/r = 5 or d = 5*r

Train B = (910 - d)/(r + 10) = 5    or

Substitute d = 5*r   into Train B

(910 - 5*r)/(r + 10) = 5        Multiply both sides by r + 10

(910 - 5r) = 5 * (r + 10)       Remove the brackets on both sides

910 - 5r = 5r + 50             Add 5r to both sides

910 = 5r + 5r + 50

910 = 10r + 50                  Subtract 50 from both sides

910 - 50 = 10r                  Combine the left

860 = 10r

10r = 860                         Divide by 10

r = 860/10

r = 86

r + 10 = 96

Check

Train A distance: 5*r = 5 * 86 = 430

Train B distance: 5*r = 5 * 96 = 480

Total =                                         910

Answer:

The solution to the system of equations be:

[tex]y=4,\:x=0[/tex]

As the consistent system of equations has only one solution, it is independent.

Step-by-step explanation:

Given the system of equations

[tex]3y + 2x= 12[/tex]

[tex]36 - 9y = -6x[/tex]

solving the system of equations

[tex]\begin{bmatrix}3y+2x=12\\ 36-9y=-6x\end{bmatrix}[/tex]

Arrange equation variables for elimination

[tex]\begin{bmatrix}3y+2x=12\\ -9y+6x=-36\end{bmatrix}[/tex]

[tex]\mathrm{Multiply\:}3y+2x=12\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:9y+6x=36[/tex]

[tex]\begin{bmatrix}9y+6x=36\\ -9y+6x=-36\end{bmatrix}[/tex]

so

[tex]-9y+6x=-36[/tex]

[tex]+[/tex]

[tex]\underline{9y+6x=36}[/tex]

[tex]12x=0[/tex]

[tex]\begin{bmatrix}9y+6x=36\\ 12x=0\end{bmatrix}[/tex]

solve 12x=0 for x

[tex]12x=0[/tex]

Divide both sides by 12

[tex]\frac{12x}{12}=\frac{0}{12}[/tex]

[tex]x=0[/tex]

[tex]\mathrm{For\:}9y+6x=36\mathrm{\:plug\:in\:}x=0[/tex]

[tex]9y+6\cdot \:0=36[/tex]

[tex]9y=36[/tex]

Divide both sides by 9

[tex]\frac{9y}{9}=\frac{36}{9}[/tex]

[tex]y=4[/tex]

Thus, the solution to the system of equations be:

[tex]y=4,\:x=0[/tex]

As the consistent system of equations has only one solution, it is independent.

Answer:

1) 150 kg

2) 97.5 kg

3) 5%

Step-by-step explanation:

Ratios of each metal to total mass of metal can be computed by dividing its corresponding value by the sum of all the values in the ratio

The ratio of zinc to metal = 6/(13 + 6 + 1) = 6/20 = 3/10

Let the total mass of the metal be X

Then mass of zinc = (3/5)X = 90 kg (given)

1) Multiplying both sides by 5/3 gives X = 5/3 x 90 = 150 kg which is the total mass of metal

2) Ratio of copper to metal mass = 13/20
Mass of copper = 13/20 x 150 = 97.5 kg

3) Mass of lead as a ratio of metal = 1/20 = 0.05

As percentage, multiply by 100 to get 0.05 x 100 = 5%

Dividing both sides by MK yields

[tex]\boxed{Y=\frac{V}{MK}}[/tex]

Answer:

n< -18

Step-by-step explanation:

Answer:

this is step by step

Step-by-step explanation:

||x+4| -7<5

|x+4|<12

{(x+4)+(-4)>–12 + (–4)

{(x+4)+(–4)<–12 + (–4)

{x+4–4>–12–4

{x+4–4<12–4

{x> – 16

{x<8

–16<x<8

x€(–16,8 )

I hope naka tulong