Find the distance between M and N. The locations of M and N are -10 and -20

Answer:

a) The standard form of [tex]z = 4\cdot (\cos 60^{\circ}+i\cdot \sin 60^{\circ})[/tex] is [tex]z = 2 + i\cdot 2\sqrt{3}[/tex], b) [tex]z = (2+i\cdot 3)^{6} = 1219.585 + i \cdot 1829.381[/tex].

Step-by-step explanation:

a) The standard form of the complex number is [tex]z = a + i\cdot b[/tex], [tex]\forall \,a,b \in \mathbb{R}[/tex]. If we get that [tex]z = 4\cdot (\cos 60^{\circ}+i\cdot \sin 60^{\circ})[/tex], whose standard form is obtained by algebraic means:

1) [tex]z = 4\cdot (\cos 60^{\circ}+i\cdot \sin 60^{\circ})[/tex] Given

2) [tex]z = (4\cdot \cos 60^{\circ})+i\cdot (4\cdot \sin 60^{\circ})[/tex] Distributive and Associative properties.

3) [tex]z = 2 + i\cdot 2\sqrt{3}[/tex] Multiplication/Result.

The standard form of [tex]z = 4\cdot (\cos 60^{\circ}+i\cdot \sin 60^{\circ})[/tex] is [tex]z = 2 + i\cdot 2\sqrt{3}[/tex].

b) The De Moivre's Theorem states that:

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

Where:

[tex]r =\sqrt{a^{2}+b^{2}}[/tex] and [tex]\theta = \tan^{-1} \left(\frac{b}{a}\right)[/tex].

If we know that [tex]z = (2+i\cdot 3)^{6}[/tex], then:

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

[tex]r =\sqrt{13}[/tex]

[tex]r \approx 3.606[/tex]

[tex]\theta = \tan^{-1}\left(\frac{3}{2} \right)[/tex]

[tex]\theta \approx 56.310^{\circ}[/tex]

The resulting expression is:

[tex]z = 3.606^{6}\cdot (\cos 56.310^{\circ}+i\cdot \sin 56.310^{\circ})[/tex]

[tex]z = 1219.585+i\cdot 1829.381[/tex]

Therefore, [tex]z = (2+i\cdot 3)^{6} = 1219.585 + i \cdot 1829.381[/tex].

Answer: x = 60

Step-by-step explanation: Notice that these two angles are vertical angles.

Whenever two lines intersect, a pair of vertical angle is always formed.

Now, vertical angles are always congruent.

So we can setup the equation 2x + 24 = 144.

Solving from here, we first subtract 24 from both sides to get 2x = 120.

Now dividing both sides by 2, we find that x = 60.

So x = 60.

Answer:

c. 60°

Step-by-step explanation:

[tex](2x +24)\° = 144\°\\\\2x+24\°=144\°[/tex]

Collect like terms and simplify

[tex]2x\° =144\°-24\°\\\\2x\°=120\°[/tex]

Divide both sides of the equation by 2 and simplify

[tex]\frac{2x}{2} = \frac{120}{2} \\\\x =60\°[/tex]

AB = x

BC = 3x

AC = 20 inches = AB + BC

Let's plug our values into the equation above.

20 inches = x + 3x

Combine like terms

20 inches = 4x

Divide both sides by 4

5 = x

AB = x = 5 inches

BC = 3x = 3(5) = 15 inches

The value of x is

✔ 5

The length of Line segment A B in inches is

✔ 5

The length of Line segment B C  in inches is

✔ 15

<3

In integers , we represent quantity of terms such as rise, above , increment by positive integers whereas its opposite such as fall,  below, decrement is denoted by negative integers.

1. an 8 degree rise in temperature

Required integer = 8

2. 47 feet below sea level

Required integer =  =  -47

3. a 19-yard gain

Required integer =  19

4. overdrawing(taken more money out of account than the account has) an account by $124

Required integer =  - 124

5. two strokes below par

Required integer =   -2

6. a 20-foot extension

Required integer =  20

Answer:

-2f

Step-by-step explanation:

Answer:

600

Step-by-step explanation:

0+.80x=60+.70x

-.70x=60-.70x

.10x=60

÷.10=÷.10

C=600

0+.80(600)=480

60+.70(600)=480

Answer:

The generated Taylor series is;

f(x) = 1/6 + (x-3)/36 + (x-3)^2/216 + (x-3)^3/1296......

Kindly note that the series here is truncated at the third derivative, but if wanted, evaluation could be more than this

Step-by-step explanation:

Here, we are to find the Taylor series generated by f at x = a

Mathematically;

f(x)= 1/(9-x)

The f(a) at this point is calculated below;

f(a) = 1/(9-3) = 1/6

The first derivative is calculated below;

f'(x) = 1/(9-x)^2

f'(3) = 1/6^2 = 36

The second derivative is calculated below;

f''(x) = 2/(9-x)^3

f''(3) = 2/(9-3)^3 = 2/6^3 = 2/216 = 1/108

The third derivative is calculated as follows

f'''(x) = 6/(9-x)^4

f'''(3) = 6/(9-3)^4 = 6/6^4 = 1/216..

The Taylor series is thus given by;

f(x) = f(a) + f'(a) (x-a) + f''(a) (x-a)^2/2! + f'''(a) (x-a)^3/3! +...

Substituting the values of 3 for a at each of the points , we obtain the Taylor series as shown below;

f(x) = 1/6 + (x-3)/36 + (x-3)^2*1/108*1/2 + (x-3)^3*1/216*1/6 +...

f(x) = 1/6 + (x-3)/36 + (x-3)^2/216 + (x-3)^3/1296......

Answer:[tex]5^{3}[/tex]

Step-by-step explanation:

Answer:

-5 to the forth power

Step-by-step explanation:

Answer:

10:4

Step-by-step explanation:

5:2=10:4 because 5 times 2 is 10,

and 2 times 2 is 4.

So they make up to be 10:4

Answer:

40 is the answer

Step-by-step explanation:

x+10-50

x+40

The population is the entire set of registered voters (11100) in the city. This is what the election officials care about, so they won't focus on any other city data.

Inside that population, the much smaller sample is generated to try to make an educated guess about what the population will do. In this case, the sample is the 400 people surveyed. If the sample was generated randomly enough, then it should be unbiased to give a good idea of what the population will do.

Answer:

[tex]-\frac{28}{99}[/tex]

Step-by-step explanation:

To divide a fraction by a fraction, flip the second fraction and change the divide sign into a multiplication sign.

[tex]\frac{4}{9}\div -\left(\frac{11}{7}\right)=\frac{4}{9} *-\frac{7}{11}[/tex]

Multiply:

[tex]-\frac{4*7}{9*11}[/tex]

[tex]-\frac{28}{99}[/tex]

Answer: -6

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

Rule: When multiplying or dividing two numbers with the same sign (both positive or both negative), the answer is positive. When multiplying or dividing two numbers with different signs (one positive and one negative), the answer is negative.

Here you have a negative number and a positive number. Since their signs are different, the product is negative.

(-3) * 2 = -6

Add the number he gave away to the number he has left.

28 + 4 = 32

He started with 32 books

Answer:

C

Step-by-step explanation:

Answer: c

Step-by-step explanation:

I just took the test and got it correct

Answer:

10×10=100

The grid has 100 squares

75 squares are shaded blue

so that is 75 out of 100 or 75/100

which 75/100 = 0.75 which equals 75%

Step-by-step explanation:

The answer is choice 4 which is 75%

Answer:

D

Step-by-step explanation:

Answer:

c the answer is c

Step-by-step explanation:

Answer:

j < 3

j > -1/5

Step-by-step explanation:

Question 1:

-j - 9 > -6

-j > 3

j < 3

Question 2:

-5j + 18 < 19

-5j < 1

j > -1/5

Hey there! I'm happy to help!

Let's call this number n. We can create the following equation.

(n+45)/2=5

Let's solve. We multiply both sides by 2.

n+45=10

We subtract 45 from both sides.

n=-35.

Have a wonderful day! :D

Answer:

n=-35

Step-by-step explanation:

Given:

Number  of Vegetarian Sandwich = 3

Number of Turkey Sandwich  = 7

Number  of  Pepperoni Pizza  = 8

Number  of  Cheese Pizza  = 10

To find:

The ratio which represents the number of orders for pepperoni pizza to cheese pizza.

Solution:

The ratio of number of orders for pepperoni pizza to cheese pizza is

[tex]\text{Ratio}=\dfrac{\text{Number of orders for pepperoni pizza}}{\text{number of orders for cheese pizza}}[/tex]

[tex]\text{Ratio}=\dfrac{8}{10}[/tex]

[tex]\text{Ratio}=\dfrac{4}{5}[/tex]

Therefore, the required ratio is 4:5 and option A is correct.

Answer:

4:5 and option A is correct.

Step-by-step explanation:

edge2020

Answer:

the degree is about 120

Step-by-step explanation:

b and a is about 60 something and so is b and c so add all that up and you get about 120 degrees.

Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

[tex]d = \sqrt{( {x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

( -2 , 1) and ( 4,3)

The distance is

[tex]d = \sqrt{( { - 2 - 4})^{2} + ({1 - 3})^{2} } \\ = \sqrt{ ({ - 6})^{2} + ({ - 2})^{2} } \\ = \sqrt{36 + 4} \\ = \sqrt{40} \\ = 2 \sqrt{10} \\ = \:6.324555[/tex]

We have the final answer as

Hope this helps you

Step-by-step explanation:

Hey there!!!

Given, the points are (4,3) and (-2,1).

Then,

x1=4 x2=-2

y1=3 y2=1

Now, Using distance formula,

[tex](distance ) = \sqrt{ {(x2 - x1)}^{2} + ( {y2 - y1)}^{2} } [/tex]

Put all values.

[tex](distance ) = \sqrt{ {( - 2 - 4)}^{2} + {(1 - 3)}^{2} } [/tex]

Simplify them.

[tex](distance ) = \sqrt{( { - 6)}^{2} + ( { - 2)}^{2} } [/tex]

[tex](distance ) = \sqrt{36 + 4} [/tex]

[tex](distance ) = \sqrt{40} [/tex]

(distance )= 6.3245 units.

Therefore, the distance between the points(4,3) and (-2,1) is 6.32units.

So, your answer is option B.

Hope it helps....

Answer: equation for length 34- (6.5 times 2)  that whole thing divided by 2

Step-by-step explanation:

You know the width and a rectangle has 2 PAIRS of equal sides so if you know the width you just have to multiply that  by 2  [ to account 4 the other side with the same length] and subtract that from the perimeter! Then you divide that answer by 2 to get what one side's length is!

hope that helped if it was not helpful sorry because i am a first grader :/

Answer:

2

Step-by-step explanation:

Hey there!

[tex]Answer:\boxed{2}[/tex]

[tex]Explanation:[/tex]

[tex](-6-4)/(-5)[/tex]

First reduce the expression and then cancel the common factors.

2

Hope this helps!

Answer: -3,-1, and 1.

Step-by-step explanation: You are given the relation R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)} The domain of the relation are all possible inputs and the range of the relation are all possible outputs. So, the inputs are : -3,-1,1; and the outputs are : -2,0,2. As a result, the domain is : -3,-1,1; and the range is : -2,0,2.

Answer:

An animal or insect that only eats vegetation, such as grasses, fruits, leaves, vegetables, roots and bulbs.

Step-by-step explanation:

Answer:

Plant eating dinosaurs

Step-by-step explanation:

Herbivores have the word herb in it which refers to it being a plant eating dinosaur so a carnivore has the word carn which also refers to it being a meat eating dinosaur.

Answer:

The correct answer is B :)

Step-by-step explanation:

The difference in the area of shape A and shape B is option B which is [tex]12x^{4}+12x^{3}+26x^{2} +8x+12[/tex].

Area of rectangle and square is the extent of surface rectangle and square exhibits into them. The area of rectangle is length * breadth and the area of square is side*side.

We have been given the length of shape A=[tex]7x^{2} +4x+8[/tex] and breadth be [tex]3x^{2} +2[/tex] and the side of shape B be [tex]3x^{2} +2[/tex].

Shape A looks like rectangle and shape B looks like square.

So the area becomes:

Area of shape A =[tex](3x^{2} +2) ( 7x^{2} +4x+8)[/tex]

we have to multiply both expressions

=[tex]21x^{4} +12x^{3} +24x^{2} +14x^{2} +8x+16[/tex]

=[tex]21x^{4} +12x^{3} +38x^{2}+8x+16[/tex]

Area of shape B=[tex](3x^{2} +2)(3x^{2} +2)[/tex]

=[tex]9x^{4} +6x^{2} +6x^{2} +4[/tex]

=[tex]9x^{4} +12x^{2} +4[/tex]

Difference=[tex]21x^{4}+12x^{3}+38x^{2} +8x+16-9x^{4} -12x^{2} -4[/tex]

=[tex]12x^{4} +12x^{3}+26x^{2} +8x+12[/tex]

Hence the difference between shape A and shape B is [tex]12x^{4} +12x^{3}+26x^{2} +8x+12[/tex].

Learn more about area at https://brainly.com/question/25965491

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