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Answer:

[tex]Z_{1} Z_{2} = 3 i[/tex]

Step-by-step explanation:

Step(i):-

Given z 1 = 3(cos 37° + i sin 37°)

          z 2 = (cos 53° + i sin 53°)

by using complex numbers

      [tex]Z_{1} = r_{1} ( cos\alpha_{1} + isin\alpha_{1} ) = r_{1} cis\alpha _{1}[/tex]

      [tex]Z_{2} = r_{2} ( cos\alpha_{2} + isin\alpha_{2} ) = r_{2} cis\alpha _{2}[/tex]

step(ii):-

now

   [tex]Z_{1} Z_{2} = r_{1} r_{2} cis (\alpha _{1} + \alpha _{2})[/tex]

       z ₁ = 3(cos 37° + i sin 37°) = 3 c i s 37°

       z ₂ = (cos 53° + i sin 53°) = c i s 53°

we will use formula

     [tex]Z_{1} Z_{2} = r_{1} r_{2} cis (\alpha _{1} + \alpha _{2})[/tex]

     [tex]Z_{1} Z_{2} = 3 X 1 cis (37 + 53) = 3cis (90) = 3 cis(\frac{\pi }{2} )[/tex]

    [tex]Z_{1} Z_{2} = 3(cos(\frac{\pi }{2} ) + isin(\frac{\pi }{2}))[/tex]

    [tex]Z_{1} Z_{2} = 3(0 + i (1)) = 3 i[/tex]

Conclusion:-

       [tex]Z_{1} Z_{2} = 3 i[/tex]

Answer:

2i

Step-by-step explanation:

z 2 = 2/3(cos53° + isin53°

I got it right on odyssey ware

Answer:

event A and B are independent because  P(A and B)  = P(A) x P(B) = 0.15

Step-by-step explanation:

When two events are independent, the probability of both occurring is the product of their separate probabilities, as expressed below;

P(A and B)  = P(A) x P(B)

Given;

P(A) =  0.25

P(B) = 0.60

P(A and B) = 0.15

Now, let's check if  P(A and B) will be equal to P(A) x P(B)

P(A) x P(B) =  0.25 x 0.60 = 0.15

P(A and B)  = P(A) x P(B), thus event A and B are independent.

Answer:

61 3/5

Step-by-step explanation:

we realize that 8 4/5 can be written as [8 + (4/5)]

hence 7 x 8 4/5

= 7 x [8 + (4/5)]

= 7 [8 + (4/5)]   (use the distributive property, see attached for reference)

= 7(8) + 7(4/5)

= 56 + 28/5  (convert 28/5 into mixed fraction)

= 56 + 5 3/5

= 61 3/5 (answer)

Answer:

I'm not 100% sure but I believe the answer is 27

because -48/-4=12

12+15=27

Answer:

Write the equation and go backwards.

N - 15 x -4 = -48

Instead of multiply divide and add instead of subtract

-48/-4=12

12+15=27

check if 27 is correct. 27-15=12 x -4 = -48

27 is your number. Hope this helps

Step-by-step explanation:

Answer:

one pint

Step-by-step explanation:

This is because one pint is larger than one cup, there are two cups in a pint.

One milliliter is way smaller than one liter and there are 0.473176473 liters in a pint.

Answer:

pint

Step-by-step explanation:

1 Pint is equal to 0.47317647299 liter.

Liter and Pint are the largest on there, and pint is bigger.

Hope this helps! :)

Answer:

answer is -27 a^3b^6

Step-by-step explanation:

use power rules (b^n)^m = b^(n⋅m)

Answer:

tan 30 = height of building / 40

height = 40 × 1/√3=40/√3

or = 23.1 feet

Answer:

Side AB is 10 cm.

Step-by-step explanation:

The given quadrilaterals ABCD and EFGH are similar.

From the given figure, we can observe the following angles and sides are corresponding.

[tex]\angle A = \angle E=90^\circ\\\angle B = \angle F=63^\circ\\\angle C = \angle G=117^\circ\\\angle D = \angle H=90^\circ[/tex]

Ratio of corresponding sides will be equal:

AB:EF = BC: FG = CD:GH = DA:HE

We have to find the side AB.

Given the sides

EF = 5 cm

BC = 9 cm

DA = 8 cm

EH = 4 cm

So, ratio DA:EH = 8:4 = 2:1

We know that ratio of corresponding sides will be same:

AB:EF = DA:EH

[tex]\Rightarrow \dfrac{AB}{5} = \dfrac{2}{1}\\\Rightarrow AB = 10 cm[/tex]

So, side AB is 10 cm.

Answer:

M=2

Step-by-step explanation:

m=2 Make sure to move the terms, then collect the like terms, then subtract, then divide both sides by 6

Answer:

m = 2.

Step-by-step explanation:

-7 + 4m + 10 = 15 - 2m

4m + 2m = 15 + 7 - 10

6m = 12

m = 2.

c is the lowest range

a has the highest y incerpt

d is the best value

Answer: 55  

Step-by-step explanation:

2/5  * x = 22

2/5x = 22

x=  55

Answer:

1/9

Step-by-step explanation:

3/8 = 1/3

1/3 × 1/3 = 1/9

Answer:

1/9

Step-by-step explanation:

3/9 of original recipe

3/9=1/3 (on simplifing) Is the recipe we want to make

so 1/3 of the recipe we want to make

=(1/3) * (1/3)

=1/9

Hope it helps, Pls Marks as Brainliest!!

Answer:

V≈628.32 units³

Step-by-step explanation:

I used the formula:

V=πr2h/3 (h/3 as in a fraction)

Hope this helps!

The answer is 628.32

because the formula is

V=πr2h/3

Answer:

7 days

Step-by-step explanation:

Based on the amount of iced tea in the pitcher and the amount drank per day, you will run out of iced tea in 7 days.

The total number of cups drank per day is:

= 0.75 + 1.75

= 2.5 cups

With 2.5 cups being drank per day, the pitcher would last:

= Pitcher quantity / Cups per day

= 17.5/2.5

= 7 days

In conclusion, you will run out after 7 days.

Find out more at https://brainly.com/question/13426420.

Answer:

50/50

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

399,876

Step-by-step explanation:

So, 400,000 DVD sales with a 31% decline means in the first year following, there will be a decline of 124,000 DVDs sold. So we need to take 400,000-124,000 which equals a starting point for your two is 276,000 dvds. Then, add 123,876, which gives you 399,876.

The area of a 2D form is the amount of space within its perimeter. The area of the composite figure is 249 cm².

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The area of the composite figure can be written as,

Area = ABCG + DEFG =  (4×10.5) + (11.5×18) = 42+207 = 249cm²

Hence, the area of the composite figure is 249 cm².

Learn more about Area:

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Answer:

The theoretical probability is greater than the experimental probability of landing on an even number. The experimental  probability is 72/120 and the theoretical probability is 80/120.

Step-by-step explanation:

Experimental probability of landing on an even number: (30+25+17)/120 = 72/120 = 0.6

Even outcomes: 4

Total outcomes: 6

Theoretical probability of landing on an even number: 4/6 = 0.67

After 120 spinners it is expected 4/6*120 = 80 even results

Answer:

(2b)

Step-by-step explanation:

Answer:

x=51

Step-by-step explanation:

Formula:  35+16=x

Step 1: Simplify both sides of the equation.

35+16=x

(35+16)=x(Combine Like Terms)

51=x

51=x

Step 2: Flip the equation.

x=51

Hope this helps.

Answer:

(1,5)

Step-by-step explanation:

plug in the x and y values to see if they are equal in the equation. If not, then you know the answer is wrong.

Answer: if you need help ask

Step-by-step explanation:

First you start by finding a problem

Next you ask someone to help you with the problem, simple :)

Answer:

3141.59

Step-by-step explanation:

Answer:

[tex]3141.59 \: \: {ft}^{3} [/tex]

Step-by-step explanation:

[tex]V

=

π

{r}^{2}

\frac{h}{3}

\\

=

π

·

{10}^{2}

·

\frac{30}{3}

\\

≈

3141.59265

[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

2/2

Step-by-step explanation:

There are only red and green jump ropes so she is for sure going to get a red or green jump rope. If she wants specifically a red or green jump rope her chances are 1/2.

Answer:

Step-by-step explanaAnswer:

\frac{-2y+5x}{3x-2y}

Step-by-step explanation:

Given:

\frac{\frac{-2}{x}+\frac{5}{y}}{\frac{3}{y}-\frac{2}{x}}

To simplify this expression, first make the addition and the subtraction, to get:

\frac{\frac{-2y+5x}{xy}}{\frac{3x-2y}{xy}}=

Next, simplify the two denominators, to get:

\frac{-2y+5x}{3x-2y}tion:

So the right answer is of option B.

Look at the attached picture

Hope it will be helpful to you ..

Answer:

5 helmets

31 caps

8.25, 16.50 24.75 33 x 10 = 330

330/2 = 165 = 20 helmets

363.50 - 165 = 198.50

5 x 21.50 = 107.50 (+ 11 x 8.25 = 16.50+24.75 +24.75+24.75 = 49.50+41.25) =£91 + 107.50 =  198.50

20+11 = 31

31 caps

5 helmets

Step-by-step explanation:

There are 10 helmets did the coach purchase.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

A baseball coach purchased a total of 28 helmets and caps.

And, Each helmet cost $21.50, and each cap cost $8.25. and the coach spent a total of $363.50.

Let number of helmets = x

And, Number of caps = y

Here, A baseball coach purchased a total of 28 helmets and caps.

Hence, We get;

⇒ x + y = 28  ..(i)

And, Each helmet cost $21.50, and each cap cost $8.25. and the coach spent a total of $363.50.

Hence, We get;

⇒ 21.50x + 8.25y = 363.50

⇒ 5 (4.30x + 1.65y) = 5 × 72.7

⇒ 4.30x + 1.65y = 72.7  .. (ii)

Multiply by 4.30 in (i) ad subtract from (ii);

⇒ 4.30x + 4.30y - 4.30x - 1.65y = 120.4 - 72.7

⇒ 2.65y = 47.7

⇒ y = 18

And, From (i);

⇒ x + y = 28

⇒ x + 18 = 28

⇒ x = 10

Hence, Number of helmets = 10

Learn more about the mathematical expression visit:

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Answer:

x=-3   x=-2

Step-by-step explanation:

x^2 = 5x-6

Subtract x^2 from each side

x^2 - x^2 = -x^2 -5x-6

0 = -x^2 -5x-6

0 =-(x^2 +5x+6)

Factor

0 = (x+3)(x+2)

Using the zero product property

0=x+3   0=x+2

x=-3   x=-2

Answer:

6

Step-by-step explanation:

Answer:

6 units on edge

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

width = 2 units

Step-by-step explanation:

If the length of a rectangle is (x) units, then that means that the width of a rectangle is x - 4 units.

the area of a rectangle is length * width

so just substitute the values that we have now.

x (length) * (x-4) width = 12 (area of rectangle)

so that gives us

x^2 - 4x =12

subtract 12 from both sides

x^2 - 4x - 12 =0

now factor this equation

x^2 + 2x - 6x -12 = 0

x(x+2) - 6(x+2) = 0

(x-6)(x+2) = 0

x = 6, or x = -2 REMEMBER THAT VALUE OF x = LENGTH, IT CANNOT BE NEGATIVE AS YOU CANT HAVE NEGATIVE VALUE OF A SIDE

length = 6, and width = 6 -4 = 2

Answer:

W=2 units

Step-by-step explanation:

Length=L

Width=L-4

Area of a rectangle= L*W

L(L-4)=12

L^2-4L=12

L^2-4l-12=0

Now we have a quadratic equation

(L-6)(L+2)=0

L=6, L=-2

L cannot be -2 because it is negative, so L must be 6.

BUT it is asking for the width

and it is given that the width is the length minus 4 units, so

6-4= 2 units