Mrs. Ashton buys journals for the students in her language arts class. She pays $64.48 for all of the journals. If there are 26 students in her class, how much does each journal cost?

We have a group of 169 students that needs to be seated in a square formation. Then, the number of rows has to be the square root of 169 :-

[tex]r = \sqrt{169} = 13[/tex]

Then, a square of 13 rows and 13 columns will fit the 169 students.

If the number of students is 1024, then the number of rows N can be calculated as :-

[tex] {N}^{2} = 1024[/tex]

[tex]N = \sqrt{1024} [/tex]

[tex]N = 32[/tex]

169 students will seat in a 13×13 formation.

1024 students will seat in a 32×32 formation (N=32)

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Explanation:

We use De Moivre's Theorem. It says that if you started with

[tex]z = r*\left[\cos\left(\theta\right)+i*\sin\left(\theta\right)\right][/tex]

then raising both sides to the nth power leads to

[tex]z^n = r^n*\left[\cos\left(n*\theta\right)+i*\sin\left(n*\theta\right)\right][/tex]

The term out front r is raised to the nth power. We also have copies of n inside the trig functions.

The square root operation undoes the squaring operation, so we'll be dealing with n = 2.

If you were to go through each answer choice, then you'll find that squaring choice B will lead to the original expression given.

[tex]z = \sqrt{3}*\left[\cos\left(\frac{\pi}{4}\right)+i*\sin\left(\frac{\pi}{4}\right)\right]\\\\\\z^2 = (\sqrt{3})^2*\left[\cos\left(2*\frac{\pi}{4}\right)+i*\sin\left(2*\frac{\pi}{4}\right)\right]\\\\\\z^2 = 3*\left[\cos\left(\frac{\pi}{2}\right)+i*\sin\left(\frac{\pi}{2}\right)\right]\\\\\\[/tex]

Note that working this process in reverse means we apply the square root and we'll go from the expression in choice B to the original expression again.

The complex number Z =  √3[cosπ/4 + i sinπ/4] represents the complex number √(3[cosπ/2 + i sinπ/2]) after using the De Moivre's theorem option (B) is correct.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number in the trigonometric form:

Z = √(3[cosπ/2 + i sinπ/2])

It is required to find the square root of the complex number.

To find the square root of the complex number we can use the De Moivre's theorem:

If

Z = r[cosθ + i sinθ]

Zⁿ = rⁿ[cosnθ + i sinnθ]

Using the above theorem:

Z =  √3[cos[(1/2)π/2] + i sin[(1/2)π/2]]

Z =  √3[cosπ/4 + i sinπ/4]

Thus, the complex number Z =  √3[cosπ/4 + i sinπ/4] represents the complex number √(3[cosπ/2 + i sinπ/2]) after using the De Moivre's theorem option (B) is correct.

Learn more about the complex number here:

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Answer:

$258

Step-by-step explanation:

Answer:

you multiple two numbers and you devide both sides you get the answer

Answer:

y=5x+200

Step-by-step explanation:

x=number of handbags

y-intercept=200

slope=5

please give me brainly since I'm trying to level up!

Answer:

D. y = 58

Step-by-step explanation:

Answer:

The value of the polynomial   is 58 for x = 6.

Step-by-step explanation:

Here, the given quadratic function polynomial is given as:

or,  

Now, to find the value of y, when x = 6

⇒  

                 = 2(36 - 6 -1)  = 2(29)  

                 = 58

⇒y(6)  = 58

Hence, the value of the given polynomial   is 58 for x = 6.

Step-by-step explanation:

Given,

The product of Algebraic Expression is equal to the ________ of their H.C.F& L.C.M.

Solution,

Consider the the numbers are a, b.

a \times b = LCM\,of\,\left( {a,b} \right) \times HCF\,of\,\left( {a,b}Given,

Answer:

each company will earn $38 when they ship a 12-pound package

Step-by-step explanation:

you can solve this algebraically by setting up two equations:

let 'c' = charges per pound

Lone Star:  y = 2c + 14

Discount:  y = 1.5c + 20

now set each equation equal to the other to solve for 'c':

2c + 14 = 1.5c + 20

subtract 14 from each side to get:

2c = 1.5c + 6

subtract 1.5c from each side to get:

0.5c = 6

c = 6/0.5

c = 12

if you plug 12 in for 'c' in each equation you will get y = 38

(12,38) is the point where these two companies would each earn $38 for shipping a 12-pound package

Answer:

x=116°

Step-by-step explanation:

we have two parallel line and x=116

Answer:

6

Step-by-step explanation:

when calculating (g of f)(3) you first have to substitute 3 in the f(x) equation which would be -2(3)+8=-6+8=2. then you have to do g of f, which is g(2) in this case, and 3(2)=6.

hope this helps! :D

Answer:

Step-by-step explanation:

24 ) Before, so -5 sec

25) after. So,  + 5 sec

26) + 50 c

27) -50 c

28) - 1 min

29)  + $ 50

30)  - $ 5

31)  +5

32) - 5

Answer:

576

Step-by-step explanation:

5 + 3 = 8

5 - 2 = 3

8 x 3 = 24

24 to the second power is 576

Answer:

27x+5

Step-by-step explanation:

5+3x(5-2)^2

5+3x(3)^2

5+3x*9

5+27x

27x+5

Answer:

I believe it's 6/10

Step-by-step explanation:

3/5 times 2 = 6/10

Answer:

15 stones

Step-by-step explanation:

1) It is easier to convert to one unit. So i chose to convert everything to inches.

1 foot = 12 inches

10 feet = 120 inches

2) we then simply divide the size of the stones to see how much we need to cover the path

120/8 = 15 stones  

Answer: Is 6.4

Step-by-step explanation: I hope I helped in some way shape or form.

Answer:

This is a contradiction

Answer:

no.

Step-by-step explanation:

no. thanks.

..........

..

Answer:

1. Loss ₹50

2. - 60

3. 50 km towards North

4. 1000

5. - 30

6. - 15° C

Answer:

-7

Step-by-step explanation:

Y2 - Y1 / X2 - X1

-1-6/2-1

-7/1

= -7

Answer:

y=-2x+10

Step-by-step explanation:

Answer:

33 1/3%

Step-by-step explanation:

Answer:

33.3%

Step-by-step explanation:

We can also work this out in a simpler way by first converting the fraction 1/3 to a decimal. To do that, we simply divide the numerator by the denominator:

1/3 = 0.33333333333333

Once we have the answer to that division, we can multiply the answer by 100 to make it a percentage:

0.33333333333333 x 100 = 33.3333%

(Hope this helps can I pls have brainlist (crown)☺️)

Answer:

Step-by-step explanation:

m is only raised to the 3rd power. The 8 effects only the n

Numerator

m^3

(n^8 )^3 = n ^24

denominator

(n^9)^3 = n^27

Answer: m^3 * n^24 / n^27 = m^3 / n^(27 - 24) = (m/n )3

Hi!

Given:

[tex](\cfrac{mn^8}{n^9} )^3[/tex]

First, let's do what is inside the parenthesis. Since we're dividing, we subtract unlike exponents, and if there are any negatives, we switch them to make them positive:

[tex]8-9=-1[/tex]

Switch since it's negative:

[tex]\frac{m}{n} ^3[/tex]

Answer:

y = 3/4x - 6 1/4

Step-by-step explanation:

I hope that the slope 3 4 - - means 3/4

Slope = 3/4

Using slope = 3/4 and the point (-1, -7) substitute into y = mx + b and solve for "b"

y = mx + b

-7 = 3/4(-1) + b

-7 = -3/4 + b

-7 + 3/4 = b             3/4 as a decimal = .75

-7 + .75 = b

-6.25 = b

The equation of the line is y = 3/4x - 6.25  or y = 3/4x - 6 1/4

Answer:

140 inches

Step-by-step explanation:

one decagon has 10 sides

14*10= 140

Answer:

Maybe 34cm

Sana makatulong..

Answer:

A

Step-by-step explanation:

Answer:

conversion from gram to kilogram

u divide the gram by 1000

which is 722/ 1000

=0.722kilograms

i.e answer is A