The video suggests you consider these 4 things before deciding to take out a loan: Is it necessary? Do the monthly payments fit in your budget? Could you save instead of borrow? Is it worth the added interest?

1. If you were trying to decide whether to take out an auto loan for $6500 to buy your first car, thereby allowing you to commute for an impressive summer internship program next year, would that loan meet the requirements?

Answer:

10.75 miles

Step-by-step explanation:

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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:

Maybe 34cm

Sana makatulong..

Answer:

x=116°

Step-by-step explanation:

we have two parallel line and x=116

Answer:

$258

Step-by-step explanation:

Answer:

140 inches

Step-by-step explanation:

one decagon has 10 sides

14*10= 140

Answer: Is 6.4

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

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:

Well to calculate slope you just do

y2-y1/ X2-x1

In this case

9-8/3-2

Which is 1/1

THe slope is 1

Answer:

1

Step-by-step explanation:

The slope is going to be the ratio between the difference of y coordinates, and the difference in x coordinates.

[tex]m= \frac{\Delta y}{\Delta x} = \frac{3-2}{9-8} = \frac11 = 1[/tex]

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.

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:

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

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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Answer:

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

Answer:

y=-2x+10

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

Y2 - Y1 / X2 - X1

-1-6/2-1

-7/1

= -7

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

Answer:

1)36

2)1/36

Step-by-step explanation:

Hope it can help you lovelots

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:

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:

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:

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:

4/7

Step-by-step explanation:

6 -2/2+5 = 4/7

thats it simple

Answer: 10

Step-by-step explanation:

6-x/x+5

6-(2)/(2)+5

Order of Operations

6-1+5

5+5

10

Answer:

4800$

Step-by-step explanation:

1 day = 600

7 years = 600 x 2 = 1200$

14 years = 1200 x 2 = 2400$

21 years = 2400 x 2 = 4800$

Answer:

1. Loss ₹50

2. - 60

3. 50 km towards North

4. 1000

5. - 30

6. - 15° C

Answer:

This is a contradiction

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