the quotient of 40 and 5

Answer:

1-i and -1+i

Step-by-step explanation:

We are to find the square roots of [tex]z=0-2i[/tex]. First, convert from Cartesian to polar form:

[tex]r=\sqrt{a^2+b^2}\\r=\sqrt{0^2+(-2)^2}\\r=\sqrt{0+4}\\r=\sqrt{4}\\r=2[/tex]

[tex]\theta=tan^{-1}(\frac{b}{a})\\ \theta=tan^{-1}(\frac{-2}{0})\\\theta=\frac{3\pi}{2}[/tex]

[tex]z=2(\cos\frac{3\pi}{2}+i\sin\frac{3\pi}{2})[/tex]

Next, use the formula [tex]\displaystyle \sqrt[n]{r}\biggr[\cis\biggr(\frac{\theta+2\pi k}{n}\biggr)\biggr][/tex] where [tex]\displaystyle k=0,1,2,...\:,n-1[/tex] to find the square roots:

When k=1

[tex]\displaystyle \sqrt[2]{2}\biggr[cis\biggr(\frac{\frac{3\pi}{2}+2\pi(1)}{2}\biggr)\biggr][/tex]

[tex]\displaystyle \sqrt{2}\biggr[cis\biggr(\frac{3\pi}{4}+\pi\biggr)\biggr][/tex]

[tex]\sqrt{2}\biggr(cis\frac{7\pi}{4}\biggr)[/tex]

[tex]\sqrt{2}(\cos\frac{7\pi}{4}+i\sin\frac{7\pi}{4})\\ \\\sqrt{2}(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i)\\ \\1-i[/tex]

When k=0

[tex]\displaystyle \sqrt[2]{2}\biggr[cis\biggr(\frac{\frac{3\pi}{2}+2\pi(0)}{2}\biggr)\biggr][/tex]

[tex]\sqrt{2}\biggr(cis\frac{3\pi}{4}\biggr)[/tex]

[tex]\sqrt{2}(\cos\frac{3\pi}{4}+i\sin\frac{3\pi}{4})\\ \\\sqrt{2}(-\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i)\\ \\-1+i[/tex]

Thus, the square roots of -2i are 1-i and -1+i

Answer: 4. A 5. C 6. D

Step-by-step explanation: that’s it!!!!!!!!!!

Using a system of equations, it is found that the ratio of Jessica's age to India's age is of 2.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Harley is 8 years younger than India, hence:

x = y - 8.

Jessica is three times older than Harley, hence:

z = 3x.

The sum of the three ages is 88, hence:

x + y + z = 88.

x + x + 8 + 3x = 88

5x = 80

x = 16.

Hence:

y = x + 8 = 24.

z = 3x = 48

The ratio of Jessica's age to India's age is given by:

z/y = 48/24 = 2.

More can be learned about a system of equations at https://brainly.com/question/24342899

Answer:

b

Step-by-step explanation:

i hope this helped

Answer:

A is the correct answer

Step-by-step explanation:

Answer:

[tex]x=5\pm10i[/tex]

Step-by-step explanation:

[tex]y=x^2-10x+125\\\\0=x^2-10x+125\\\\0-100=x^2-10x+125-100\\\\-100=x^2-10x+25\\\\-100=(x-5)^2\\\\\pm10i=x-5\\\\5\pm10i=x\\\\x=5\pm10i[/tex]

Answer:

14/10 or 1 2/5

Step-by-step explanation:

Hey there!

In order to simplify this expression, we need to add the numerators and not the denominator since they are the same

14/10 is what you will get or this is also 1 2/5

Answer:

A.

[tex]1 \frac{2}{5} [/tex]

Explanation:

6/10 + 8/ 10 = 7/5

[tex] \frac{6}{10} + \frac{8}{10} = \frac{6 + 8}{10} = \frac{14}{10} = \frac{7}{5} = 1 \frac{2}{5} [/tex]

hope this helps.

Answer:

88 inches

Step-by-step explanation:

Divide the shape into 2 shapes and add all side lengths.

20+8+8+16+12+24=88

Answer:

x = 52

Step-by-step explanation:

I have included a chart to identify which angles are congruent (only alternate exterior/interior and corresponding). Basically if they are not alternate exterior/interior or corresponding, then they add up to = 180 degrees.

So since these angles are same side interior, they add up to = 180 degrees. We can write this as: A + B = 180

A + B = 180

2x + 76 = 180

2x = 104

x = 52

I hope this helps!

Answer: x=52

Step-by-step explanation:

uh i just knew

Answer:

V = (4/3)πr3 ≅ (4/3)(3.14)(3 in)3 ≅ 113.0 in3

Step-by-step explanation:

Step-by-step explanation:

-5(x + 4)² + 8 = -5(x² + 8x + 16) + 8 =

= -5x² - 40x - 80 + 8 = -5x² - 40x - 72

so, the third answer option must be correct, but you made a mistake there and forgot the "x" as factor of -40.

Answer:

6(2a+4)-4(3a-4)= (12a+24) +(-12a+16) = 40

Answer:

60 times.

Step-by-step explanation:

Prob( of rolling  a 2) = 1/6

Prob( of rolling  a 3) = 1/6

So Prob( 2 or 3) = 1/6 + 1/6 = 1/3,

So the prediction is 1/3 * 180 = 60.

Answer:

Survey all families from a smaller town.

Step-by-step explanation:

It would be more easier to survey families in a small town

Given the values for the length and width of the rectangle, area of the rectangle is 16.625 square centimeter.

A rectangle simply a is a 2-dimentional shape in geometry with 2 equal opposite sides and 4 corners each at 90 degrees.

The area of a rectangle is;

A = Length × Width

A = L × W

Given the data in the question;

To determine the area of the retcangle, we substitute our given values into the expression above.

A = L × W

A = 4.5cm × 3.25cm

A = 16.625cm²

Therefore, the area of the rectangle with the given length and width is 16.625cm².

Learn more about area of rectangle here: https://brainly.com/question/12019874

Answer:

D

Step-by-step explanation:

Got it right on edge 2022

Answer:

0.6

Step-by-step explanation:

I used 30 60 90 triangle.

7x + 4 = 46

7x = 46-4

7x = 42

x = 42/7

x = 6

THEREFORE, x = 6

HOPE IT HELPS :)

Answer:

Step-by-step explanation:

The domain is the set of x-values in the ordered pairs.

So it is {0, 2, 5}

Yes it is a function as for each x value there is  1 y-value  (its a one-to-one function)

The value of x for the circle h with chords jk and lm intersecting at n inside the circle is 10.

The interseting chord theorem states that, when two chords in a circle intersect each other, then the product of their segment is equal.

For circle h in the given problem,

[tex]JN = 5, \\NK= 4, \\LN =2[/tex],

The value of segment NM is x.  The figure of the circle h is attached below. In this figure, using the interseting chord theorem the chords can be given as,

LN×NM=JN×NK

2×x=5×4

x=20/2

x=10

Thus, the value of x for the circle h with chords jk and lm intersecting at n inside the circle is 10.

Learn more about the interseting chord theorem here;

https://brainly.com/question/5432495

Answer:

f(4)=-10

x=0

Step-by-step explanation:

Answer:

x = 5/2

y = -2

Step-by-step explanation:

(1+i)² (x+yi) = 4+5i

(1+2i+i²)(x+yi) = 4+5i

(1+2i-1)(x+yi) = 4+5i

2i(x+yi) = 4+5i

2i²y + 2xi = 4+5i

-2y + 2xi = 4 + 5i

By comparing both sides,

-2y = 4

y = -2,

2x = 5

x = 5/2

Answer:

Step-by-step explanation:

The degree of each term in a polynomial is the exponent of the variable. If there are multiple variables in a term, the degree is the sum of their exponents. The degree of the polynomial is the highest of the degrees of the terms.

__

The three terms of the polynomial given here have degrees of 2, 0, and 3. Since the highest degree is 3, the polynomial is 3rd-degree, or "cubic." The "leading term" is the one of highest degree, and its coefficient is the "leading coefficient." The constant term is the one with degree 0 (no variables).

"The expression represents a cubic polynomial with 3 terms. The constant is -2, the leading term is 1/4x³, and the leading coefficient is 1/4."

Step-by-step explanation:

I hope u are asking for average speed

average speed = total distance/total time

= 225/7.5

= 30 km/h or 30 km per hour

Answer:

As Per Provided Information

We have to determine the average speed of his car in kilometres per hour .

Using Formulae

[tex] \boxed {\bf \: Average\: Speed \: = \cfrac{Total \: Distance \: Covered}{ Total \: Time \: Taken }}[/tex]

On substituting the value we get

[tex]\sf \qquad \: \longrightarrow\: Average\: Speed \: = \cfrac{225}{7.5} \\ \\ \\ \sf \qquad \: \longrightarrow\: Average\: Speed = \cancel \cfrac{225}{7.5} \\ \\ \\ \sf \qquad \: \longrightarrow\: Average\: Speed = 30km {h}^{ - 1} [/tex]

Therefore,

So your answer is A) 30 kph .

9(x+6)

Hope it helps.

Do comment if you have any query.

Answer:

7 people

Step-by-step explanation:

Given:

$272 total money for all friends

parking costs $7.75 for all

tickets cost $37.75 per person

Solution;

Take away the money for parking to see how much money we have left for tickets

272 - 7.72 = $ 264.25

We divide the $264.25 to the price of 1 ticket $37.75 to see how many tickets we have money for

264.25 / 37.75 = 7

If we have money for 7 tickets then 7 friends can go to the amusement park.

The rule y = -3 - x is an illustration of a linear equation

The points on the coordinate plane with the rule y = -3 - x are (0,-3), (1,-4) and (2,-5)

The rule of the points is given as:

y = -3 - x

When x = 0, we have:

y = -3 - 0

y = -3

When x = 1, we have:

y = -3 - 1

y = -4

When x = 2, we have:

y = -3 - 2

y = -5

From the above computation, we have the following points

(0,-3), (1,-4) and (2,-5)

Hence, the points on the coordinate plane with the rule y = -3 - x are (0,-3), (1,-4) and (2,-5)

Read more about coordinate planes at:

https://brainly.com/question/10737082