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aliya0001 [1]
3 years ago
9

Which of the following is a complex number? a. -7 b. 2+√3 c. 4+9i d. π

Mathematics
2 answers:
Feliz [49]3 years ago
3 0
Hello,

Answer C
=============

scoundrel [369]3 years ago
3 0

Answer: C. 4+9i

Step-by-step explanation:

A combination of a real and an imaginary number is called complex number.

Since, - 7 is the negative integer and an integer is always the real number only therefore it can not be the complex number,

2+√3 is the irrational number which is only a real number therefore,  it can not be the complex number,

In  number 4+9i, 4 is the real number and 9i is the imaginary number, Therefore it is a complex number,

π is the irrational number and an irrational number is always a real number therefore it can be the complex number.

Thus, Option C is correct.


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7(x-2)=28 Can somebody help me and show the steps?
olya-2409 [2.1K]
Since the 7 is in front of the parentheses you must multiply it by everything inside the parentheses. 7 times X is 7X and 7 times -2 is -14. Then you need to make the X be by itself on one side, to do that you have to add 14 to -14 to make it disappear, and also add 14 to the other side, to 28. Then you divide both sides by 7 to make X be by itself.

7(x-2)=28
7X-14=28
7x=42
X=6

6 0
2 years ago
Part 4: Identify the vertex, focus and directrix of each. Then sketch the graph.
Nezavi [6.7K]

Answer: 1) Vertex: (6, -2)    Focus: (6, -7/4)     Directrix: y = -9/4

              2) Vertex: (-2, -1)   Focus: (-7/4, -1)     Directrix: x = -9/4

<u>Step-by-step explanation:</u>

Rewrite the equation in vertex format y = a(x - h)² + k   or   x = a(y - k)² + h by completing the square. Divide the b-value by 2 and square it - add that value to both sides of the equation.

  • (h, k) is the vertex
  • p is the distance from the vertex to the focus
  • -p is the distance from the vertex to the directrix

    \bullet\quad a=\dfrac{1}{4p}

1) y = x² - 12x + 34

y-34=x^2-12x\\\\y-34+\bigg(\dfrac{-12}{2}\bigg)^2=x^2-12x+\bigg(\dfrac{-12}{2}\bigg)^2\\\\\\y-34+36=(x-6)^2\\\\y+2=(x-6)^2\\\\y=(x-6)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(6,-2)\\

a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(6,-\dfrac{7}{4}\bigg)\\\\\\\text{Directrix: y= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad y=-\dfrac{9}{4}

*******************************************************************************************

2) x = y² + 2y - 1

x+1=y^2+2y\\\\x+1+\bigg(\dfrac{2}{2}\bigg)^2=y^2+2y+\bigg(\dfrac{2}{2}\bigg)^2\\\\\\x+1+1=(y+1)^2\\\\x+2=(y+1)^2\\\\x=(y+1)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(-2,-1)\\

a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(-\dfrac{7}{4},-1\bigg)\\\\\\\text{Directrix: x= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad x=-\dfrac{9}{4}

4 0
3 years ago
A water tank in the shape of a right cylinder has a diameter of 14 feet and a height of 18 feet. What is the volume?
Doss [256]
Volume = (pi 3.14)(r^2)(h)

(3.14)(49)(18)

(153.86)(18)

2769.48
7 0
3 years ago
A wheel has a radius of 13”; calculate the circumference.
Anit [1.1K]

Answer:

81.71"

Step-by-step explanation:

Circumference = 2*pi*radius

pi = 22/7

radius = 13

Circumference = 2*22/7*13 = 44*13 / 7 = 572/7 = 81.71"

4 0
2 years ago
A castle is surrounded by a circular moat which is 5 m wide
Elanso [62]

Answer:

  1414 kL

Step-by-step explanation:

The volume of the donut-shaped moat is the product of its surface area and depth. The area is the product of its centerline length and its width.

<h3>Moat area</h3>

The diameter of the centerline of the moat is (50 m -5 m) = 45 m. The length of that centerline is ...

  C = πd = π(45 m) = 45π m

The area is this length times the width of the moat:

  moat area = (45π m)(5 m) = 225π m²

<h3>Moat volume</h3>

The volume is the product of the area and the depth of the moat:

  V = Ah = (225π m²)(2 m) = 450π m³ ≈ 1413.72 m³

1 cubic meter is 1000 liters, 1 kiloliter.

The volume of the moat is about 1414 kL.

5 0
1 year ago
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