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3 years ago

Find the distance between -2-3i and 3+9i

Mathematics

1 answer:

kow [346]3 years ago

5 0

Answer:

Step-by-step explanation:

We can consider the complex number $x+iy$ as point with coordinates $(x,y),$ where $x$ is real part of the complex number and $y$ is an imaginary part of the complex number.

The distance between two complex numbers is exactly tha distance between two points corresponding to each number.

$z_1=-2-3i\Rightarrow A(-2,-3)\\ \\z_2=3+9i\Rightarrow B(3,9)$

Now find the distance between A and B:

$AB=\sqrt{(-2-3)^2+(-3-9)^2}=\sqrt{(-5)^2+(-12)^2}=\sqrt{25+144}=\sqrt{169}=13\ units$

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Find the equation of a line, in slope intercept form of a line that passes through the point (-5,-1) and is parallel to the line

Ludmilka [50]

Answer:

y = 1/2x + 3/2

Step-by-step explanation:

Using the equation of the line

y - y_1 = m ( x - x_1)

First find the slope of the line

-2x + 4y = 8

It must be in this form

y = mx + C

4y = 8 + 2x

divide through by 4

4y/4 = 8 + 2x / 4

y = 8 + 2x/4

Let's separate

y = 8/4 + 2x/4

y = 2 + 1/2x

y = 1/2x + 2

Therefore, our slope or m is 1/2

Using the equation of the line

y - y_1 = m ( x - x_1)

With point (-5, -1)

x_1 = -5

y_1 = -1

y - (-1) = 1/2(x - (-5)

y + 1 = 1/2( x + 5)

Opening the brackets

y + 1 = x + 5 / 2

y = x + 5/2 - 1

Lcm is 2

y = x + 5 / 2 - 1/1

y = x + 5 -2/2

y = x +3/2

We can still separate it

y = x /2 + 3/2

y = 1/2x + 3/2

The equation of the line is

y = 1/2x + 3/2

The correct answer is A

3 0

3 years ago

There are 7 tigers in a castle,each tiger has 7 children,each child has 7 tiger friends,then how many tigers are there in the ca

Ksenya-84 [330]

There are 7 parent tigers
Parents = 7

7 tigers each have 7 children. That means there's total of 7 × 7 children.
Children = 7 × 7 = 49

Each child has 7 friends. That means there's total of 49 × 7 friends.
Friends = 49 × 7 = 343

Total = 7 + 49 +343 = 399 TIGERS
I'm not a tiger so I'm not counting myself.

3 0

4 years ago

Y = x² + 6x + 3

olganol [36]

Vertex is at $\left(-3,-6\right)$

y-intercept is 3.

The parabola opens up.

Step-by-step explanation:

The graph of the equation is hereby attached in the answer area.

Vertex is the point on the parabola where the graph crosses its axis of symmetry. The axis of symmetry here( $x =-3$ ), is shown with the dotted line in the graph attached.

y-intercept is defined as the value of y where the graph crosses the y-axis. In other words, when $x=0$ . Putting

And, the graph opens up as shown the graph figure as well. It is also evident from the co-efficient of $x$ in the given equation $y =x^{2} + 6x + 3$ . Here, co-efficient of

So, vertex is at $\left(-3,-6\right)$

y-intercept is 3.

The parabola opens up.

7 0

3 years ago

The vertex of this parabola is at (3,5). When the Y value is 6X value is negative one what is the coefficient of the squared ter

iren2701 [21]

We know that equation of a parabola is given by :-

y = a(x-h)² + k

Where (h,k) is the vertex of parabola and (x,y) is any point on its curve.

Given that vertex of parabola is (3,5) and one point (x,y) is (6,-1).

We can plug the given information in the equation of parabola and solve it for value of 'a' :-

-1 = a(6 - 3)² + 5

-1 = a(3)² + 5

-1 = 9a + 5

9a = -1 -5 = -6

a = $\frac{-6}{9} = \frac{-2}{3}$

a = $\frac{-2}{3}$ is the final answer.

7 0

3 years ago

You are buying shirts for an organization. You have $120 to spend. The number of short-sleeved shirts y you buy after buying x l

Makovka662 [10]

The given equation is ⇒ y = -1.2 x + 24

Part A : Graph the equation.

To graph the equation, substitute with values of x then find y

The attached figure represents the table to graph the equation and the graph of the equation.

=============================================

Part B : x-intercept

To find x-intercept substitute with y = 0 and solve for x

∴ 0 = -1.2 x + 24

∴ 1.2 x = 24

∴ x = 24/1.2 = 20

x-intercept is at point (20,0)

==================================================

Part C : y-intercept

To find y-intercept substitute with x = 0 and solve for y

∴ y = -1.2 * 0 + 24

∴ y = 24

∴ y-intercept is at point (0,24)

5 0

4 years ago