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Cerrena [4.2K]
3 years ago
12

A segment in the complex plane has a midpoint at –1 + i. If the segment has an endpoint at –5 – 7i, what is the other endpoint?

Mathematics
1 answer:
saul85 [17]3 years ago
3 0

Answer:

Option D. 3 + 9i

Step-by-step explanation:

We know that the formula to find the middle point is:

(\frac{x_1 + x_2}{2},\frac{z_1 + z_2}{2})

We know that the middle point is:

-1 + i

And the end point (x_2, z_2) is: -5 -7i

We wish to find the point x_1,z_1

So we can write the following equation

\frac{x_1 + (-5)}{2} = -1                   (i)

and

\frac{z_1 + (-7i)}{2} = i                     (ii)

Now we clear x_1 from equation (i) and clear z_1 from equation (ii)

For equation (i) we have:

-2 = x_1 -5 \\\\x_1 = 3

For equation (ii) we have:

2i = z_1 -7i\\\\z_1 = 9i

Then the initial point x_1, z_1 is: 3 + 9i

The correct answer is the last option 3 +9i

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Find the area of the circle.
juin [17]

Answer:

See Explanation Below

Step-by-step explanation:

Your question isn't clear; However, I'll solve in two ways

1. Diameter = 14 cm

2. Radius = 14 cm

<em></em>

<em>When Diameter = 14 cm</em>

Given

Area = \pi r^2

Diameter = 14cm

Required

Calculate the area of the circle

First, the radius has to be solved;

Radius = \frac{1}{2} Diameter

Radius = \frac{1}{2} * 14cm

Radius = 7cm

Using the given formula;

The area is as follows

Area = \pi r^2

Area = 3.14 * 7^2

Area = 3.14 * 49

Area = 153.86cm^2

<em>When Radius = 14 cm</em>

Given

Area = \pi r^2

Radius = 14cm

Required

Calculate the area of the circle

Using the given formula;

The area is as follows

Area = \pi r^2

Area = 3.14 * 14^2

Area = 3.14 * 196

Area = 615.44cm^2

7 0
3 years ago
Given that 2x + 1 =5, what is the value of (x+3)^3
Alla [95]

Answer: 125

Step-by-step explanation:

First, solve for x in the first equation.

1) Subtract 1 from both sides.

2x = 4

2) Divide by 2 on both sides.

x = 2

Next, substitute the value of x into the second expression.

(2 + 3)^3

= 5^3

= 125

5 0
3 years ago
Read 2 more answers
I NEED ANSWERS FOR THESE ASAP!!
Goryan [66]
Yesss yea yesss yea yesss yea

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7 0
2 years ago
In ΔABC, m∠ACB = 90°, CD ⊥ AB and m∠ACD = 45°. Find: CD, if BC = 3 in
IRISSAK [1]
We can find m∠BCD like follows: m∠BCD=90°-45°=45<span>°
Now, m</span><span>∠DBC= 180°-(90°+45°)=45°

Remember that </span>sin \alpha = \frac{opposite leg}{hypotenuse}, so oppositeleg=(hypotenuse)(sin \alpha )

We know that hypotenuse= BC= 3in and \alpha=∠DBC)=45°, so replacing the values we get:
CD=3sin(45)=2.12

We can conclude that the segment CD is 2.12 in
4 0
3 years ago
Read 2 more answers
Hi ! How to solve this question?
tester [92]

You should actually have

-x^2-4x-10=-(x^2+4x+10)=-(x^2+4x+4+6)=-((x+2)^2+6)=-(x+2)^2-6

Now, remember that x^2 is always non-negative, so (x+2)^2\ge0 for any value of x. This means -(x+2)^2\le0 for any x, and so

-(x+2)^2-6\le0-6=-6

i.e. f(x) is at most -6, and hence negative for all x.

4 0
3 years ago
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