ALGEBRA 1 HONORS EASY QUICK QUESTION

Misha Larkins [42]

And what I need more information to answer your question.

4 0

3 years ago

A circle has a center at 4 – 5i and a point on the circle at 19 – 13i. Which of the following points is also on the circle? –11

TiliK225 [7]

To solve the problem we must know about the equation of a circle and complex numbers.

<h2>Equation of circle</h2>

Radius² = (Distance between the center and any point on the circle)²

Radius = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

<h2>Complex Number </h2>

Complex Number, z = (x +iy)

Another point that will lay on the same circle is (12 + 10i).

<h2>Explanation</h2>

Given to us

center = (4 – 5i)
point on the circle = (19 – 13i)

Solution

We know that equation for a circle can be written as,

<h3>Radius of the Circle </h3>

Radius of the Circle

= √(Distance between the center and any point on the circle)²

Radius of the Circle = √[4-19]²+[-5 -(-13)]²

= √[-15]²+[8]²

= √225 + 64

= √289

= 17

Now compare the distance between the center of the circle and the points.

<h3>Comparison</h3>

A.) –11 –3i

Distance between the center and point on the circle

= √[4-(-11)]² + [-5 - (-3)]²

= √[15]² + [-2]²

= √225 + 4

= √229

B.) –4. 5+3. 5i

Distance between the center and point on the circle

= √[4-(-4.5)]² + [-5 - (3.5)]²

= √[9.5]² + [-8.5]²

= √90.25+ 72.25

= √162.5

C.) 12 + 10i

Distance between the center and point on the circle

= √[4-(12)]² + [-5 - (10)]²

= √[-8]² + [-15]²

= √64+ 225

= √289

= 17

D.) 21 + 12i.

Distance between the center and point on the circle

= √[4-(21)]² + [-5 - (12)]²

= √[17]² + [-17i]²

= √289+ 289

= √578

Hence, another point that will lay on the same circle is (12 + 10i).

Learn more about Equation of Circle:

brainly.com/question/10165274

3 0

2 years ago

Consider a collection of envelopes consisting of 3 red envelopes, 3 blue envelopes, 3 green envelopes, and 3 yellow envelopes

kvv77 [185]

3/10 x 2/9 x 1/8=1/120

5 0

3 years ago

-4 = 8m please show step by step

GREYUIT [131]

so you do 8÷-4=2. so m equals 2

5 0

3 years ago

Read 2 more answers

Will mark brainliest! Questions are in the picture!

alexdok [17]

Answer:

52.9 inches .

Step-by-step explanation:

Given that the triangular indentation has an area of 100 in.² and the base and height of this traingle are represented by expressions 3x and x+3 respectively . We need to find out the <u>perimeter </u>to the nearest tenth.

As we know that the area of triangle is ,

$\rm\longrightarrow Area_{\triangle}=\dfrac{1}{2}(base)(height)$

Substituting the respective values,

$\rm\longrightarrow 100\ =\dfrac{1}{2}(x+3)(3x)\\\\\rm\longrightarrow 2(100) = 3x(x+3)\\\\\rm\longrightarrow200 = 3x^2+9x\\\\\rm\longrightarrow 3x^2+9x-200=0$

On using the <u>Quadratic</u><u> formula</u> , we have;

$\rm\longrightarrow x =\dfrac{-9\pm\sqrt{9^2-4(3)(-200)}}{2(3)} \\\\\rm\longrightarrow x =\dfrac{-9\pm \sqrt{81+1200}}{6}\\\\\rm\longrightarrow x =\dfrac{-9\pm \sqrt{1281}}{6}$