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3 years ago

Write the standard equation for the circle center (-6,8) that passes through (0,0)

Mathematics

1 answer:

Reil [10]3 years ago

4 0

Answer:

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (- 6, - 8), thus

(x + 6)² + (y + 8)² = r²

The radius is the distance from the centre to a point on the circle

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 6, - 8) and (x₂, y₂ ) = (0, 0)

r = $\sqrt{(0+6)^2+(0+8)^2}$ = $\sqrt{36+64}$ = $\sqrt{100}$ = 10

Hence

(x + 6)² + (y + 8)² = 100 → D

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Drag the tiles to the correct boxes to complete the pairs.

Mashcka [7]

Answer:

Part 1) $-17\frac{8}{9}$ -----> $-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}$

Part 2) $-15.11$ ------> $-12.48-(-2.99)-5.62$

Part 3) $-19\frac{8}{9}$ -----> $-19\frac{2}{9}-4\frac{1}{9}-(-3\frac{4}{9})$

Part 4) $-201.65$ -----> $-353.92-(-283.56)-131.29$

Part 5) $74$ ------> $83\frac{1}{5}-108\frac{2}{5}-(-99\frac{1}{5})$

Step-by-step explanation:

Part 1) we have

$-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}$

To calculate the subtraction convert the mixed numbers to an improper fractions

$6\frac{4}{9}=\frac{6*9+4}{9}=\frac{58}{9}$

$3\frac{2}{9}=\frac{3*9+2}{9}=\frac{29}{9}$

$8\frac{2}{9}=\frac{8*9+2}{9}=\frac{74}{9}$

substitute

$-\frac{58}{9}-\frac{29}{9}-\frac{74}{9}=-\frac{(58+29+74)}{9}=-\frac{161}{9}$

Convert to mixed number

$-\frac{161}{9}=-(\frac{153}{9}+\frac{8}{9})=-17\frac{8}{9}$

Part 2) we have

$-12.48-(-2.99)-5.62$

To calculate the subtraction eliminate the parenthesis first

$-12.48-(-2.99)-5.62=-12.48+2.99-5.62=-15.11$

Part 3) we have

$-19\frac{2}{9}-4\frac{1}{9}-(-3\frac{4}{9})$

To calculate the subtraction convert the mixed numbers to an improper fractions

$19\frac{2}{9}=\frac{19*9+2}{9}=\frac{173}{9}$

$4\frac{1}{9}=\frac{4*9+1}{9}=\frac{37}{9}$

$3\frac{4}{9}=\frac{3*9+4}{9}=\frac{31}{9}$

substitute

$-\frac{173}{9}-\frac{37}{9}-(-\frac{31}{9})$

Eliminate the parenthesis

$-\frac{173}{9}-\frac{37}{9}+\frac{31}{9}=\frac{(-173-37+31)}{9}=-\frac{179}{9}$

Convert to mixed number

$-\frac{179}{9}=-(\frac{171}{9}+\frac{8}{9})=-19\frac{8}{9}$

Part 4) we have

$-353.92-(-283.56)-131.29$

To calculate the subtraction eliminate the parenthesis first

$-353.92+283.56-131.29=-201.65$

Part 5) we have

$83\frac{1}{5}-108\frac{2}{5}-(-99\frac{1}{5})$

To calculate the subtraction convert the mixed numbers to an improper fractions

$83\frac{1}{5}=\frac{83*5+1}{5}=\frac{416}{5}$

$108\frac{2}{5}=\frac{108*5+2}{5}=\frac{542}{5}$

$99\frac{1}{5}=\frac{99*5+1}{5}=\frac{496}{5}$

substitute

$\frac{416}{5}-\frac{542}{5}-(-\frac{496}{5})$

Eliminate the parenthesis

$\frac{416}{5}-\frac{542}{5}+\frac{496}{5}=\frac{(416-542+496)}{5}=\frac{370}{5}=74$

3 0

3 years ago

If the circumference of a circle is doubled, how does the diameter of the circle change?

jeyben [28]

diameter will be doubled

6 0

3 years ago

What is the best first step in solving the equation 3 +<img src="https://tex.z-dn.net/?f=3%5Csqrt%5B6%5D%7Bx%7D" id="TexFormula1

Andreas93 [3]

$3+3\sqrt[6]{x}~~ = ~~5\implies \stackrel{\textit{1st step,-3 to both sides}}{3\sqrt[6]{x}~~ = ~~2}\implies \sqrt[6]{x}=\cfrac{2}{3} \\\\\\ (\sqrt[6]{x})^6=\left( \cfrac{2}{3} \right)^6\implies x=\cfrac{2^6}{3^6}\implies x=\cfrac{64}{729}$

6 0

2 years ago

A boat sails 285 miles south and then 132 miles west. What is the magnitude of the boats resultant vector?

Delicious77 [7]

The magnitude of the boats resultant vector is 314.1 mi

<h3>What is a vector?</h3>

A vector is a physical quantity that has both magnitude and direction.

<h3>What is a resultant vector?</h3>

A resultant vector is the sum of two or more vectors.

<h3>How to find the boats resultant vector?</h3>

Since the boat sails 285 miles south and then 132 miles west, we have that its first direction vector is r = (285 mi)j. Also, its direction vector west is r' = -(132 mi)i

So, the resultant vector R = r + r'

= (285 mi)j + (132 mi)i

= (132 mi)i + (285 mi)j

So, the magnitude of the resultant vector is R = √(r² + r'²)

So, substituting thevalues of the variables into the equation, we have

R = √(r² + r'²)

R = √((285 mi)² + (132 mi)²)

R = √(81225 mi² + 17424 mi²)

R = √(98649 mi²)

R = 314.08 mi

R ≅ 314.1 mi

So, the resultant vector is 314.1 mi

Learn more about magnitude of resultant vector here:

brainly.com/question/28047791

#SPJ1

8 0

1 year ago

Find the 7th term of the geometric sequence with the given terms.

ohaa [14]

Answer:

1. 1458

2. 500 or -500

Step-by-step explanation:

1. a4=54, a5=162

r = 162/54 = 3

a7 = a5 × r²

= 162 × 3² = 1458

2.a4=-4, a6=-100

r² = -100/-4 = 25

r = +/- 5

a7 = a6 × r

= -100 × +/- 5

= +/- 500

3 0

3 years ago