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3 years ago

The equation x^2 + y^2 + 21 = 40 + 18y. What is the radius of this cookie?

Mathematics

1 answer:

trapecia [35]3 years ago

6 0

Answer:

The radius is 10

Step-by-step explanation:

Given

$x^2 + y^2 + 21 = 40 + 18y.$

Required

The radius

Rewrite as:

$x^2 + y^2 - 18y = 40-21$

Subtract 81 from both sides

$x^2 + y^2 - 18y +81= 40-21+81$

Expand

$x^2 + y^2 - 9y - 9y +81= 40-21+81$

Factorize

$x^2 + y( y- 9) - 9(y -9)= 40-21+81$

Factor out y - 9

$x^2 + (y- 9) (y -9)= 40-21+81$

Express as squares

$x^2 + (y- 9)^2= 100$

$x^2 + (y- 9)= 10^2$

The equation of a circle is:

$(x - a)^2 + (y- b)= r^2$

By comparison:

$r^2=10^2$

$r = 10$

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Step-by-step explanation:

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2 years ago

Cuanto es la respuesta de -126=14k?

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Answer:

$\boxed{ \bold{ \huge{ \boxed{ \text{k = - 9}}}}}$

Step-by-step explanation:

$\star{ \text{ - 126 = 14k}}$

$\text{step \: 1 \: : Intercambia los lados de la ecuación}$

$\hookrightarrow{ \sf{14k = - 126}}$

$\text{step \: 2 : Divide ambos lados por 14}$

$\hookrightarrow{ \sf{ \frac{14k}{14} = \frac{ - 126}{14}}}$

$\text{step \: 3 \: : Calcular}$

$\hookrightarrow{ \sf{k = - 9}}$

$\text{el valor de k es - 9}$

------------------------------------------------------------

Translation in English:

Step 1 : Swap the sides of the equation

Step 2 : Divide both sides by 14

Step 3 : Calculate

$\sf{Hope \: i \: helped ! }$

$\sf{Best \: regards !!}$

~ $\sf{TheAnimeGirl}$

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3 years ago

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3 years ago

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Step-by-step explanation:

(1) 2x - 6y = -12

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There is a -6y and a +2y. Since they have opposite signs, I'll try to eliminate the y terms. (That's my choice. There is more than one way to solve these.)

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2(6) - 6y = -12

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-6y = -24

y = 4

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3 years ago

The equation x^2 + y^2 + 21 = 40 + 18y. What is the radius of this cookie?​

The equation x^2 + y^2 + 21 = 40 + 18y. What is the radius of this cookie?