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2 years ago

Write the equation of the circle in general form. Show all your work.

Mathematics

1 answer:

Sergio [31]2 years ago

3 0

Answer:

(x + 3)^2 + (y - 2)^2 = 25

Step-by-step explanation:

Looking at the circle we can see the origin and the radius from the origin to the edge of the circle.

radius = 5

Origin of the circle (h,k) = (-3,2)

Equation of a circle: (x - h)^2 + (y - k)^2 =r^2

Plug in our (h,k) and radius into the equation.

(x - (-3))^2 + (y - (2))^2 = 5^2

(x + 3)^2 + (y - 2)^2 = 25

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18 is 60% of what number

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18/0.6=n
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3 years ago

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NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 11z

Roman55 [17]

Answer:

$(x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}$

$(x,y)=\left(\; \boxed{5,16} \; \right)\quad \textsf{(larger $x$-value)}$

Step-by-step explanation:

Given system of equations:

$\begin{cases}y=x^2-9\\y=4x-4\end{cases}$

To solve by the method of substitution, substitute the first equation into the second equation and rearrange so that the equation equals zero:

$\begin{aligned}x^2-9&=4x-4\\x^2-4x-9&=-4\\x^2-4x-5&=0\end{aligned}$

Factor the quadratic:

$\begin{aligned}x^2-4x-5&=0\\x^2-5x+x-5&=0\\x(x-5)+1(x-5)&=0\\(x+1)(x-5)&=0\end{aligned}$

Apply the zero-product property and solve for x:

$\implies x+1=0 \implies x=-1$

$\implies x-5=0 \implies x=5$

Substitute the found values of x into the second equation and solve for y:

$\begin{aligned}x=-1 \implies y&=4(-1)-4\\y&=-4-4\\y&=-8\end{aligned}$

$\begin{aligned}x=5 \implies y&=4(5)-4\\y&=20-4\\y&=16\end{aligned}$

Therefore, the solutions are:

$(x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}$

$(x,y)=\left(\; \boxed{5,16} \; \right)\quad \textsf{(larger $x$-value)}$

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Answer: A trapezoid is always a parallelogram.

Step-by-step explanation:

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zaharov [31]

Answer:

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Step-by-step explanation:

My explanation is in the picture. All I did was replace the known variable with the proper letter!

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