Write the slope-intercept form of the equation of the line through the given points.

Write an equation of the circle with center (4,5) and radius 9.

mixer [17]

Answer:

I'm going to write both of these because maybe you have a fill in the blank question. I don't know.

$(x-4)^2+(y-5)^2=9^2$

Simplify:

$(x-4)^2+(y-5)^2=81$

Step-by-step explanation:

$(x-h)^2+(y-k)^2=r^2$ is the equation of a circle with center (h,k) and radius r.

You are given (h,k)=(4,5) because that is the center.

You are given r=9 because it says radius 9.

Let's plug this in.

$(x-4)^2+(y-5)^2=9^2$

Simplify:

$(x-4)^2+(y-5)^2=81$

6 0

3 years ago

Read 2 more answers

There is an equal number of men, women and children at a party. How many persons could be at the party?

astra-53 [7]

Answer:

3, 6, 9, 12, and so on, basically any number that can be divided by 3

3 0

2 years ago

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Factor the polynomial, x2 + 5x + 6

patriot [66]

Answer:

Choice b.

$x^{2} + 5\, x + 6 = (x + 3)\, (x + 2)$ .

Step-by-step explanation:

The highest power of the variable $x$ in this polynomial is $2$ . In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to $0$ .)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

Apply the quadratic formula to find the two roots that would set this quadratic polynomial to $0$ . The discriminant of this polynomial is $(5^{2} - 4 \times 1 \times 6) = 1$ .

$\begin{aligned}x_{1} &= \frac{-5 + \sqrt{1}}{2\times 1} \\ &= \frac{-5 + 1}{2} \\ &= -2\end{aligned}$ .

Similarly:

$\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}$ .

By the Factor Theorem, if $x = x_{0}$ is a root of a polynomial, then $(x - x_0)$ would be a factor of that polynomial. Note the minus sign between $x$ and $x_{0}$ .

The root $x = -2$ corresponds to the factor $(x - (-2))$ , which simplifies to $(x + 2)$ .
The root $x = -3$ corresponds to the factor $(x - (-3))$ , which simplifies to $(x + 3)$ .