4.

Find an equation of the circle that satisfies the given conditions. (Use the variables x and y.)

prohojiy [21]

Answer:

$x^2 + y^2 = 52$

Step-by-step explanation:

Distance between two points:

Suppose that we have two points, $(x_1,y_1)$ and $(x_2,y_2)$ . The distance between them is given by:

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

Equation of a circle:

The equation of a circle with center $(x_0,y_0)$ and radius r has the following format:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

Center at the origin;

This means that $x_0 = 0, y_0 = 0$

So

$(x - x_0)^2 + (y - y_0)^2 = r^2$

$(x - 0)^2 + (y - 0)^2 = r^2$

$x^2 + y^2 = r^2$

Passes through (4, 6)

The radius is the distance from this point to the center. So

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

$r = \sqrt{(4-0)^2+(6-0)^2}$

$r = \sqrt{16+36}$

$r = \sqrt{52}$

So

$r^2 = 52$

Then

$x^2 + y^2 = r^2$

$x^2 + y^2 = 52$

8 0

3 years ago

Mr. Allen bought a new computer. His monthly payment plan is shown in the table.

Andrei [34K]

Is it this problem if it is i can help you if not please provide a questions and the data.

5 0

4 years ago

for a fundraiser, Hailey raises $27, plus 1.50 for each lap she swims. Tariana raises $18, plus $3 for each lap she swims what i

borishaifa [10]

Answer:

The number of laps for which two swimmers have raised the same amount of money is 6 .

Step-by-step explanation:

Given as :

The amount raised by Hailey = $27 + $1.50 × each lap she swim

The amount raised by Tariana = $18 + $3 × each lap she swim

Let The number of laps after which both swimmer raised same amount = n

Now, According to question

<u>For both swimmer to raised same amount</u>

I.e The amount raised by Hailey = The amount raised by Tariana

Or, $27 + $1.50 × each lap she swim = $18 + $3 × each lap she swim

Or, $27 + $1.50 × n = $18 + $3 × n

Or, $27 - $18 = $3 n - $1.50 n

Or, 9 = 1.5 n

∴ n = $\dfrac{9}{1.5}$

I.e n = 6

So, number of lap for same amount of both = n = 6

Hence The number of laps for which two swimmers have raised the same amount of money is 6 . Answer

5 0

3 years ago

Solve for n <br> 4 + 3n = –6 + 4n

Nikolay [14]

Answer: 10

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Can someone help me answer these two questions? I wanna know what's right and wrong. Please correct me if Necessary

agasfer [191]

Remember that the general equation of a line is $y=mx+b$ , where:
$m$ is the slope, and $b$ is the y-intercept; so to find the y-intercept, solve for $y$ and identify $b$ .
Now, to find the x-intercept, just replace $y$ in your line equation with $0$ , and solve for $x$
Lets apply those procedures to our two questions:

1. - y-intercept:
$-10x+5y=40$
$5y=10x+40$
$y= \frac{10x+40}{5}$
$y=2x+8$
Notice that now we have our line equation in the form $y=mx+b$ with $m=2$ and $b=8$ ; sine $b$ is the y-intercept, we can conclude that the y-intercept of our equation is 8.

x-intercept:
First, lets replace $y$ with $0$ :
$0=2x+8$
And then, we can solve for $x$ to find our x-intercept:
$2x=-8$
$x= \frac{-8}{2}$
$x=-4$
We can conclude that our x-intercept is -4; thus the correct answer in your list is the fourth one: x-intercept is -4; y-intercept is 8.

2. y-intercept:
$5x+4y=80$
$4y=-5x+80$
$y= \frac{-5x+80}{4}$
$y=- \frac{5}{4} x+20$
We can conclude that our y-intercept is 20.

x-intercept:
$0=- \frac{5}{4} x+20$
$- \frac{5}{4} x=-20$
$x=( \frac{4}{5} )(20)$
$x=16$
We can conclude that our x-intercept is 16; thus the correct answer in your list is, once again, the fourth one: x-intercept is 16; y-intercept is 20.

7 0

3 years ago