Which statement is true about the pattern above?

Select interior, exterior, or on the circle (x - 5) 2 + (y + 3) 2 = 25 for the following point. (2, 3)

lozanna [386]

Standard equation of a circle: <em>(x-h)² + (y-k)² = r²</em> where <em>(h, k)</em> is the center and <em>r </em>is the radius. In the case of our equation here, <em>(x-5)² + (y+3)² = 25</em>, we can conclude that our circle has a center at (5, -3) and a radius of 5 units.

We can use the distance formula with the center (5, -3) and our point (2, 3) to see how far away they are...if the distance between them is less than the radius of the circle, it is on the interior. If it's equal, it's on the circle. If it's greater, it's on the exterior.

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

Distance = $\sqrt{(-3-3)^2+(5-2)^2}$

Distance = $\sqrt{(-6)^2+3^2}$

Distance = $\sqrt{36+9}$

Distance = $\sqrt{45}\approx6.7082$

$6.7082>5,\ so\ (2,3)\ is\ on\ the\ \boxed{exterior}$

8 0

2 years ago

Elizabeth has a swimming pool at home. She wants to build a deck all the way around her rectangular swimming pool. The width of

galben [10]

Using the perimeter of a rectangle, it is found that she can make a deck of 122 ft wide.

<h3>What is the perimeter of a rectangle?</h3>

The perimeter of a rectangle of length l and width w is given by:

$P = 2(l + w)$

In this problem:

She has enough wood to build a deck that is 280ft, hence P = 280.

The length is of 10 feet, hence l = 10.

Considering that the deck's width will be added to the actual width of 8 feet, we have that w = 8 + w.

Then:

$P = 2(l + w)$

$280 = 2(10 + 8 + w)$

$36 + 2w = 280$

$2w = 244$

$w = \frac{144}{2}$

$w = 122$

She can make a deck of 122 ft wide.

You can learn more about the perimeter of a rectangle at brainly.com/question/10489198

7 0

2 years ago

How many gal is in 32 qt?

spin [16.1K]

There are 8 gallons in 32 quarts becuase 4 quarts = 1 gallon so 32 divided by 4 is 8. Hope this helped! :)

6 0

3 years ago

Twenty motors were put on test under a high-temperature setting. The lifetimes in hours of the motors under these conditions are

natta225 [31]

Answer:

Step-by-step explanation:

The step by step explanation is given in the attached document.

3 0

3 years ago

A center-pivot sprinkler system operated by Colorado Land & Agriculture, Inc., is used to water the alfalfa in a circular fi

omeli [17]

Answer:

The answer is "1.448 miles".

Step-by-step explanation:

X= The distance to both the nozzle clogged from of the starting point.

X $\sim$ Uniform(0,2) miles.

They are simulating the random number Y=0.724, and the Y has both a distribution uniform(0,1). Therefore 2Y is distributed evenly (0.2). And They model the clogging of its nozzle at 2Y=1.448 miles

8 0

2 years ago