Answer: p = 4, r = 4
<u>Step-by-step explanation:</u>
The equation of a circle is: (x - h)² + (y - k)² = r² where
- (h, k) is the center of the circle
- r is the radius of the circle
Complete the square:
x² - 10x + _____ + y² + py + _____ = -13 + ___ + ___
x² - 10x + <u> (-10/2)² </u> + y² + py + <u> (p/2)²</u> = -13 + <u> (-10/2)² </u> + <u> (p/2)²</u>
(x - 5)² + (y + p/2)² = -13 + 25 + (p/2)²
↓ ↓ |_____<u>↓</u>_____|
h = 5 k = -p/2 r²
Given: (h, k) = (5, -2)
-2 = -p/2
-4 = -p
4 = p
r² = -13 + 25 + (p/2)²
= -13 + 25 + (4/2)²
= -13 + 25 + 4
= 16
r = 4
If x and y vary inversely, then xy = const.
x = 10, y = 8
Answer:
All men are mortal. Joe is a man. Therefore Joe is mortal. If the first two statements are true, then the conclusion must be true.[2]
Bachelors are unmarried men. Bill is unmarried. Therefore, Bill is a bachelor.[3]
To get a Bachelor’s degree at Utah Sate University, a student must have 120 credits. Sally has more than 130 credits. Therefore, Sally has a bachelor’s degree.
Two rectangles. Left: General Principle. Right: Special Case. An arrow pointing left to right above them is labeled "deductive reasoning." An arrow pointing right to left below them is labeled "inductive reasoning."
Step-by-step explanation:
2b^2. This is because you have a positive a^2 and a negative so they cross it one another so it just leaves the b’s.
Hey there :)
8P5 and 12C4
⁸P₅ = is 8! divided by ( 8 - 5 )!! is called the factorial You can see in the picture I have attached of how factorial is calculated
Let us do it separately:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
3! = 3 x 2 x 1 = 6
Let us combine:
=
6720¹²C₄ is 12! divided by ( 4! times ( 12 - 4 )! )
=
Let us do it separately:
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 479001600
( 4! )( 8! ) = ( 4 x 3 x 2 x 1 )( 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 ) = 24 x 41320 = 967680
Let us combine:
= 495
