A circle has the equation x2+y2−8x−2y−17=0.
What is the equation of the circle in standard form?

(x−4)2+(y−1)2=34

(x+4)2+(y−1)2=34

(x−4)2+(y−1)2=17

(x+4)2+(y−1)2=17

A

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² - 8x - 2y - 17 = 0

Collect the x- terms and the y- terms together and add 17 to both sides

x² - 8x + y² - 2y = 17

Use the method of completing the square on both x and y terms.

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(- 4)x + 16 + y² + 2(- 1)y + 1 = 17 + 16 + 1

(x - 4)² + (y - 1)² = 34 → A

solution:

as, mean is defined as sum of all the observations divided by total number of observations.

and , median is mid value of the data whether arranged in ascending order or descending order.

consider, roadsters:

2,3,4,5,6,7,8,9

mean =

also, median= , because number of observations is even, so median is mean of two mid values.

now, coming to bandits

2,3,4,5,6

mean =  

median = 4, as number of observations is odd.

so, roadsters has greater median as well mean than bandits.

→option a is true about the repairs performed on 2 types of cars:

bandits have lower median and mean than roadsters.

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations: