Answer:
centre = (- 2, 3 )
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 + 4x - 6y = 12 ( collect x/ y terms )
x² + 4x + y² - 6y = 12
using the method of completing the square
add ( half the coefficient of the x/ y terms)² to both sides
x² + 2(2)x + 4 + y² + 2(- 3)y + 9 = 12 + 4 + 9
(x + 2)² + (y - 3)² = 25 ← in standard form
with centre (- 2, 3 ) and r = = 5
Answer: There are 7 crayons in each box.
Step-by-step explanation: First, the most difficult part is coming up with the equation. You know that she has a total of 59 since it mentioned “a collection of 59 crayons”. Then you also know there are 17 crayons on the side, so you can subtract 17 from 59, the total (which is now 42). Then you have 6x. 6 is for the number of boxes and x is for the unknown number of crayons found in each box. Then you can just simply solve after identifying each factor of the equation.
