Answer:
Center = (2, 3) radius =
<u>Step-by-step explanation:</u>
When both the x² and y² values are equal and positive, the shape is a circle. Complete the square to put the equation in format:
(x-h)² + (y-k)² = r² where
- (h, k) is the vertex
- r is the radius
1) Group the x's and y's together and move the number to the right side
4x² - 16x + 4y² - 24y = -51
2) Factor out the 4 from the x² and y²
4(x² - 4x ) + 4(y² - 6y ) = -51
3) Complete the square (divide the x and y value by 2 and square it)
= 4(x - 2)² + 4(y - 3)² = -51 + 4(-2)² + 4(-3)²
= 4(x - 2)² + 4(y - 3)² = -51 + 4(4) + 4(9)
= 4(x - 2)² + 4(y - 3)² = -51 + 16 + 36
= 4(x - 2)² + 4(y - 3)² = 1
4) Divide both sides by 4
- (h, k) = (2, 3)
50 < 8 - 6x
50 - 8 < 6x
42 < 6x
7 < x
I know the Answer I dont know how to show you. do you?
Treat this as you would the quadratic equation x^2 - 4x - 3 + 0. Solve this by completing the square:
x^2 - 4x + 4 - 4 - 7 = 0
(x^2 - 4x + 4) = 11
(x-2)^2 = 11, and so x-2 = plus or minus sqrt(11).
Graph this, using a dashed curve (not a solid curve). Then shade the coordinate plane ABOVE the graph.
Answer:
AB // CD and AD // BC, then ABCD is a parallelogram
Step-by-step explanation:
Step 2: Show AD // BC
A = (-3 , 3) and D = (0 , 0)
Find the slope of AD
B = (2 , 5) and C = (5 , 2)
The slope of AD = the slope of BC
So AD // BC because they have the same slope
Step 3:
Each two opposite sides are parallel in quadrilateral ABCD
So the quadrilateral is a parallelogram