For this case, what we must do is fill squares in all the expressions until we find the correct result.
We have then:
x2 + y2 − 4x + 12y − 20 = 0 x2 + y2 − 4x + 12y = 20
x2 − 4x + y2 + 12y = 20
x2 − 4x + (12/2)^2 + y2 + 12y + (-4/2)^2 = 20 + (12/2)^2 + (-4/2)^2
x2 − 4x + (6)^2 + y2 + 12y + (-2)^2 = 20 + (6)^2 + (-2)^2
x2 − 4x + 36 + y2 + 12y + 4 = 20 + 36 + 4
(x − 2)2 + (y + 6)2 = 60
3x2 + 3y2 + 12x + 18y − 15 = 0
x2 + y2 + 4x + 6y − 5 = 0
x2 + y2 + 4x + 6y = 5
x2 + 4x + (4/2)^2 + y2 + 6y + (6/2)^2 = 5 + (4/2)^2 + (6/2)^2
x2 + 4x + (2)^2 + y2 + 6y + (3)^2 = 5 + (2)^2 + (3)^2
x2 + 4x + 4 + y2 + 6y + 9 = 5 + 4 + 9
(x + 2)2 + (y + 3)2 = 18
2x2 + 2y2 − 24x − 16y − 8 = 0
x2 + y2 − 12x − 8y − 4 = 0
x2 + y2 − 12x − 8y = 4
x2 − 12x + (-12/2)^2 + y2 − 8y + (-8/2)^2 = 4 + (-12/2)^2 + (-8/2)^2
x2 − 12x + (-6)^2 + y2 − 8y + (-4)^2 = 4 + (-6)^2 + (-4)^2
x2 − 12x + 36 + y2 − 8y + 16 = 4 + 36 + 16
(x − 6)2 + (y − 4)2 = 56
x2 + y2 + 2x − 12y − 9 = 0
x2 + y2 + 2x - 12y = 9
x2 + 2x + y2 - 12y = 9
x2 + 2x + (2/2)^2 + y2 - 12y + (-12/2)^2 = 9 + (2/2)^2 + (-12/2)^2
x2 + 2x + (1)^2 + y2 - 12y + (-6)^2 = 9 + (1)^2 + (-6)^2
x2 + 2x + 1 + y2 - 12y + 36 = 9 + 1 + 36
(x + 1)2 + (y − 6)2 = 46
Answer:
56.4 degrees
Step-by-step explanation:
90 degrees - 33.6 degrees = 56.4 degrees
Answer:
a.) 1.38 seconds
b.) 17.59ft
Step-by-step explanation:
h(t) = -16t^2 + 22.08t + 6
if we were to graph this, the vertex of the function would be the point, which if we substituted into the function would give us the maximum height.
to find the vertex, since we are dealing with something called "quadratic form" ax^2+bx+c, we can use a formula to find the vertex
-b/2a
b=22.08
a=-16
-22.08/-16, we get 1.38 when the minuses cancel out. since our x is time, it will be 1.38 seconds
now since the vertex is 1.38, we can substitute 1.38 into the function to find the maximum height.
h(1.38)= -16(1.38)^2 + 22.08t + 6 -----> is maximum height.
approximately = 17.59ft -------> calculator used, and rounded to 2 significant figures.
for c the time can be equal to (69+sqrt(8511))/100, as the negative version would be incompatible since we are talking about time. or if you wanted a rounded decimal, approx 1.62 seconds.
Answer:
31.1
Step-by-step explanation:
This is an isosceles triangle. Let us name the unnamed side y. y will also equal 22. We also know that this is a right triangle so using the pythagorean theorem we can calculate x. x = √(22^2+22^2) so x = 31.1.
Answer: 5 = y
Step-by-step explanation:
