Answer:
see attached
Step-by-step explanation:
The equation is in the form ...
4p(y -k) = (x -h)^2 . . . . . (h, k) is the vertex; p is the focus-vertex distance
Comparing this to your equation, we see ...
p = 4, (h, k) = (3, 4)
p > 0, so the parabola opens upward. The vertex is on the axis of symmetry. That axis has the equation x=x-coordinate of vertex. This tells you ...
vertex: (3, 4)
axis of symmetry: x = 3
focus: (3, 8) . . . . . 4 units up from vertex
directrix: y = 0 . . . horizontal line 4 units down from vertex
Answer:
90 inches
Step-by-step explanation:
The perimeter of the inscribed triangle is 1/2 that of the enclosing triangle. So, the total of perimeters is ...
(3·16 in)(1 +1/2 +1/4 +1/8) = (48 in)(15/8) = 90 inches
Answer:
Step-by-step explanation:
5x + 2 = 4x - 9
Collecting like terms
5x - 4x = -9 - 2
x = -11
An example is the number 5i
If complex coefficients are allowed, the answer is 3.
If the polynomial must have real coefficients, then each complex root comes as a pair of complex conjugate roots.
Root -5 is real, so that is 1 root, and degree 1.
Root 1 + 4i is complex, so it must come with its complex conjugate, 1 - 4i. This adds 2 roots to the polynomial, and now we're up to degree 3.
Root -4i is also complex. It also must come with its complex conjugate, 4i. That adds two more roots, and the degree is 5.
Answer: The least possible degree is 5 with real coefficients.
