Answer:
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
(x + 9)² + (y - 6)² = 10² is in this form
with centre = (- 9, 6) → A
Watch this video it might help you out https://www.brightstorm.com/math/geometry/constructions/duplicating-a-line-segment-problem-1/
Answer:
x = 6 and DF = 3*6-3 = 15
Step-by-step explanation:
Given triangles are similar and their side lengths are proportional
the similarity ratio for this pair is 4/8 = 1/2
the length of DF:
(7.5)/(3x - 3) = 1/2 cross multiply expressions
3x - 3 = 15 add 3 to both sides
3x = 18 divide both sides by 2
x = 6 and DF = 3*6-3 = 15
The graph is a parabola with roots at (-4.5, 0) and (0.5, 0) and vertex at (-2, -13)
Equation using roots is a(x + 9/2)(x - 1/2) = a(x^2 + 4x - 9/4) = ax^2 + 4ax - 9/4 a . . . . . . . . (1)
Equation using vertex is a(x + 2)^2 - 13 = a(x^2 + 4x + 4) - 13 = ax^2 + 4ax + 4a - 13 . . . . . . . . (2)
From (1) and (2), -9/4 a = 4a - 13
13 = 4a + 9/4 a = 25/4 a
a = (4 x 13)/25 = 2.08 = 2 approx
Therefore required equation is y = 2x^2 + 4(2)x + 4(2) - 13 = 2x^2 + 8x + 8 - 13 = 2x^2 + 8x - 5
