Consider a system of equations formed by a line and a parabola. how many solutions are possible? sketch a graph to show each possibility.

answer:

centre = (2, 6)

step-by-step explanation:

the centre is at the midpoint of the diameter.

use the midpoint formula to find the centre

centre = [(- 2 + 6), (8 + 4)] = (2, 6)

answer:

it is acute.

step-by-step explanation:

81^2 =   6561

80^2 = 6400

18^2 =   324

80^2 + 18^2 = 6724

so 81^2 < 80^2 + 18^2 , therefore the triangle is acute.

note:   in a triangle with sides a, b and c with   a = longest side,

if a^2 < b^2 + c^2 the triangle is acute. in a right angled triangle a^2 = b^2 + c^2. in an obtuse angled triangle a^2 > b^2 + c^2.

answer:

y = 100 is the easiest function with these points.

another one is  

y = (x - 2)(x - 3) + 100 = x^2 - 5·x + 106

answer:

step-by-step explanation:

there are three angles so it means this is a triangle and sum of all angles of a triangle is always 180°. these all angles add up to 180°.

65°+(3x-10)+(2x)=180°

open the brackets: 65°+3x-10+2x=180°

arrange the numbers and valuables: 65°-10°+3x+2x=180°

calculate: 55°+5x=180°

5x=180°-55°

5x=125°

x=125°÷5

x=25

hence, angle 1: 65°

angle 2: 3x-10°

=3(25°)-10°

=65°

angle 3: 2x

=2(25°)

=50°