we know 2 points so we can find the slope
(-4,5) and (0,6)
m = (y2-y1)/(x2-x1)
a reflection is well a reflection! the shape will be exactly the same as the one that is being reflected. congruent is just a synonym for same, two figures that are congruent are the exact same.
radius = 5 in
using the formula for calculating the area (a) of a circle
a = πr² ( r is the radius )
here a = 78.5, hence
3.14r² = 78.5 ( divide both sides by 3.14 )
r² = = 25 ( take the square root of both sides )
r = = 5
yes to all 3 questions.
3x^2(x-1) + -3x^3+ 4x^2-2x+1
= 3x^3 - 3x^2 - 3x^3 + 4x^2 - 2x + 1
= x^2 - 2x + 1,
so a + b is a polynomial.
3x^2(x-1) - (-3x^3+ 4x^2-2x+1)
= 3x^3 - 3x^2 + 3x^3 - 4x^2 + 2x - 1
= 6x^3 - 7x^2 + 2x - 1.
so a - b is also a polynomial.
3x^2(x-1)( -3x^3+ 4x^2-2x+1)
= (3x^3 - 3x^2) ( -3x^3 + 4x^2 - 2x + 1)
= -9x^6 + 12x^5 - 6x^4 + 3x^3 + 9x^5 - 12x^4 + 6x^3 - 3x^2
= -9x^6 + 21x^5 - 18x^4 + 9x^3 - 3x^2.
so a * b is a polynomial.