Let $f(x) = x^3 + 3x ^2 + 4x - 7$ and $g(x) = -7x^4 + 5x^3 +x^2 - 7$. What is the coefficient of $x^3$ in the sum $f(x) + g(x)$?

6

Step-by-step explanation:

Adding the two polynomials gives

(x^3 + 3x^2 + 4x - 7) + (-7x^4 +5x^3 + x^2 - 7) =

-7x^4 + (x^3 + 5x^3) + (3x^2 + x^2) + 4x + (-7-7) =

- 7x^4 + 6x^3 + 4x^2 + 4x -14

The x^3 term is 6x^3, so the desired coefficient is 6.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

22

step-by-step explanation: