Step-by-step explanation:
(f+g)(x) means we just add the 2 functions, so we have
(x-3) + 2x² = 2x² + x - 3
(f-g)(x) means we subtract g(x) from f(x), so we have
(x-3) - (2x²) = -2x²+x-3
Assuming that the dot signifies a multiplication sign and not a composition sign, we have
(f*g)(x) = f(x) * g(x)
= (x-3) * 2x²
= 2x³ - 6x²
Plugging -2 in, we get
2(-2)³-6(-2)² = -16 -24 = -40
Answer:
y = -
x - 7
Step-by-step explanation:
Parallel lines have equal slopes.
Calculate the slope m of the given line using the slope formula
m = 
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (3, - 2) ← 2 points on the line
m =
= -
, thus
y = -
x + c ← is the partial equation
To find c substitute P(- 3, - 3) into the partial equation
- 3 = 4 + c ⇒ c = - 3 - 4 = - 7
y = -
x - 7 ← equation of parallel line
Answer:

Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
Consecutive angles of a parallelogram are supplementary, so:

This means
and that
.
Since opposite angles of a parallelogram are congruent,
