AP Calc AB If, for all real numbers x, f (x) = g (x) + 5, then on any closed interval [a, b] the area of the region between the graphs of f and g is

The area between the graphs of f(x) and g(x) over an interval [a, b] is

Since f(x) = g(x) + 5, it follows that |f(x) - g(x)| = |5| = 5, so the value of the integral is always 5.

hi there!

the answer to this question is d: 35

step-by-step explanation:

5 to the power of 2 is 25

2 multiplied by 5 is 10

then you add the 2 numbers and you get 35

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b