The first one is incorrect
Answer:
4 - 4x³ + 20x² - 20x
Step-by-step explanation:
(g × f)(x) = g(x) × f(x) = (x³ + 5x)(4x - 4)
Each term in the second factor is multiplied by each term in the first factor, that is
x³(4x - 4) + 5x(4x - 4) ← distribute both parenthesis
= 4 - 4x³ + 20x² - 20x
This can also be done using FOIL, that is
(x³ + 5x)(4x - 4)
= 4 - 4x³ + 20x² - 20x
The initial population of the town is 7000, rate of reduction is 3%, thus the function modeling the new population will be given by:
f(t)=7000(0.97)^t
thus since our t=0 is in the year 2010, in the year 2019, t=19. The new population will be:
f(19)=7000(0.97)^19
f(19)=3,924.29
Thus the estimated population will be 3,924.29
If we were to view the ramp from its side, the profile would resemble a right triangle with a 90 degree angle where the sofa meets the floor.
In this case, the two legs of the right triangle are 55 inches and 28 inches, and we looking for the length of the hypotenuse.
We can use Pythagorean Theorem which states:
where a and b are the legs, and c is the hypotenuse.
c = 61.717 inches
To the nearest tenth, the answer is 61.7 inches.